From: AAAI-93 Proceedings. Copyright © 1993, AAAI (www.aaai.org). All rights reserved. ame Proble Richard B. Scherl* and Hector J. Levesquet Department of Computer Science University of Toronto Toronto, Ontario Canada M5S 3A6 email: [email protected] [email protected] Abstract knowledge-producing actions, that is, actions whose ef- fects are to change a state of knowledge. This paper proposes a solution to the frame prob- A standard example of a knowledge-producing ac- lem for knowledge-producing actions. An example tion is that of reading a number on a piece of pa- of a knowledge-producing action is a sense opera- per. Consider the problem of dialing the combination tion performed by a robot to determine whether of a safe [McCarthy and Hayes, 1969; Moore, 1980; or not there is an object of a particular shape Moore, 19851. If an agent is at the same place as the within its grasp. The work is an extension of safe, and knows the combination of the safe, then he Reiter’s solution to the frame problem for ordi- can open the safe by performing the action of dialing nary actions and Moore’s work on knowledge and that combination. If an agent is at the same place action. The properties of our specification are as both the safe and a piece of paper and he knows that knowledge-producing actions do not affect that the combination of the safe is written on the pa, fluents other than the knowledge fluent, and ac- per, he can open the safe by first reading the piece of tions that are not knowledge-producing only affect paper, and then dialing that combination. The effect the knowledge fluent as appropriate. In addition, of the read action, then, is to change the knowledge memory emerges as a side-effect: if something is state of the agent, typically to satisfy the prerequisite known in a certain situation, it remains known of a later action. Another example of a knowledge- at successor situations, unless something relevant producing action is performing an experiment to de- has changed. Also, it will be shown that a form termine whether or not a solution is an acid [Moore, of regression examined by Reiter for reducing rea- 19851. Still other examples are a sensing operation soning about future situations to reasoning about performed by a robot to determine the shapes of ob- the initial situation now also applies to knowledge- jects within its grasp [Lesperance and Levesque, 1990; producing actions. Lesperance, 19911 and the execution of UNIX com- mands such as Is [Etzioni et al., 19921. Introduction To incorporate knowledge-producing actions like The situation calculus provides a formalism for rea- these into the situation calculus, it is necessary to soning about actions and their effects on the world. treat knowledge as a fluent that can be affected by ac- Axioms are used to specify the prerequisites of actions tions. This is precisely the approach taken by Moore as well as their effects, that is, the fluents that they [1980]. What is new here is that the knowledge flu- change. In general, it is also necessary to provide frame ent and knowledge-producing actions are handled in axioms to specify which fluents remain unchanged by a way that avoids the frame problem: we will be the actions. In the worst case this might require an able to prove as a consequence of our specification axiom for every combination of action and fluent. Re- that knowledge-producing actions do not affect flu- cently, Reiter [1991] (generalizing the work of Haas ents other than the knowledge fluent, and that ac- [1987], Schubert [1990] and Pednault [1989]) has given tions that are not knowledge-producing only affect the a set of conditions under which the explicit specifica- knowledge fluent as appropriate. In addition, we will tion of frame axioms can be avoided. In this paper, show that memory emerges as a side-effect: if some- we extend his solution to the frame problem to cover thing is known in a certain situation, it remains known at successor situations, unless something relevant has *National Sciences and Engineering Research Council of changed. We will also show that a form of regression Canada International Postdoctoral Fellow examined by Reiter for reducing reasoning about fu- ‘Fellow of the Canadian Institute for Advanced ture situations to reasoning about the initial situation Research now also applies to knowledge-producing actions. This Representationfor Actions& Motion 689 has the desirable effect of allowing us to reduce reason- in 3 and 4. ing about knowledge and action to reasoning about General Positive Effect Axiom for Fluent F knowledge in