University of Pennsylvania ScholarlyCommons

IRCS Technical Reports Series Institute for Research in Cognitive Science

October 1993

Search Plans

Michael B. Moore University of Pennsylvania

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Moore, Michael B., "Search Plans" (1993). IRCS Technical Reports Series. 185. https://repository.upenn.edu/ircs_reports/185

University of Pennsylvania Institute for Research in Cognitive Science Technical Report No. IRCS-93-29.

This paper is posted at ScholarlyCommons. https://repository.upenn.edu/ircs_reports/185 For more information, please contact [email protected]. Search Plans

Abstract People often do not know where things are and have to look for them. This thesis presents a formal model suitable for reasoning about how to find things and acting ot find them, which I will call sear“ ch behavior”. Since not knowing location of something can prevent an agent from reaching his desired goal, the ability to plan and conduct a search will be argued to increase the variety of situations in which an agent can succeed at his chosen task.

Searching for things is a natural problem that arises when the blocks world assumptions (which have been the problem setting for most planning research) are modified by providing the agent only partial knowledge of his environment. Since the agent does not know the total world state, actions may appear to have nondeterministic effects. The significant aspects of the search problem which differ from previously studied planning problems are the acquisition of information and iteration of similar actions while exploring a search space.

Since introduction of the situation calculus [MH69], various systems have been proposed for representing and reasoning about actions which involve knowledge acquisition and iteration, including Moore's work on the interaction between knowledge and action [Moo80]. Such systems can be used to infer properties of plans which have already been constructed, but do not themselves construct plans for complex actions. My concern with searching has to do with a sense that Moore's knowledge preconditions are overly restrictive. Morgenstern [Mor88] examined ways to weaken knowledge preconditions for an individual agent by relying on the knowledge and abilities of other agents. Lesperance's research [Les91] on indexical knowledge is another way of weakening the knowledge preconditions. I am trying to reduce the amount of information an agent must know (provided he can search a known search space). If you dial the right combination to a safe it will open, whether or not you knew in advance that it was the right combination. Search is a way to guarantee you will eventually dial the right combination. So what I am exploring is how to systematically construct a search that will use available knowledge to accomplish something the agent does not currently know enough to do directly.

I claim it is possible for automated agents to engage in search behavior. Engaging in search behavior consists in recognizing the need for a search, constructing an effective plan, and then carrying out that plan. Expressing such a plan and reasoning about its effectiveness requires a representation language. I will select a representation language based on criteria derived from analyzing the search planning problem. Each of the three components of a system for engaging in search behavior will be designed and implemented to demonstrate that an automated agent can find things when he needs o.t

Comments University of Pennsylvania Institute for Research in Cognitive Science Technical Report No. IRCS-93-29.

This other is available at ScholarlyCommons: https://repository.upenn.edu/ircs_reports/185 The Institute For Research In Cognitive Science

Search Plans (Dissertation Proposal) P

by

Michael B. Moore E

University of Pennsylvania Philadelphia, PA 19104-6228 N October 1993

Site of the NSF Science and Technology Center for Research in Cognitive Science N

University of Pennsylvania IRCS Report 93-29 Founded by Benjamin Franklin in 1740

Search Plans

Michael B Mo ore

July

This researchwas supp orted by the following grants DARPA no NJ AROno

DAAL C NSF no IRI and Ben Franklin no SC

A DISSERTATION PROPOSAL

in

COMPUTER AND INFORMATION SCIENCE July

Abstract

People often do not know where things are and have to lo ok for them This thesis presents

a formal mo del suitable for reasoning ab out how to nd things and acting to nd them

which I will call search b ehavior Since not knowing lo cation of something can prevent

an agent from reaching his desired goal the ability to plan and conduct a search will b e

argued to increase the varietyofsituationsinwhichanagent can succeed at his chosen

task

Searching for things is a natural problem that arises when the blo cks world assumptions

whichhave b een the problem setting for most planning research are mo died by providing

the agent only partial knowledge of his environment Since the agent do es not know the

total world state actions may appear to have nondeterministic eects The signicant

asp ects of the search problem which dier from previously studied planning problems are

the acquisition of information and iteration of similar actions while exploring a search

space

Since intro duction of the situation calculus MH various systems have b een prop osed

for representing and reasoning ab out actions whichinvolveknowledge acquisition and iter

ation including Mo ores work on the interaction b etween knowledge and action Mo o

Such systems can b e used to infer prop erties of plans whichhave already b een constructed

onstruct plans for complex actions My concern with searching has but do not themselves c

to do with a sense that Mo ores knowledge preconditions are overly restrictive Morgen

stern Mor examined ways to weaken knowledge preconditions for an individual agent

by relying on the knowledge and abilities of other agents Lesp erances research Les on

indexical knowledge is another wayofweakening the knowledge preconditions I am trying

to reduce the amount of information an agentmust know provided he can searchaknown

search space If you dial the rightcombination to a safe it will op en whether or not you

knew in advance that it was the rightcombination Searchisaway to guarantee you will

eventually dial the rightcombination So what I am exploring is how to systematically

construct a search that will use available knowledge to accomplish something the agent

do es not currently know enough to do directly

I claim it is p ossible for automated agents to engage in search b ehavior Engaging

in searchbehavior consists in recognizing the need for a search constructing an eective

plan and then carrying out that plan Expressing such a plan and reasoning ab out its

eectiveness requires a representation language I will select a representation language

based on criteria derived from analyzing the search planning problem Each of the three

comp onents of a system for engaging in searchbehavior will b e designed and implemented

to demonstrate that an automated agent can nd things when he needs to ii

Acknowledgement

Iowe debts of gratitude to manyteachers and colleagues who have help ed shap e this

research I esp ecially appreciate the help of my advisor Bonnie Lynn Webb er and fellow

students who havecontributed to the AnimNL pro ject includin g Chris Geib Breck

Baldwin Libby Levison Mike White and Barbara Di Eugenio This work has b eneted

from discussion with other memb ers of Penns Computational Linguistics FeedbackForum

CLiFF and our informal planning discussion group including Charlie Ortiz and Ron

Rymon Finally the comments and advice of my dissertation committee Henry Kautz of

ATT Norm Badler Dale Miller and Greg Provan all of Penn havebeeninvaluable

in helping me clarify the direction in which this research will evolve iii

Contents

Abstract ii

Acknowledgement iii

Finding something

The search planning problem

Novel asp ects of the search planning problem

A scenario calling for a searchplan

Previous approaches to related problems

Classical planning

Informative actions

Conditional planning

Diagnosis

Abstract search actions

Planning for iteration

Reactive systems or situated agents

Monitoring plan execution

A new approach to planning a search

Application to the AnimNL pro ject

Thesis claim

Plan of prop osal

Plan representation

Criteria for a representation

Indexicality

Candidate formalisms

Time and causation

Attitudes

Combined theories of change and mental state

Meeting representation criteria

Situation calculus examples

Example searchplan

A representation language for searchplans iv

Prop erties of search plans

Avoiding rep etition

Ability

Lo op termination

Ability and search plans

Ecient strategies

Summary Correctness of a searchplan

Plan construction

Iteration schemata for search

Interrupting a search

Abandoning a search

Recursive planner invocation

Planning for a search

Plan execution

Description of execution of a searchplan

Evaluating conditional expressions

Selecting obstaclesite to search

Executing a search plan

Thesis

Review of currentstate

System Description

Remaining op en issues

Remaining software development

Prop osed work

Conclusion

A Representation for searchplans

A Syntax rst order mo dal logic

A Semantics p ossible worlds

A Situation calculus

A Inference mo dal axioms

A Inferring prop erties of situations

A Static Epistemic axioms

A Dynamic Epistemic axioms v

List of Tables

Prop erties of logics of change vi

List of Figures

Nondeterministic eects and the need for conditional plans

Example searchplan

Search plan for nding a ball

Searchschema

Interrupted searchschema

Relativized searchschema

System Diagram

Planner System Diagram vii

Chapter

Finding something

People often do not know where things are and have to lo ok for them Or they are

given a generic description of where something is and have to lo ok for it Even if rob ots

like elephants never forget our ways of communicating lo cations are such that rob ots

instructed by p eople are going to have to lo ok for things

This thesis presents a formal mo del suitable for reasoning ab out how to nd things and

acting to nd them which I will call search b ehavior Since not knowing somethings

lo cation can prevent agents from reaching their desired goals the ability to plan and

conduct a search will b e argued to increase the variety of situations in which an agentcan

succeed at his chosen task

Search is concerned with increasing an agents awareness of his environment the

agent acts to acquire knowledge of the lo cation of an ob ject Conducting the search

may also require changing the state of the world includin g agents moving themselves

or removing various obstacles to their p erception Thus in search two kinds of state

information must b e represented and monitored the agents internal epistemic state and

the external environment state

My research on search plans diers from the considerable work that has b een done on

ecient algorithms for search problems see for example Knu in that it is aimed at

identifying the reasoning process required of an automated agen t to decide to conduct a

search and to monitor its progress In contrast work on search algorithms aims to achieve

eciency by compiling out the reasoning involved with monitoring a search and leaveto

the programmer the decision of when to search Planning has often b een construed as a

search problem Kor Here I construe physical search that is the pro cess of lo oking

for things as a planning problem

The search planning problem

The research problem I am addressing is a planning problem An agent has a goal to

achieveinanenvironment The agent is able to p erform several dierent actions and has

information ab out the eects of dierent actions on the environment

The original planning problem was to discover a sequence of actions which result in

the goal b eing satised when executed in the currentenvironment The planning problem

for search will require plans whichhave more complex structure than sequential ordering

as will b e argued in this chapter Therefore the agent is provided with additional plan

construction op erators for forming sequential conditional or iterated plans

Unlike the original planning problem searchinvolves discovering information ab out the

environment The notion of environmentmust b e enriched to distinguish what information

is known to the agentatanygiven time and what is unknown

In its most general form the search planning problem can b e stated as discovering

a plan structure which will determine the truth or falsity of a goal prop osition when

executed in the currentenvironment The search planning problem can also b e viewed as

discovering a plan which will determine the identity of an ob ject in the environment which

satises a goal prop erty when executed in the currentenvironment

The rest of this chapter discusses these novel asp ects of the search problem in more

detail The requirement for additional control structure in plans is derived from attempts

to use existing planning techniques to solve the search planning problem

One example of the search planning problem which is used throughout this prop osal

to illustrate searchbehavior is an environmentwithavarietyofcontainers which hide a

ball from the agent The agent has the goal of lo cating the ball In this example the

containers provide the environmental device which is the basis for distinguishing what the

agent knows ab out the world from what it do es not know

To give the reader a sense of the class of search problems a variety of other examples

are presented

An areasearch uses the device of sweeping a limited p erceptual sensor over an area of

the environment larger than the area immediately p erceivable to the agent to explore a

search space An illustration of area search is the b ehavior that a Coast Guard Searchand

Rescue mission might undertake to scan a large area of o cean for missing b oaters

A kind of search which mightbecalledatheory search might b e used byanagent

attempting to answer the question Is it feasible for me to buy a house Information

which the agent can use to develop a theory for answering this question is initially hidden

from the agent in b o oks Reading various texts may provide direct answers to the goal

prop osition indirect answers whichmay b e used to infer the truth of the goal prop osition

or secondary information ab out other texts

An agentmay b e faced with a search problem when in a maze The goal prop osition

might b e Can I exit this maze The walls immediately surrounding the agent in this

environment hide information ab out the rest of the maze Similarly when searching for an

ob ject in a cluttered environment obstacles other than containers may blo ck the agents

p erception

The rest of this prop osal will fo cus on searches where the goal is to determine the

lo cation of an ob ject Most examples will involve searching through containers for a ball

which is one of the simplest kinds of search problems The advantage of this instance of

the search problem is that geometric reasoning can b e simplied if we consider that an

agent can see any ob ject that is not inside a closed container The dissertation will present

e kinds of search a general mechanism which can plan for all the ab ov

Novel asp ects of the search planning problem

From the p ersp ective of planning search plans constitute another step in the evolution of

plans from simple sequences of actions to structures which more closely resemble computer

programs The planning problem for search diers from earlier planning problems The

earliest recognition of the distinct character of plans for search in the cognitive science

literature is in Miller et al MGP

The original planning problem assumed certain prop erties ab out the b ehavior of the

environment in which an agentwas acting and the agents relation to that environment

These assumptions are called the blocks world assumptions

Only one agent is activeintheenvironment nothing else causes change

That agent has total knowledge of the environment

Actions are deterministic in their eects

Searching for things is a natural problem that arises when the blo cks world assumptions

are mo died by providing the agent only partial knowledge of his environment

Rather than relax the requirement that actions have deterministic eects I consider

the case that the agentmay not have total knowledge of the environment Since the agent

do es not know the total world state actions may appear to have nondeterministic eects

There is a subtle dierence b etween these two planning problems Conditional planning is

an appropriate resp onse to nondeterminism but something more is necessary for epistemic

nondeterminism

A scenario calling for a searchplan

ointro duce the notions of search knowledge and search plans consider an agentwho T

knows that one eect of op ening a container is to reveal things inside that container The

agent might use this information to nd a ball b that unbeknownst to him is hidden in

some container cby reasoning as follows

I do not currently see the ball but I do know of an action which will make

the ball visible opening the container it is in The obvious container to op en

is the one containing the ball but the reason I am searching is b ecause I do

not knowwhatcontainer that is Perhaps I have an indep endentway to know

where the ball is eg by shaking the container it is in This is no solution

since I still do not know whichcontainer to shake

IfInow see seven containers then I may consider that either it is in the

rst the second or the seventh Each of these things I am able to assume

in turn Acting on those assumptions will exhaustively search the space of

containers and will nd the ball Fortunately the nature of this problem is

that op ening an emptycontainer is useful as it p ermits me to eliminate the

p ossibility that the ball is there

Whenever a new container is discovered inside an old one that discovery

can b e easily accommo dated since I will do the same thing to check inside it as

with all the other containers

The agentknows the disjunctive prop osition that the ball is in the rst container or

the second or the seventh That information is insucient for the agent to knowhe

can nd the ball by op ening the rst container or any of the other containers Section

presents this formal characterization of abilityHowever it is sucient for the agentto

know that the eect of conducting a search through those containers is to know the lo cation

of the ball or know that the ball is not lo cated in any of the containers

Previous approaches to related problems

The relationship b etween an agent and his environment determines the kind of plans he

will need to form in order to act eectively Initial planning research assumed that the

agentwas acting in a blo cks world This section considers planning research which shares

characteristics with mine None of these research directions adequately addresses the

problem of planning to conduct a search

Classical planning

Search is a purp oseful and conscious activity in which agents engage A ma jor research

theme in Articial Intelligence AI is that purp oseful b ehavior can b e guided by delib erate

plans The prominent paradigm for such planned activity is planning as a state space

search with the resulting plan b eing subsequently carried out by the agent This paradigm

has its origins in the situation calculus of McCarthy MH and was originally implemented

as a planner in STRIPS by Fikes and Nilsson FN

State space search planning considers an initial state and a goal state The goal state

describ es some future time when the purp ose of the plan has b een achieved The initial

state describ es the wa y the world is now A planner searches for a sequence of actions

which will get the agent from the initial state to the goal state Following the development

of a plan to traverse a path from the currentworld state to the desired goal state the plan

is executed Because agents have total knowledge of their environment in this planning

problem the need for conducting a searchnever arises

A sequential planner might b e used as part of a system to pro duce searchbehavior Let

an agent replan when its environment do es not resp ond as exp ected Let it guess which

container the ball was lo cated in It can plan to nd the ball by op ening that container If

the assumption is correct the agentdiscovers the ball when it executes that plan If the

ball is not discovered in the container the agent can notice this and replan for the new

environment

Guessing and replanning are required to adapt sequential planning for use in solving

the search problem Guessing comp ensates the planner for not having complete knowledge

of the environment Replanning comp ensates for guessing incorrectlyBelow I will argue

that plans for search require conditional and iterative plans The conditional nature of

searchbehavior is still present in that the sequential planning agent conditionally decides

to replan The iterative nature is still there in the p ossible rep eated invo cation of the

planner Representing conditionals and iteration explicitly in the plan provides several

advantages It makes proving correctness of an agents b ehavior easier by making the agent

mo dular It provides a level of representation which completely sp ecies the interaction

between the planner and the execution engine since it is the plan for the entire search

If the planner pro duces a correct plan and that plan is correctly executed then the agent

b ehaves correctly

Informative actions

In his pioneering work in the theory of knowledge and action Mo ore Mo o dened

informative actions to b e those which result in knowledge of the truth or falsityofa

prop osition These actions are like tests with litmus pap er After the test the tester either

knows that the pap er is blue or that it is not blue From the test result the agentcan

infer other information ab out the state of the world whether the solution tested was acid

or base The nature of tests is that the outcome is not known in advance they have

nondeterministic eects

Sequencing other actions after informative actions can b e problematic b ecause infor

mative actions have nondeterministic eects In order to sequence one action after another

the earlier action should have eects whichhave more information than required for the

the preconditions of the later action However for nondeterministic actions eects are

typically less informative than required by the preconditions of any single action Combin

ing actions using conditional op erators or nondeterministic choice is one resp onse to this

problem I discuss informative actions further in Section

Conditional planning

Relaxing the assumption that actions are deterministic creates new problems for an agent

Research in AI planning systems has addressed the issue of planning for actions with

nondeterministic eects byintro ducing conditional plans Conditional plans were rst

intro duced in WarplanC byWarren War Recently an approachwas suggested for

developing conditional nonlinear plans PS Whenever a plan included an action which

had a nondeterministic eect the rest of the plan would b e conditional on which state of

the world actually o ccurred When the conditional was reached the agentwould examine

the world to determine which branc h of the conditional to take

Figure illustrates the interaction with nondeterministic eects Supp osing action

has as its preconditions A B This can b e sequenced in a plan after action which

has eect AHowever to sequence action with precondition C after action with

eect C D requires rst combining it with another action in a conditional A suitable

combination would b e to combine action with action which has precondition D These

short plans are shown in gure Note that A B is less than A in the information

ordering

Conditional planning is not sucient for agents with only limited knowledge of their

environment since the latter prevents them from b eing able to reliably evaluate the ex

pressions which will decide whichbranch of a conditional to execute Conditional planning

might b e considered as a solution to the search planning problem provided that additional

restrictions are placed on the expression which decides the conditional The simplest re

striction is to require the expression to b e a prop erty of the agents mental state This

will b e eectiveprovided that the agent has accurate introsp ection The simplicity of this

approach is that it can rely on the simple syntactic marking of a formula as b eing known

to the agent Under this regime acceptable expressions are just those which are prop erties 1 A A v B 2