the initial situation, where techniques Poss(a, s) A r,‘(u,s) 4 F(do(a,s)) such as those discussed in [Frisch and Scherl, 1991; (3) Scherl, 19921 can be used. Finally, we show that if General Negative Effect Axiom for Fluent F certain useful properties of knowledge (such as posi- Poss(a, s) A y; (a, s) - lF(dO(U, s)) (4 tive introspection) are specified to hold in the initial state, they will continue to hold automatically at all Here 7: (a, s) is a formula describing under what condi- successor situations. tions doing the action a in situation s leads the fluent In the next section, we briefly review the situation F to become true in the successor situation do(a, s) calculus and Reiter’s solution to the frame problem. In and similarly y~(u, s) is a formula describing the con- the following section, we introduce an epistemic fluent ditions under which performing action a in situation into the situation calculus as an accessibilit relation s results in the fluent F becoming false in situation over situations, as done by Moore[1980; 1985 s . Our so- do(u, s). lution to the frame problem for knowledge producing For example, 5 is a positive effect axiom for the fluent actions, based on this epistemic fluent, is developed Broken. and illustrated over the next four sections. In the next Poss(u, s) A [(u = drop(y) A Fragile(y)) to the last section, we consider regression for the situ- V((3b)u = explode(b) A Nexto(b, y, s))] (5) ation calculus with knowledge-producing actions. Fi- + Broken (y, do(u, s)) nally, future work is discussed in the last section. Sentence 6 is a negative effect axiom for broken. The Situation Calculus and the Frame Poss(u, s) A a = repair(y) Problem -+ lBroken( y, do(u, s)) (6) The situation calculus (following the presentation in It is also necessary to add the frame axioms that [Reiter, 19911) is a first-order language for represent- specify when fluents- remain unchanged. The frame ing dynamically changing worlds in which all of the problem arises because the number of these frame ax- changes are the result of named actions performed by ioms in the general case is 2 x A x ,T, where A is the some agent. Terms are used to represent states of the number of actions and F is the number of fluents. world-i.e. situations. If CYis an action and s a situ- The solution to the frame problem [Reiter, 1991; ation, the result of performing cv in s is represented Pednault, 1989; Schubert, 19901 rests on a complete- by do(cr,s). The constant Se is used to denote the ness assumption. This assumption is that axioms 3 initial situationl. Relations whose truth values vary and 4 characterize all the conditions under which ac- from situation to situation, called jhents, are denoted tion a can lead to R becoming - true (respectively, false) by a predicate symbol taking a situation term as the in the successor situation. Therefore, if action a is pas- last argument. For example, Broken (x, s) means that sible and R’s truth value changes from false to true as object 2 is broken in situation s. a result of doing a, then yi(u,s) must be true and It is assumed that the axiomatizer has provided for similarly for a change from true to false. Addition- ally, unique name axioms are added for actions and situations. Reiter[l991] s h ows how to derive a set of successor Act ion Precondition Axiom state axioms of the form given in 7 from the axioms (positive effect, negative effect and unique name) and Poss(a(Z), s) E 7rra(Z, s) (1) the completeness assumption. Successor State Axiom An action precondition axiom for the action drop is given below. Poss(u, s) - [F(do(a, s)) z r,‘(% 4 v (F(s) A 1YF(a, s))l (7) Poss(drop(x), s) E HoZding(x, s) (2) Similar successor state axioms may be written for func- Furthermore, the axiomatizer has provided for each tional fluents. A successor state -axiom is needed for fluent F, two general eflect axioms of the form given each fluent F, and an action precondition axiom is needed for each action a. The unique name axioms 1 By convention, single lower case letters (i.e. roman), need not be explicitly represented as their effects can possibly with subscripts or superscripts, are used to rep- be compiled. Therefore only F+d axioms are needed. resent variables, strings of letters beginning with a capital From 5 and 6 the following successor state axiom for letter are used for predicate symbols, strings of lower case Broken is obtained. letters are used for function symbols, and possibly sub- scripted strings of letters beginning with a capital letter Poss(u, s) - [Broken(y, do(u, s)) z are used for constants.