34C v D C

D5

Figure Nondeterministic eects and the need for conditional plans

of the agents knowledge

An alternate approach to adopting conditional planning solutions to the search planning

problem is to insert plan steps to acquire information to decide the branch to take Under

this approach the planner must b e invoked to attempt to construct a plan to determine

if the expression deciding the condition is acceptable Acceptable expressions are those

which the agent can reliably plan to know

Since none of the work to date on conditional planning has distinguished the agents

epistemic state from the actual state of the world neither of these two approaches to

restricting the conditional expression has yet b een explored

Diagnosis

The goal of a search plan is the acquisition of information ab out the environment rather

than some mo dication of the environment This is a feature that search plans share

with plans for diagnosis RWC SWMR That actions may b oth b e informative

and eect changes in the world has b een recognized as early as McCarthy and Hayes

MH and used in recentwork on medical decision supp ort RWC That one may

havetotakemultiple knowledgeacquisition actions b efore ones knowledge is sucient

to takedecisive action has b een recognized in work by McIlraith and Reiter MRon

incremental diagnosis

Plans for incremental diagnostic tests suchasproposedby McIlraith and Reiter are

similar to search plans except that they sp ecically exclude the p ossibility that the test

actions will change the state of the world As a consequence of expressing exp ected test

outcomes in a prop ositional logic their diagnostic approach do es not p ermit taking advan

tage of serendipity and nding things other than what one was lo oking for

The literature on diagnosis has not addressed the issue of deciding branches of con

ditional action Howeverifonechose to adopt the more general approach to extending

conditional planning to the search problem existing research on diagnostic plans provides

go o d mo dels for how to acquire information needed to decide what action to take

Abstract search actions

While it would b e p ossible to mo del searches at a more abstract level as individual actions

as suggested bySchopp ers Sch there are at least two reasons for constructing detailed

plans to drivesearchbehavior First searches for dierent kinds of ob jects share a common

control structure which I prop ose to use as the basis for my representation of search plans

Second the actions whichmust b e taken to conduct the search are not dierentfrom

actions the agent takes to achieve other goals having two dierentways of representing

the same actions is undesirable

Schopp ers presents a mo dal logic of time and mental state for application to planning

He also presents a singleaction search op erator for lo cating an ob ject The application

domain he considers is that of a spaceb orne rob ot assisting a human EVA He represents

abstract search op erations In his planning language the rob ot may p erform a complete

rotation to acquire an arbitrary ob ject in the eld of view of its camera

rotatingX

b soon sust incamerafovX true

A rough gloss of the ab ove formula for the rotating action is that an unconditional

eect of this action is that the agent b elieves that at some time in the future the ob ject

Xwillenter and remain in the eld of view of the camera This is a compact description

of a search

Clearly a simple wa y to incorp orate search b ehavior into existing planning systems is

for the designer of the system to characterize the preconditions and eects of the entire

search This abstracts away from the details of how the search is planned and conducted

and the changes in mental state of the agent during the search It is these issues that I am

addressing in this work

Planning for iteration

Tate et al THD claim that planning systems exist which plan for iteration They cite

NOAH Sac and SIPE Wil as taking a black box approach to construct iterative

plans To the extent that iterative parts of plans can b e abstracted to single actions they

can b e incorp orated into these plans The representation system used do es not p ermit

reasoning ab out the details of the iterative part of the plan

However b oth these planning systems use a pro cedural net representation whichpre

vents rep etition of actions Drummond Dru extends pro cedural nets to plan nets which

can represent iteration

Reactive systems or situated agents

Since the mid s there has b een a countercurrent in AI planning research whichadvo

cates reactivebehavior in resp onse to the immediate situation over execution of delib erate

plans A feature of reactive systems which is emphasized in the literature is that agents ex

ploit features of their environment to reduce their need to delib erate ab out actions While

search can exploit features of the environment the environment is not enough the envi

ronmentmay b e identical at dierent stages of a search The choice of search action thus

dep ends on the agents awareness of what progress has b een made in the search Therefore

search can b e used to argue for the need for more internal state

Current reactive systems and situated agents with the exception of Rosenscheins work

are constructed manually for a particular task When that task necessitates a search the

designer recognizes this need and manually enco des a pro cedure for a search

Monitoring plan execution

The environments where agents carry out plans are frequently unpredictable This has led

to the suggestion that plans b e augmented with sensor actions to ensure that exp ected

states of the world o ccur at the appropriate times DAD This is not a dierent plan

ning problem simply a resp onse to the inappropriate characterization of an unpredictable

environmentby blo cks world assumptions

A new approach to planning a search

This exploration of related planning systems leaves me with the conclusion that no existing

system can b e used for planning searchbehavior The signicant asp ects of the search

problem which dier from previously studied planning problems are the acquisition of

information and iteration of similar actions while exploring the search space Various

ve b een prop osed for representing and reasoning ab out actions whichinvolve systems ha

knowledge acquisition and iteration including Mo o Les Such systems can b e used

to infer prop erties of plans whichhave already b een constructed but do not themselves

construct plans for complex actions

By incorp orating information ab out the agents epistemic state into situation descrip

tions and action descriptions meansend planning can b e mo died to plan for knowledge

acquisition Such a mo died meansend planning system may b e able to incorp orate search

into a plan if search is sp ecied as a single action with a set of preconditions and a set of

eects However planning how to conduct the search requires representing and reasoning

ab out actions whose outcome the agent do es not know Existing approaches to conditional

planning do not suciently restrict the form of conditional expressions to guarantee they

can b e executed in the mo died blo cks world I consider After a brief discussion of the

application which motivates this planning problem I state the claim of my thesis

Application to the AnimNL pro ject

The problem of getting agents to lo ok for things has come up in the pro cess of developing

the planning comp onent of a system to pro duce human gure animation from instruction

texts Details of this system called AnimNL Animation from Natural Language can b e

found in WBB

The problem raised in the AnimNL pro ject is that of referencegrounding Grounding

naturallanguage referring expressions to ob jects in a simulated physical environment

often requires exploration on the part of the simulated agent to lo cate them Information

from the interpretation of instructions will b e used directly in forming search plans

In the application of this researchtothe AnimNL pro ject the description of the search

ob ject is derived in part from the interpretation of natural language referring expressions

Descriptions can come from other parts of the interpretation as well and also from common

sense world knowledge etc

Ob jects may also b e intro duced during planning or in reasoning ab out how to carry

out actions that also need to b e grounded in the sp ecic environment eg remove

the lid of the paint can requires a atbladed to ol to pry the lid o Also instructions

may directly sp ecify that the agent conduct a search to nd an ob ject eg Get me a

screwdriver

Search plans are develop ed in resp onse to an inability of the agent to act In the

AnimNL pro ject this is detected after the planner has pro duced an atomic action but

b efore the agent can commit to p erforming it Commitment is only p ossible when the

ob jects required to p erform the action are all p erceived by the agent Without the required

ob jects a searchmust b e undertaken to lo cate them

Thesis claim

I claim it is p ossible for automated agents to engage in search b ehavior Engaging in search

b ehavior consists in recognizing the need for a search constructing an eective plan and

then carrying out that plan

Further I claim that explicitly representing a plan for an entire searchinadvance has

tages for an agent The agent has more information ab out its intentions and several advan

can thus provide b etter explanations of its b ehavior The agent need not replan during

the course of a normal search

Finallyeven constructing a search plan can b e more ecient when the entire search

is represented This is b ecause features common to dierent sites in the search space can

b e exploited to avoid redundant planning eort Agents who represent search plans as I

suggest can plan and act more eciently than agents that construct only sequential plans

Expressing such a plan and reasoning ab out its eectiveness requires a representation

language I will select a representation language based on criteria derived from analyzing

the search planning problem Each of the three comp onents of a system for engaging in

search b ehavior recognizing a search problem planning and executing a plan will b e

designed and implemented to demonstrate that an automated agent can nd things when

he needs to

The problem of planning searchbehavior diers from the planning problems that have

previously b een studied In particular I do not assume that agents have total knowledge

of their environment I prop ose a planning system for this mo died problem that includes

This assumption is shared with some planners for diagnostic actions see RWC Rymons system

do es not construct a complete plan at once and information seeking actions do not need to b e rep eated

a logic for reasoning ab out the interaction b etween an agent and his environment I claim

that this system p ermits an agent to plan eectivebehavior in situations that call for a

search to b e conducted

The need for a search plan is recognized automatically when knowledge ab out an ob

jects lo cation is needed The abstract characterization of a search plan as a single action

is expanded into a plan that has an iterativecontrol structure This detailed search plan

sp ecies exploring dierent sites in the search space until the desired ob ject is found or

the search space is exhausted A logic for reasoning ab out the eects of various actions on

the agents internal epistemic state and on his surrounding environment is used to guide

construction of this detailed search plan and to insure its correctness Correctness for a

search plan requires that no search site is explored twice and that the exploration of all

sites precedes abandoning the search in the plan Correctness is discussed in Chapter

There may arise situations where some element of information is needed by the agent

and is not known to him This problem has b een discussed b efore in the planning literature

as the problem of knowledge acquisition Knowledge acquisition actions are inherently

nondeterministic in their eects on the agents knowledge state If they were not then

it could only b e b ecause the eects were already known to the agent I am restricting

the problem of planning for knowledge acquisition to circumventing obstacles to direct

p erception of ob jects Actions such as op ening do ors or lifting the lid of a b oxhave the

potential to reveal ob jects that were previously hidden While any action that moves

either the agent or the ob ject b eing sought or the obstacle that stands b etween them

may p otentially reveal the ob ject to the agent I am primarily interested in op erations on

ob jects that are conventionally understo o d to function as obstructions do ors and lids

I call plans that manipulate these conventional obstructions systematically to rev eal the

lo cation of an unknown ob ject search plans

When the agent b elieves that a desired ob ject is lo cated in one of a nite set of sites and

needs to gain access to that ob ject for some purp ose a search plan may b e employed by the

agenttoachieve his goal The two prop erties of nonrep etition and eventual termination

of the search ensure that when the ob ject exists in the search space b ehaving as sp ecied

in the search plan will satisfy the goal of lo cating the search ob ject

Reasoning ab out the eectiveness of an iterative plan requires reasoning ab out the ter

mination of the iteration Agents do frequently have some information ab out the lo cation

of a desired ob ject which acts to delimit or order the space they are willing to search This

lo cation information is less than what is needed by the agent The combination of partial

information ab out the lo cation of the ob ject and the nondeterministic knowledge eects

of manipulating obstacles in that search space suggests rep eatedly going to some dierent

obstacle in the search space and moving it until they have all b een tried exhaustive

search Placing some constraint on the search space plays an imp ortant role in ensuring

that the search will eventually terminate

Iteration of the only action whose successful p erformance cannot b e assumed chest tub e insertion is

handled by an ad ho c mechanism

Plan of prop osal

The remainder of this prop osal will present the general problem of automating planning

reasoning ab out and carrying out physical searches I present a formalism for representing

search plans whichisderived from recent research in reasoning ab out knowledge and action

The unique requirements on a representation for search plans are identied and used to

argue against adopting existing formalisms Chapter presents a formalism for reasoning

ab out search plans Chapter discusses criteria for evaluating the correctness of search

plans Chapter describ es constructing search plans by instantiating a generic search

plan schema Chapter discusses the execution of these plans Finally I conclude with

discussion of the remaining work to complete my thesis

Chapter

Plan representation

Since the previously discussed planning approaches are insucient for planning searches

I turn to an analysis of the representational needs a search planner This chapter presents

an analysis of the search planning problem framed largely in terms of criteria for a repre

sentation After presenting criteria for a logic in which to express search plans I use these

criteria to analyze previous formalisms

Criteria for a representation

A plan for conducting a search should call for rep eated selection of some action whichmay

change the agents knowledge ab out the lo cation of an ob ject The previous discussion

showed some of the failings of existing planning systems in attempting to represent plans

for search b ehavior

I argue that the following are required to plan conduct and reason ab out search plans

The representation system should include terms for various ob jects to represent the

search ob ject and distinguish it from other ob jects whichmight b e encountered

Ob jects are lo cated at sites which should also b e represented

Agents p erform actions to explore sites It is useful for the actions to have parametric

description so that an abstract plan for searching an abstract site can b e represented

Some representational mechanism is necessary for expressing the selection of a site

to explore and an action to explore that site

Some representational device is required to distinguish what the agent knows and

perceives from what is actually the case but not known to him

Due to the epistemic nondeterminism inherent in the search problem some means

of expressing conditional plans is necessary It is also necessary to represent the

iterativecontrol strategy of a search plan

Indexicality

It is also desirable that the representation of search plans b e indexical for eciency and

to reect the appropriate knowledge preconditions of actions Lesp erance Les argues

that knowledge requirements for actions are largely indexical knowledge knowledge of the

environment from the p ersp ective of the agent In order to op en a container an agent need

only know that the container is here ie at the agents own lo cation The agentdoes

not need to know where here is in some external co ordinate system Similarly the agent

need not know the identity of the container except that it is the one that is here

Lesp erance provides indexical functions and op erators to change the context of inter

pretation which p ermits him to characterize the dierence b etween indexical knowledge

and ob jective knowledge He further shows that indexical knowledge is usually required as

a precondition for action rather than ob jective nonindexical knowledge

Lesp erance presents an example plan whichinvolves search He proves that an agent

is able to move to where an ob ject is lo cated if he knows that the ob ject is within some

b ounded distance in front of him The search space for this action is the nite collection of

lo cations in front of the agent The action terminates when the agent arrives at the search

ob ject after iterating the action of moving forward one lo cation at a time

It is the nature of moving forward that changes the agents physical p osition Thus

the nature of the indexically sp ecied action means that the agent explores a dierent

p ortion of the search space each time Few actions have the prop erty that rep eating them

will constitute exploring dierent parts of the search space and it is only for such actions

that Lesp erances approach will adequately represent a search

According to Subramanian and Wo o dll SW indexical representations can lead to

more ecient implementations In particular they can b e implemented in combinatorial

circuits which can execute in constant time So an indexical representation is advantageous

since it b oth represents knowledge accurately and aords an ecient implementation

Ensuring that the plan is represented in an indexical representation and makes use of

indexical information when necessary is an ultimate goal of my researchinsearch planning

However given the existence of a mechanism for translating from a situation calculus

notation to an indexical representation I consider this of secondary imp ortance

Candidate formalisms

Thereisnolack of formal theories of action suitable for use in this thesis There are

also several comp eting formal theories of internal states of intelligentagents This section

presents an analysis of their relative merits for purp oses of representing reasoning and

proving correctness of search plans

In general b oth logics of action or change and logics of epistemic state extend rst

order logic with additional mechanism to make inference dep end on a particular time or

on a particular b elief state of some individual

Time and causation

Among logics of change one can distinguish b etween logics of time and logics of causation

Although b oth have to do with the changes in context as time passes and events o ccur

change context duration

causal temp oral explicit implicit interval point

situation calculus X X X

dynamic logic X X X

event calculus X X X

temp oral logic X X X X X

Table Prop erties of logics of change

logics of time take times as primitives while logics of causation takeevents as primitives

and often do not include times at all When they do time is often just an index into a

sequence of events which determines howcontext changes Although logics of time can

describ e the temp oral relation b etween a cause and its eect they require some additional

mechanism to distinguish causation from other reasons for temp oral ordering Conversely

logics of causation require additional mechanism to express temp oral relations b etween

noncausally related events

Logics of change may consider times to have no duration p oints or some duration

intervals or they maycombine p oint and interval times The relevance of this distinction

is in sp ecifying the duration or lack thereof over which formulas are evaluated In p oint

logics formulas are evaluated with resp ect to an instantaneous state In interval logics

formulas are prop erties of a span of time

There are roughly sp eaking two approaches to logics of time or causation Either

times may b e added to the ontology of a rstorder theory or time may b e considered an

element of the context which determines the interpretation of formula The rst approach

results in a rstorder logic the second in a mo dal logic

Having identied relevant distinctions I will now use them in characterizing the relative

merits of candidate formalisms for representing and reasoning ab out search plans

Dynamic Logic Dynamic logic is a causal logic that was invented by Pratt Pra for

use in analyzing programs Dynamic logic is a mo dal logic with mo dal op erators for each

action Because of the way actions are interpreted as mo dal op erators there are no event

individuals and consequently no quantication over actions in dynamic logic It is therefore

unsuited for representing plans where the selection of actions is expressed by quantication

over the action

Event calculus Kowalskis event calculus KS p ermits quantication over events and

relates the truth of prop ositions and the o ccurrence of events to intervals In the event

calculus intervals are describ ed relativetoevents instead of indexically related to the

current time Kowalski do es not include op erators to express conditionals or iteration of

events In general the only events which are considered are those which instantaneously

achieveachange in the world Representing complex actions such as needed in search

plans in such a framework would b e dicult Thus it is not appropriate for my purp oses

Temp oral Logic Dynamic logic and the situation calculus have b een criticized bymany

researchers for restricting the p ossible temp oral relations b etween actions and b etween

causes and their eects Allens use of an intervalbased temp oral logic is one attempt to

overcome these limitations All

Temp oral logics are a family of logics rather than a single formalism For a recent

survey see Van Bentham vB In dierent temp oral logics the world may b e describ ed

at instants or over intervals Both mo dal and nonmo dal formalisms have b een studied

However additional mechanism is needed to express causality in temp oral logic since it

primarily concerned with reasoning ab out when things happ en instead of reasoning ab out

the eects of actions Rather than complicate a temp oral logic with additional mechanism

for reasoning ab out causation I deem it appropriate to use a causal logic based on the

situation calculus

Situation Calculus The situation calculus was invented by McCarthyandHayes MH

for representing intelligent actions In it doing an action is a relation or function b e

tween two situations Situation calculus is therefore classied as a causal logic of change

In contrast to dynamic logic it is p ossible to quantify over actions in the situation calculus

However it is a sorted rstorder logic not an indexical representation This makes it

dicult to capture the correct knowledge preconditions of actions

I expecttoovercome this diculty using a technique prop osed by Subramanian and

Wo o dll SW to derive an indexicalfuncti onal representation from a restricted form of

the situation calculus

Attitudes

There are rst order logics of mental attitudes just as there are rst order logics of change

Such logics formalize the ob jects of mental attitudes as strings which represent prop osi

tions Similarly mo dal logics have b een prop osed to capture the context dep endent nature

of reasoning ab out mental states A recent alternative to these two approaches departs

markedly from rst order logic to take arbitrary sets of prop ositions as constituting situa

tions

Although there are arguable dierences b etween these diering approaches to reasoning

ab out mental attitudes they are all more or less suitable for use in conducting searches

The imp ortant p oint is that some means to distinguish the state of the world from the

mental state of the agent is required

Syntactic Epistemic Logic A rstorder logic was used by Morgenstern in her work

on reasoning ab out knowledge and action Mor In her formalism ob jects of epistemic

predicates are strings Functions are included in the logic to manipulate those strings

Syntactic epistemic logic is most compatible with a rstorder logic of change suchas

the situation calculus This was the combination used by Morgenstern

This approachisunwieldy as the functions which manipulate strings must b e dened

within the logic and reasoning ab out inferences drawn by an agent requires app eal to

the denition of these string manipulation functions A mo dal alternative to this will b e

discussed b elow

Situation Theory Situation theory was invented by Barwise and Perry BP and ex

tended by Keith Devlin Dev and others Situations are arbitrary collections of prop o

sitions and hence may b e inconsistent or incomplete This contrasts with b oth mo dal

epistemic logics and syntactic epistemic logics which start from complete and consistent

p ossible worlds and achieve incompleteness through quantication Since arbitrary col

lections of prop ositions are considered situation theory do es not require that tautologies

b e b elieved nor do es it require that b eliefs are closed under logical consequence Indeed

situations maycontain inconsistencies

Situation theory contains mechanism for representing spatiotemp oral lo cations so it

alone might b e sucient for the purp ose of representing search However it is fairly new

and less well understo o d than the alternatives Since there are no readily available auto

mated inference engines for situation theory it cannot b e considered a viable alternative

on engineering grounds

Epistemic Logic Hintikka Hin prop osed mo dal logics of knowledge and b elief In

epistemic logics mo dal context is used to prevent substitution into expressions which

describ e the internal state of agents This approach has b een extended to multiple agents

Epistemic logic is most compatible with mo dal logics of change such as the mo dal

temp oral logic argued for ab ove A consequence of adopting mo dal logics for mental

attitudes is that tautologies are automatically included as ob jects of b elief knowledge

and p erception This is a consequence of the necessitation rule of inference whichispart

of all common mo dal logics Also a common mo dal axiom sp ecies consequential closure

of mental attitudes This is the approach I prop ose to take for representing the knowledge

of the agent

Combined theories of change and mental state

wledge and action along the lines Rob ert C Mo ore Mo o rst provided a logic of kno

suggested by McCarthy and Hayes MH His logic combined a mo dal logic of knowledge

with a situation calculus logic of action To a basic situation calculus of actions he added

action constructors which build sequences conditional actions and iterated actions from

other actions

Mo ores theory of informative actions illustrates the knowledge eects of an action An

action is said to b e informative ab out prop osition P if after the action the agent knows P

and every world accessible via the knowing accessibility relation from the world resulting

from the action is the result of doing a similar action in a p ossible world whichwas accessible

again via the knowing relation in the initial world To express this formallyMoore

app eals to a rstorder metalanguage for his logic in which R is the accessibility relation

which expresses that world w results from the o ccurrence of E v ent in w and Know is



the accessibility relation which expresses that worlds w and w are indistinguishabl e given

 

what Ag ent knows The expression Truew P indicates that P is true at world w The

condition for informative actions ab out P is expressed as

w w RE v ent w w

 

w KnowAg ent w w

  

w KnowAg ent w w

 

RE v ent w w

 

Truew P Truew P

 

Not included in the ab oveformula is the characterization of the lackofknowledge of

P in the initial world w When an informative action is successful there are two p ossible

outcomes either the agent knows the truth of P or knows that P is false

As has b een argued by Lesp erance it is indexical knowledge which is the prerequisite

for most action rather than the ob jectiveknowledge which Mo ore uses in his knowledge

preconditions Aside from that ob jection Mo ores formalism addresses most of the re

quirements of a representation for search plans

Another approachtocombining representation of actions and epistemic state is taken

by Drummond Dru This approach is based on pro cedural net descriptions of actions

Sac Drummond presents a Petrinet like graph representation of plans which distin

guishes b etween eects on the external environment and eects on the agents internal

state However all the preconditions on actions in his representation are on the agents

t and those that must b e b elief state He distinguishes b etween b eliefs whichmust b e presen

absent in order to p ermit an action The approach I prop ose is more general in p ermitting

preconditions on either the external environment or on the agents internal state

Meeting representation criteria

Here I argue that the criteria for a search plan representation system are largely met in

the formalism I prop ose The prop osed formalism is a combination of a mo dal logic of

epistemic state b eliefs knowledge and p erceptions Section with the situation

calculus Section

Search plans are represented in a mo dal predicate logic for time and mental state This

approach is similar to that taken bySchopp ers Sch Using this formalism I can show

howsearch plans increase the abilityoftheagent In particular they p ermit agents to act

in the face of knowledge of disjunctive formulas

Action selection is managed through a twostage approach that uses conditional actions

and an action of selecting a site to searchfromasetofalternatives Mo dal op erators

maintain a distinction b etween mental state and actual truth Axioms are presented in

Section A to formalize their interaction Iteration is represented using an op erator which

combines a condition and an action into a whilestatement The formalism is presented

as a logic complete with inference rules suitable for constructing pro ofs of the abilityof

agents to act eectively See App endix A for more details

Situation calculus examples

The situation calculus is useful for reasoning ab out situations b efore and after actions

occur To represent that ball b is in container c in situation s I will use the formula

inb c s

To represent that the ball is in the container after doing action a in situation sIuse

inb c do a s

Plans suchassearch plans are expressed as actions in this extended situation calculus

From disjunctive information ab out the lo cation of the ball in the initial situation s we

want to determine a searchplan p such that after doing p in s the agent will know the

lo cation of the ball The initial situation might b e represented with an existential quantier

as

cinb c s

The expression of the goal for search plan p is that the agentknow which of the containers

the ball is in The next section will explore details of the form which the search plan p

might take to makeitpossibletoachieve this goal This might b e expressed as

cKinb c dops

Information may b e passed from one action to another by storing it in a variable Thus

an imp ortant kind of action is assigning a value to a variable Assigning the value to

variable x is represented as

x

Descriptions of actions may b e atomic suchasp or a ab ove parameterized such

as openx b elow or they may b e complex actions constructed from other actions using

sequencing conditional selection or iteration The system of inference for reasoning ab out

various actions is presented in Section A

Example searchplan

As an example expression of a search plan in this representation consider the problem

of an agent carrying out the instruction step Go into the kitchen and get me the coee

urn Supp ose unbeknownst to the agent the coee urn is stored in one of several closed

cabinets in the kitchen When the agententers the kitchen he will not b e able to see the

urn and will have to lo ok for it in order to get it for the sp eaker

Figure shows a search plan for nding a coee urn ur n when openxisanaction

which constitutes steps in exploring the search space The plan consists of a while lo op

followed by a conditional statement The while lo op calls for iteration until either the

ob ject of the search is found or the search space is exhausted

The success condition is that the urn is p erceived to b e in some lo cation c The term

now in the condition is interpreted indexically with resp ect to the situation when the plan

is executed When this condition holds the plan pro ceeds to the remaining actions in the

plan which is here describ ed as win

Similarly the failure condition expresses that the search space has b een exhausted

there are no further actions to explore unexamined parts of the search space When the

failure condition holds the plan pro ceeds to actions which should b e taken under those

circumstances describ ed as lose

When the search is incomplete neither success nor failure hold then actions are se

lected and taken and the search plan rep eats Here the container x is selected to op en

An earlier representation formalism used logic variables to pass information b etween actions The

resulting formalism required a mo dal temp oral logic The most straightforward way to pass information in

the situation calculus is to intro duce variables sp ecically for that purp ose

while cSeeinur n c now Bempty sites now

do

begin

x sel ectsites

sites r emov ex sites

openx

end

if cSeeinur n c now

then

win

else

l ose

Figure Example search plan

The whilestatement expresses rep eated execution of the open action The plan also in

cludes information which constrains the selection of the container to b e one the agent has

not previously op ened Once a site to explore is selected it is removed from the candidate

sites The open action mayhave a side eect of adding new sites to the sites variable An

initial value for sites is established by examining the agents p erceptions at planning time

The various op erators used in the ab ove expressions include quantiers logical

connectives conjunction negation and mo dal op erators p erception See b elief B

y relations for The mo dal op erators are given a p ossible worlds semantics with accessibilit

epistemic contexts knowledge p erception and temp oral relations

A representation language for search plans

Ihave argued that a mo dal logic extending the situation calculus with epistemic op erators

is an adequate representation for the search planning problem An initial sp ecication is

given in App endix A Subsequent discussion of plan construction and execution will make

use of this notation The p oint of giving a precise formal semantics for search plans is that

it p ermits me to b e precise ab out how to automatically reason ab out how the complex

activity of search is related to its comp onentacts

Chapter

Prop erties of search plans

An imp ortant asp ect of reasoning ab out plans of all kinds is b eing able to determine if

agiven plan will achieve given desired eects I am interested in two dierent prop erties

of eachsearch plan that sites in the search space are not redundantly explored a safety

prop erty nothing bad happ ens and that the search ob ject is eventually found if it exists

in the search space a liveness prop erty something go o d eventually happ ens Safety

prop erties can b e veried byinvariance arguments as shown in Lam Liveness prop erties

canbeveried bywellfoundedness arguments MP OL Plans which satisfy these

safety and liveness prop erties will b e considered correct

Avoiding rep etition

As mentioned earlier the invariance to prove for the iterated step of a search plan is that

each site is explored at most once A single execution establishes conditions which preventa

rep eated execution and no other action changes those conditions Each iteration of the site

exploration action in a search plan should b e dierent from all the previous o ccurrences

so that the agentdoesnotkeep searching the same space This can b e accomplished in

search plans by preventing an agent from exploring a site whichheknows do es not contain

the search ob ject

h will still b e known Frame axioms ensure that information obtained earlier in the searc

by the agent at a later time To illustrate this reasoning consider that an agents knowledge

ab out the lo cation of an ob ject is not lost by op ening or closing another container for all

actions a situations s containers c and ob jects b

No actions change lo cation or containment This is expressed in the form of a suc

cessor state axiom

P ossa s inb c doa s inb c s

The notation Possa s represents that the preconditions for action a are satised

in situation s

This is known due to the necessitation rule for K

KP ossa s inb c doa s inb c s

Knowledge is consequentially closed axiom K for K

K K K

Assuming knowledge b efore action a and as preconditions hold

KPossa s Kinb c s

Conclude knowledge after action a

Kinb c doa s

Ability

The literature on knowledge and action formalizes the ab oveliveness prop erty with a

technical denition of ability This section discusses pro ofs of abilityforvarious search

plans The formal denitions of ability whichhave b een prop osed by Mo ore Mo o

Morgenstern Mor Lesp erance Les share the idea that an agent has the abilityto

achieve an eect by some action when he knows that every way in which he do es that

action results in that eect b eing the case When ability is used in this sense it will

app ear in italics ability In formulas the mo dal op erator can will b e used

An agentis able to bring ab out a situation which has prop erty by taking an action

a in situation s can s when the agentknows that is an eect of action This

is expressed as follows

def

can s Kdo s

Lo op termination

Givenasearch plan proving that an agentis able to accomplish some task using that

plan relies on an assumption that the search plan terminates successfully There are two

avenues I am exploring for insuring that these plans terminate The rst approach uses a

nite b ound on the search space The second approach places restrictions on the structure

of time such that only nitely many steps of the iteration are executed Lesp erance

Lestakes the rst approach These two approaches result in two dierent kinds of

wellfoundedness arguments either the search space is wellfounded or the relevantpart

of the agents resources sp ecically the amount of time the agentdevotes to the task is

some abstract wellfounded structure

Finite search space It is correct to assume that a search plan terminates when the

search space is nite and the agent do es not rep eat actions already p erformed Finite search

ance b efore p erforming the rst step of the search even spaces can usually b e known in adv

if they are large as in the case of a combination safe With nested containers though

the fact that an agent p erceives nitely manycontainers at anygiven moment do es not

Note that an agentmay still b e considered able to achieve some eect if is already true and the

action did not make false is simply true when the action is done

while cSeeinb c now Bempty sites now

do

begin

x sel ectsites

sites r emov ex sites

openx

end

if cSeeinb c now

then

win

else

lose

Figure Search plan for nding a ball

guarantee termination of the search Another argument for termination is needed in this

case

In particular one can app eal to the fact that the in relation b etween containers is

transitive and wellfounded meaning that there can b e no innite nesting of containers

Konigs lemma states that any nitely branching wellfounded tree can only have nitely

many no des So if nitely manycontainers are p erceivable to the agent in the search space

and each contains only nitely many other containers we can conclude that the search

space in this case is nite Unfortunatelywellfoundedness is not rstorder expressible

so this deduction will not b e automated

Finite iteration The alternate approach of constraining the numb er of iterations to b e

nite b y denition will not b e taken in this dissertation The problem with this approach

is that it is dicult to construct an execution engine for search plans which will resp ect

this denition

Ability and searchplans

To nd a ball which is hidden inside one of several p ossibly nested containers an agent

might adopt the plan in Figure Here the site exploration action in the searchisto

op en a new container x This step is rep eated until a ball b is found or the agent runs out

of containers to op en sites b ecomes empty

To prove that agents are able to use the Figure search plan to nd a ball hidden

in some container more must b e said ab out the open action and ab out the nature of the

search space To complete the pro of requires frame axioms and a description of the current

situation Frame axioms are needed which sp ecify that op ening containers do es not cause

the ball to move The approach to the frame problem I am considering is discussed in

App endix Section A

Ecient strategies

A minimal requirementofsearch plans is that they b e correct Better search plans are not

only correct but also make go o d use of time and other resources Search plans will also

be evaluated for their eciency

A go o d strategy for searching is to lo ok in the most likely places rst An imp ortant

area of remaining research on this thesis is to determine sources of information ab out

ordering the sites in a search space and how that information gets used to ensure ecient

searches

One p otential advantage of using an indexical representation is that it might simply

sp ecify that the search pro ceed to the nearest unsearched site if the ordering is a greedy

decision based on closeness

Once a site is selected for exploration it remains to select an action for exploring that

site The b est that may b e p ossible at planning time is to arrange for the typ e of site to

determine the action

Future research will explore whether site ordering is b est done eagerly at planning

time or delayed until immediately prior to site selection I will also study what impact

the timing of these dierentchoices has on decisions ab out actions to explore the selected

site

An obvious goal for research on planning ecientsearches would b e to determine when

sucient information was available to p ermit known search strategies suchasA tobe

employed The description of the search planning system I prop ose is mo dular in that it

sp ecies where site selection information is incorp orated into the plan More work must

b e done to determine precisely what that site and action selection information is

Summary Correctness of a search plan

Asearch plan is correct when its execution leads to the discovery of the desired ob ject

when that ob ject is present within the space describ ed by the search space constraint

Two comp onents of correctness have b een describ ed and metho ds for proving a plan b oth

avoids rep etition and terminates were discussed The central concept of deducing ability

or knowledge of the eects of a search plan was also presented

Asearch plan is ecient when its execution leads quickly to the discovery of the ob ject

Determining the order in which sites are explored has a large impact on this eciency and

will b e a ma jor topic of future research

Chapter

Plan construction

Having settled on a representation language to use in the search plans system I now present

my design for a planner which can construct these plans Discussion of the correctness of

plans develop ed by this system was already discussed in Chapter

Iteration is intro duced in a plan byschema instantiation The iterated actions must

b e planned for so the planner is recursively invoked to plan the inside of the lo op Oc

casionally there are cases where a searchisnotyet complete yet some other action is

appropriate Such cases can b e group ed into two general classes interruptions where the

search is later resumed and relativized searches where the search is prematurely termi

nated The term relativized is b orrowed from Cohen and Levesque CL where they

consider relative p ersistent goals Davis Dav discusses an alternative representation for

plans which also supp orts these kinds of alternatives to completing a search

Iteration schemata for search

Generally sp eaking search plans should b e constructed when the knowledge requirements

for direct action are not met but there is sucientknowledge to achieve the desired goal

via a search

Search plans are constructed byschema instantiation Selecting an algorithm for search

amounts to deciding which searchplanschema to use as the basis for constructing the

search That schema is then instantiated with a description of the search objectaspeci

cation of the search space and actions to take to explore the search space

Constructing search plans via a schema is similar to instantiating other action descrip

tions as is commonly done in other planners The substantive dierence is that only some

of the information is substituted while the rest is constructed byreinvoking the plan

ner The correctness of the resulting search plan can b e veried with an inductiveproof

Whether or not this pro of is carried out at planning time is yet to b e determined The

substitution also involves substituting formula instead of simply instantiating variables to

terms This formula substitution o ccurs with the search ob ject description and the search

space constraint

Once the search space constraint and the description of the searchobjecthave b een

incorp orated into the search plan the incremental actions must b e sp ecied This is

done by setting the search space constraint as the initial situation and the search ob ject

while f ound exhausted

do

step

if found

then

win

else

lose

Figure Searchschema

description as the goal situation and constructing a conditional plan whichachieves the

goal The conditions on whicheachbranch dep ends are taken as successive assumptions

which the plan execution engine must make

The pro cess of creating a search plan is simplied through the use of a generic search

plan schema see Figure that is instantiated to form dierentsearch plans Two

conditions are tested to determine what action o ccurs next Condition found indicates

that the ob ject of the search has b een lo cated When it is true the plan pro ceeds to

a successful conclusion Typically this conclusion win will b e replaced with whatever

action sequence was delayed p ending the agents nding the ob ject The failure condition

exhausted expresses that the entire search space is known not to contain the ob ject

When this is the case the plan continues with an alternate course of action whatever is

substituted for lose Otherwise the schema sp ecies that it is appropriate to continue to

search Ateach iteration of the search the exploration of some site in the search space is

sp ecied by whatever is substituted for step

Interrupting a search

Search plans maybeinterrupted and resumed due to two asp ects of a search plan Each

y state Also progress in conducting a search iteration of a searchplanmay b e b egun in an

is recorded in the agents knowledge ab out the world indep endently of the search plan

There are no preconditions on a search plan except those whichmay propagate forward

from the actions substituted for step winandl ose Preconditions from step maybe

discounted if they are incorp orated into the exhausted condition As a consequence any

iteration of a search plan may b e b egun in any state since every state will satisfy one of the

three conditions that the basic search plan sp ecies when f ound exhausted explore a

site when found terminate successfully otherwise exhausted terminate unsuccessfully

Progress in a search is recorded in the agents knowledge of the world When an agent

op ens a container his knowledge ab out the world is increased by discovering the contents

If a search is halted and some other action is p erformed b efore the search resumes the

agent will not have lost his knowledge ab out the world due to the intervening action

He mayeven have gained knowledge ab out the world When the search is resumed his

knowledge of the world determines the course of the search

Recall that an imp ortant assumption ab out the environment in whichsearch plans are

while f ound exhausted

do

if inter r upt

then

al ter nate

else

step

if found

then

win

else

lose

Figure Interrupted searchschema

executed is that the agent is the only source of change in the world Therefore even though

the intervening actions may drastically alter the world state eg if the agent set re to

the house hes b een searching through the agent can use knowledge of the eects of his

actions to up date his knowledge of the world This is the sense in whichanagent do es not

lose knowledge ab out the world

An agentmay plan for a searchtobeinterrupted using a dierentschema Figure

depicts a schema for an interruptible search plan whichtakes al ter nate actions when the

inter r upt condition holds and then resumes the plan

Abandoning a search

Cohen and Levesque CLprovide a markedly dierent approach to rational action than

researchers in the AI planning paradigm For them the imp ortant issues are committing

to intentions to act in the future and dropping those intentions when appropriate I take

their p oint that it may b e imp ortant to b e able to relativize a commitmenttoany arbitrary

condition and showhow to do that in search plans

Relativization similar to p ersistent relativized goals could b e formalized by adding

another condition to the existing conditions of a search plan sc hema Figure illustrates

a search plan with an alternative exit condition lab eled relative which when true p ermits

the agent to exit the search and p erform the steps here schematized as exit

Recursive planner invo cation

A generic plan for exploring an arbitrary search site is constructed by calling the planner

when the search plan schema is instantiated This generic plan is substituted for the step

while found exhausted r el ativ e

do

step

if f ound

then

win

else

if relative

then

exit

else

l ose

Figure Relativized searchschema

action in the schema For example the actions

begin

x sel ectsites

sites removex sites

openx

end

are substituted for step when forming the example search plan of Figure page

The initial state description for this recursiveinvo cation of the planner is an assumption

that the search ob ject is actually lo cated in the site to b e explored The goal state for the

recursiveinvo cation is that the agent has conrmed this assumption To the extent that

search sites require similar exploration the planner can plan for exploration of an arbitrary

site in the search space and leave management of the assumptions one approach to deter

mining which sp ecic site will b e explored to the plan execution engine Actions prop osed

by this recursiveinvo cation of the planner must resp ect the nonrep etition prop erty of the

search plan

Calling the planner again is motivated by the p otential that site exploration may require

a complex plan p erhaps even a nested search plan For a given container in a search

it may b e necessary to remove something from the top of the container b efore it can b e

op ened

Planning for a search

This section has develop ed an approach for constructing search plans when the need to do so

is recognized An iterativecontrol structure is assumed as part of the schemainstantiation

construction technique

The mo dications to a planning system I describ e showhow to incorp orate iteration

into a plan in a principled way This approachmay generalize to principled intro duction

of iteration for dierent purp oses but I am only interested in the principled intro duction

of iteration for the purp oses of representing a search

The planning pro cess must also determine an order which will b e used at execution time

to select the next site to explore Section describ ed desirable prop erties of orderings on

the sites in the search space Just howsuch an ordering is chosen has yet to b e determined

Because it has an impact on the eciency of the resulting search it is necessary research

to complete my thesis

Chapter

Plan execution

Description of execution of a search plan

To illustrate the execution of a search plan consider the previous example of an agent

searching for an urn in a collection of p ossibly nested containers The search plan for

this task is shown in Figure page Initially the agent do es not see the urn

cSeeinur n c now and there is some unexplored search site Bempty sites now

Thus the search plan directs the agent to pro ceed with the search That is to say the

op erational semantics of the search plan sp ecies rst checking the condition and then exe

cuting the action if the condition holds Part of the condition is expressed as a description

of the agents p erceptions This description is checked against input from the p erceptual

system of the agent The other part of the condition for the while lo op is a prop ertyof

an internal data structure It is imp ortant that only conditions whichcanbeveried by

examining the internal state of the agent ie p erceptions knowledge or b eliefs app ear

in while statements

The next action in the plan calls for the agent to select some container whichhe

has not yet visited and op en it The sel ect op eration cho oses from the available sites in

the remaining searchspace The next assignment statement up dates the sites variable

to reect this selection Then the selected site is examined For the agenttotake this

action he must b elieve that he can achieve p erception of the ob ject b y the action openx

However his knowledge is only of the search space which has less information than will

supp ort that conclusion To conclude that he can nd the ob ject by this plan he must

assume that the urn is in the selected container This assumption is added to the agents

b elief space and b elief revision is p erformed if necessary to maintain consistency of b eliefs

The action open has deterministic eects on the world the container is now op ened

and nondeterministic p erception eects on the agent After this action the agentei

ther p erceives the urn or do es not The rst case calls for the successful termination of

the search plan The second case intro duces a contradiction in the agents b elief space

since Seeinur n c now implies Binur n c now See axioms for the p erception

op erator Section A

The only remaining case of the while lo op condition is when the search space has b een

completely explored In such a situation the variable sites will b e empty In this case

the plan calls for the unsuccessful termination of the search The while lo op terminates

and the succeeding conditional is evaluated Since the urn is not seen the lose actions are

selected

Evaluating conditional expressions

Conditional expressions are restricted to b e prop erties of the agents internal state ie

p erceptions knowledge or b eliefs This ensures that the agent will always b e able to

decide whichbranch of the conditional to take at run time

Selecting obstaclesite to search

For the second comp onent of action selection a search strategy amounts to deciding on the

order in which dierent sites in the search space will b e visited From the p ersp ectiveof

b elief revision this ordering establishes an order on sets of b eliefs which will b e considered

In the pro cess of nonmonotonic revision of the agents b eliefs a consistent extension of the

agents knowledge will b e selected in suchaway as to include at least one of the assumptions

ab out the site containing the search ob ject This idea of expressing control information

through justications recorded for the purp ose of b elief revision is due to Doyle Doy

In the previous sections I have describ ed physical search in terms of the actions an

agent executes to explore a search space Another way of viewing it is in terms of the b elief

revision pro cess Having a search space in mind can b e explained as b elievin g a disjunctive

statement ab out each of the p ossible lo cations of the ob ject For each iteration some part

of the search space disjunct usually just one lo cation is assumed to b e actually true

Then the agent acts so as to reveal the truth of that assumption If as a result of that

action the ob ject is discovered the search is successfully concluded Otherwise the world

and agents p erceptions are in conict with its exp ectations and b elief revision must

take place

In general b elief revision is dicult but the structure of search plans helps to en

capsulate a set of assumptions for whichIbelieve revision is much easier For conducting

searches I identify twodisjoint sets of relevant assumptions

Internal assumptions over which the searchexertscontrol

Supp orting assumptions on which the ability to successfully search is based

Assumptions ab out the lo cation of the search ob ject are easily revised by selecting other

lo cations in the remaining search space Revising supp orting assumptions which underlie

the search itself may require abandoning the search This class of assumptions contain

things like the agents ability to recognize the search ob ject and b eliefs ab out the eects

of actions used to explore the search space Other assumptions may b e revised indep en

dently from the search since they are irrelevant to carrying out the search I am currently

implementing a b elief maintenance system to attempt to exploit this classication of as

sumptions

Kean and Tsiknis KT show that approaches based on computing prime implicants have at least

exp onential worst case complexity

Executing a searchplan

This section has illustrated the interaction b etween an execution engine for a search plan

and its environment The search plan execution engine will make use of a b elief revision

system to control the order in which sites are selected for exploration

Chapter

Thesis

Review of current state

The problem of planning for and carrying out a search has b een presented Diculties

using existing formalisms for planning and reasoning ab out conducting searches were dis

cussed Analysis of those diculties suggested a novel logic whichwas presented A simple

approach to constructing plans using this formalism was describ ed Reasoning ab out the

plans shows how they can eectively plan for goals which can not b e planned for by other

planners Finally a b elief revision system was discussed that supp orts ecient execution

of these plans

A theorem prover for the mo dal logic has b een implemented Public domain ATMS

co de can b e used to supp ort recording dep endencies b etween mo dal formulas Earlier

versions of plan execution engines for recursive plans have b een implemented but without

mechanisms to manage agent b eliefs and memory

System Description

The system for planning and conducting searches consists of three functional comp onents

and three databases Input to the system is a goal to achieve Output from the system is

searchbehavior A rstlevel decomp osition of this system is depicted in Figure

The three functional comp onents include a planner MODIFIED PLANNER which

constructs plans a plan executive EXECUTIVE which generates b ehavior based on the

plan world state and agent state and a nonmonotonic revision comp onentATMS which

maintains consistency among the agents b eliefs

The three databases include world state agent knowledge and agent assumptions

The agents internal state is a combination of his knowledge and assumptions An agents

p erceptions also part of his internal state are part of his knowledge An agents b eliefs

are the combination of his assumptions and his knowledge his entire internal state A

tained and this is the environment in which the b ehav database of the world state is main

iors are executed Part of the world state database is available to the agent as knowledge

This knowledge partition increases monotonically over time An collection of the b eliefs of

the agentismaintained separate from but consistent with the agents knowledge ASSUMPTIONS

ATMS

GOAL

PLAN BEHAVIOR

MODIFIED PLANNER EXECUTIVE ACTION LIBRARY

KNOWLEDGE WORLD

Figure System Diagram

Planning system The planning comp onent is mo died from an existing hierarchical

planner There are two mo dications which are required First the feasibility of an action

is determined by the agents state instead of the world state by PLAN EVALUATION

Second hierarchical plan expansion is mo died to include expanding an abstract search

into a more detailed searchplanby SCHEMA INSTANTIATION Figure depicts this

organization of the functional comp onent for planning

Feasibility of actions is evaluated by comparing their preconditions to the agents knowl

edge and b eliefs Actions maybeknown to b e p ossible known imp ossible or have unknown

feasibility This last category where the agentdoesnotknow the feasibility of an action

may b e b elieved to b e feasible or not or the agentmayhave no b eliefs as to the feasibility

of the action

Expanding an abstract search plan is accomplished byschema instantiation and recur

siveinvo cation of the planner

Belief revision and plan execution Nonmonotonic b elief revision is managed byan

assumptionbased truthmaintenance system ATMS Minimally this system records as

sumptions and contradictions and selects among alternative consistent extensions of the

assumptions

Plan execution is managed bycombining an existing plan execution engine with a

programming language interpreter This interpreter has access to the world state and the

agent state Only agent state may b e used to determine the value of conditional expressions

in the plan World state is used to determine the eects of b ehavior and those eects then BELIEFS

GOAL SCHEMA INSTANTIATION PLAN EVALUATION

PLAN ACTION LIBRARY EXISTING PLANNER

KNOWLEDGE

Figure Planner System Diagram

b ecome part of the world state

Remaining op en issues

Whether the complexity of the search planning problem requires the use of an ATMS

for b elief revision needs to b e more fully explored Alternatives to managing disjunctive

contexts derived from the search space will b e examined including reasoning by cases as

in a theorem prover

How the truth maintenance system if used will b e integrated in the search plan

execution is yet to b e completely sp ecied The options range from using it only to

maintain consistency of b eliefs to using it to control selection of the next searchsiteby

enforcing sequential selection of assumptions In addition various criteria for selecting

among alternative next sites to explore and alternative actions for exploring the selected

site will b e examined

A ma jor topic of remaining research is determining the ordering on sites in the search

space What information ab out the search sites or the ob ject determines which ordering

will b e used and when that ordering is applied to determine which site to explore are

questions which the dissertation must answer The timing of site ordering and selection

relative to other tasks namely selecting an action to explore a site must b e determined

Time p ermitting the claim that this representation can b e easily converted to an

indexical representation will b e demonstrated in the dissertation

Beyond these technical details the approachtaken to search in this prop osal is claimed

to generalize to other kinds of search The dissertation will demonstrate this generality

by exploring the unmo died mechanism to other domains such as the search problems

sketched on page

Remaining software development

Implementing the planning and execution engines for search plans requires mo difying an

existing planner and plan executing engine according to the design describ ed in this pro

p osal An initial attempt at implementing limited search plans used the ItPlans planner

To the extent p ossible I will continue to use ItPlans in the AnimNL pro ject WBB

as the underlying planner and plan execution engine which is mo died to construct and

execute search plans

Prop osed work

To supp ort my thesis claims I will construct search plans byschema instantiation with

ob ject descriptions search space constraints and appropriate actions for exploring the

search space I will build an execution engine for these search plans to supp ort claims for

improved execution

For the thesis I will explore the interaction of a b elief revision system with a system for

constructing and conducting search plans I may use an existing b elief revision system for

this purp ose or implement a new one if necessary Other ways of managing the selection

of alternative sites to explore will also b e examined

The entire pro cess of selecting sites to explore and selecting actions to explore those

sites will b e a fo cus of my remaining research Information ab out what sites are likely

to contain the ob ject will b e exploited by the planner to attempt to construct ecient

searches

To supp ort my prop osed architecture I will examine the inherent computational com

plexity of the search planning problem and the complexity of the system architecture I

will compare the eciency of my system to a system based on a replanning architecture

which pro duces only sequential plans

I will also clarify what inference is done at plan construction time and what if any

inference must b e done at plan execution time

Conclusion

This prop osal has identied the changes to the blo cks world assumptions which naturally

give rise to the search planning problem A solution to planning for searches has b een

prop osed which will p ermit agents to act eectively when faced with a need to nd some

ob ject

App endix A

Representation for search plans

A Syntax rst order mo dal logic

Individual variables fv v v g

 

 

Functions ff f f f g

 

 

Predicates fp p p p g

 

n

Terms T v j f t t

i n

i

for t T

i

n

Prop ositions P p t t

n

i

jP j P P

i i j

P jv

j i

j P j P

j j

Know

Perceive

j P

j

Believe

for t T and P P P

i i j

Note that the action construction op erations of the extended situation calculus are

merely functions and atomic action descriptions are ary functions constants No new

syntactic devices are required for the situation calculus

Abbreviations I adopt the standard denitions for the remaining logical op erators

disjunction material conditional and biconditional Existential quantication

is the dual of universal quantication xix Similarly the diamond op erator

is the dual of the b ox op erator
i

R R

I use the following common single letter abbreviations for temp oral and epistemic mo dal

op erators

K

Know

B

Believe

In addition I will use See as an abbreviation for

P erceive

A Semantics p ossible worlds

A mo del for this logic is an tuple

M W Believe Know PerceiveIDFR

where W is a set of worlds Believe Know and Perceive are relations on W I is a set

of individuals D is a mapping from elements w of W to subsets of individual s for that

world D F and R interpret functions and predicates

w

My logic has a p ossible worlds semantics with a dierentworld for eachwayanagent

considers the world mightbe

There are three epistemic accessibility relations The Know accessibility relation is an

equivalence relation Perceive is reexive and contains the Know relation KnowPerceive

e relation BelieveKnow Similarly Know contains the Believ

A Situation calculus

The situation calculus is a rst order logic Individuals may denote situations and actions

A function do is used to denote the situation which results from doing an action in a

situation

Action op erators are provided which express control ow among several actions A

sequencing op erator constructs a comp ound action from two actions

s doa bs s dob doa s

 

A conditional op erator constructs a conditional branch action

if enow

C C B B

then

C C B B

C C B B

a

s es doa s do

C C B B

  

C C B B

A A

else

b

if enow

C C B B

then

C C B B

C C B B

es dob s s do a

C C B B

  

C C B B

A A

else

b

An iteration op erator constructs lo ops

while enow while enow

B B C C B B C C

es do do s do a do s

A A A A

  

a a

while enow

C C B B

do s s es do

A A

  

a

As o dd as this direction of containmentmay seem for the accessibilityrelations it restricts mo dels to

those which supp ort the axioms given later

Note that now in the expressions of the conditional and iterative plans is interpreted as

referring to the situation in which that part of the plan is executed s in these examples



A Inference mo dal axioms

The inference system is presented as a Hilb ertstyle calculus In addition to the inference

rule of mo dus p onens there is an inference rule of necessitation for each mo dal op erator

The schematic presentation of this rule for the schematic mo dal op erator for an arbitrary

accessibility relation R is

R

Schema Mo dus Ponens

Schema Necessitation rule

implies that

R

Pro ofs ab out the eects of executing nitely many iterations of a search plan requires

some form of induction Section discusses alternatives for the structure over which

induction is p erformed The two options considered there are the structure of time and

the structure of the search space



The remainder of the inference system is a collection of axioms and axiom schema

Following pages discuss the various axiom collections in more detail

A Inferring prop erties of situations

Actions in the situation calculus have preconditions and eects A predicate P oss of an

action a and a situation s holds when the preconditions for that actions are satised in

that situation This is expressed as

Possa s

For example a precondition for the action of op ening a container c is that the container

is closed

cl osedc s P ossopencs

Eects of actions are describ ed using successor state axioms The idea of using successor

state axioms is not a new one and their particular form in this prop osal is similar to that

describ ed in Rei Successor state axioms are used to infer for any action and any

prop erty of a situation whether or not that prop erty holds of the situation following that

action An example of a successor state axiom is shown for the prop erty of container c

b eing op en

a cl osec openc s P ossa s openc doa s a openc

This can b e glossed as stating that container c is op en after doing some action a provided

that action was either an open action or it was not a cl ose action and c was op en b efore

aProviding that action a was p ossible at the time Note that openc is the action of

op ening container c and openc s is the prop ertyofcontainer c in situation s

The iteration and conditional action op erators require expressions to b e evaluated as

either true or false Each of these expressions corresp onds to a formula in the situation

calculus The expression evaluates to true in a situation when the corresp onding situation

calculus formula holds of the situation For example the conditional expression

if inb c now

C B C B

then

C B C B

C B C B

do s first

C B C B

C B C B

A A

else

second

Lowercase Greek symb ols like and
are used in schemata to stand for arbitrary formulas

will result in the agent taking action first if inb c s holds or action second if inb c s

holds

A Static Epistemic axioms

Static epistemic

Knowledge The S axioms are validated by the mo dal op erator K

K K K

K

K KK

K KK

Epistemic logic Since Hintikka Hin mo dal op erators have b een used to represent

epistemic attitudes of knowing that and b elieving that Frequently the S or S

axioms are selected to axiomatize the knowledge op erator The Know accessibility relation

ys a subset of those is reexive under b oth these schemes so the formulas known are alwa

actually true An intuitiveinterpretation of the formula Kisthatinevery p ossible world

which the agent currently considers a valid alternative to the way the world actually is

is true Another way to see this is that all the Knowrelated worlds are indistinguishabl e

to the agentgiven what they know

Common to this approach to formalizing knowledge is an extension to knowing the

identity of ob jects represented as quantication into a mo dal context Thus knowing the

identity of some ob ject uniquely describable as a is represented as

Schema

xKx a

Perception Since the search plans I am concerned with involve the physical world

knowledge of successful search completion is typically obtained through the agents p er

ceptions Search is not successful if the agent deduces the lo cation of the ob ject based on

having op ened all the containers but the last one since the assumption that the ob ject

is in one of them may prove false Since containers may b e nested last is really last

currently visible Search is only successful when the agent sees the ob ject I adopt from

Davis Dav the principle that p erceived facts are known formalized as

See K

Belief

K B

B B

Belief is managed outside the system of logic presented here since it must b e nonmono

tonically revised see Section Beliefs are constrained to contain what is known and

b e consistent Consistency is expressed bytheD mo dal axiom numb ered ab ove

A Dynamic Epistemic axioms

Dynamic epistemic

def

can s Kdo s

The denition of the mo dal op erator can is given in Section where reasoning ab out

the agents abilities to act eectively is discussed

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