From: AAAI Technical Report FS-93-01. Compilation copyright © 1993, AAAI (www.aaai.org). All rights reserved. Transaction Logic: Unifying Declarative and Procedural Knowledge - Extended Abstract - Anthonyt J. Bonner* and Michael Kifer 1 Introduction that check the context and then prescribe different se- quences of actions, depending on the outcome [26]. Like- This paper presents AI applications of the recently pro- wise, the classic planning system STRIPS[6] is based on posed Transaction Logic (abbr., 7-7z) [2]. Transaction procedurally-defined actions, which STRIPS combines Logic is a novel formalism that accounts in a clean into plans that achieve larger goals. Section 6.1 shows and declarative fashion for the phenomenon of updat- that STRIPSis representable in q-n and that its infer- ing first-order knowledge bases, most notably, databases ence rules are sound. Even though STRIPS was given and logic programs. Transaction Logic has a natural formal semantics in [16], this was not done within a log- model theory and a sound-and-complete proof theory. ical formalism (and, unlike [16], STRIPSis just one of Unlike many other logics, Tn allows users to program the many applications of Tn). transactions that modify the state of a knowledge base. At first glance, there might seem to be many candi- This is possible because, like classical logic, Tn has dates for a logic of procedural knowledge, since many a "Horn" version which has both a procedural and a logics reason about updates or about the related phe- declarative semantics, as well as an efficient SLD-style nomena of time and action. We have found, however, proof procedure. As a result, Tn is a unifying, logical that none of them is suitable for representing and using formalism for specifying both declarative and procedu- procedural knowledge. First, most logics of time or ac- ral knowledge. Furthermore, for a wide range of prac- tion are hypothetical: Instead of executing procedures, tical problems, the frame problem [18] is not an issue they reason about them, or about what would happen for "/-n. This is because Tn performs real updates on if certain actions were to take place. For instance, some materialized databases, much as procedural languages systems can infer that if action A precedes B, and B pre- like Pascal do. A key contribution of ~-n is capturing cedes C, then A must precede C. Others can infer that these procedural updates in a logical framework with if a student took history 400, then he could graduate. an efficient proof theory. A full development of the Such systems were intended to be observers of action, proof theory, a discussion of the frame problem, and not participants. They are therefore useful for reason- applications to database systems can be found in [2, ing about alternatives, or for analyzing programs and 3]. This paper presents the model theory of 7-~¢, and plans; but they are not very useful for defining proce- then focuses on applications of Tn to problems in AI, dures that actually accomplish state changes being rea- especially planning, temporal reasoning, constraint sat- soned about. In 7-~¢, actions can be carried out hypo- isfaction, hypothetical and counterfactual reasoning, and thetically or they can be executed and have a permanent the representation and use of procedural knowledge. effect on the knowledge base, depending on one’s desire. The importance of procedural knowledge has been In this way procedural knowledge can be used as well as extensively argued in the AI literature (see e.g., [8]). represented and reasoned about. For instance, the well-known SHRDLUprogram [26] is The second problem with many action logics is that largely based on procedural knowledge. In fact, Wino- it is awkward,if not impossible to assign names to com- grad argues in [26] that procedural knowledgeis inherent posite actions. Such logics were designed for reasoning in automated natural language understanding. For ex- about sequences of actions, not for programming them. ample, the meaningof "the" is a collection of procedures As such, they are inappropriate for defining actions since a namingfacility is needed for representing even very ba- *Department of Computer Science, University of sic procedural knowledge;i.e., specifying actions without Toronto, Toronto, Ontario MbS 1A4, Canada; bon- a naming facility is akin to programming without sub- [email protected]. Work supported in part by an Oper- ating Grant from the Natural Sciences and Engineering Re- routines. This defeats the purpose of using logic in the search Council of Canadaand by a Connaught Grant from first place, which is to free the user from the drudgery the University of Toronto. of low-level details. tDepartment of Computer Science, SUNY-StonyBrook, Third, many logics make a clear distinction between Stony Brook, NY11794, U.S.A.; [email protected]. Work queries and updates. However,this distinction is blurred supported in part by NSFgrant CCR-9102159. in object-oriented systems, where both queries and up- 17 dates are special cases of a single idea: method invo- is best for all purposes [2]. Thus, rather than commit cation. In such systems, an update can be thought of Tn to a fixed set of elementary transitions, we have cho- as a query with side effects. We would like to model sen to treat the elementary transitions as a parameter this behavior and thereby provide a logical foundation of Tze. Each set of elementary transitions thus gives for object-oriented databases. Tn achieves this by al- rise to a different version of the logic. To achieve this, lowing every logical formula to have not only a truth elementary transitions are defined by logical axioms. value, but also a "side effect" on the database. In this Elementary transitions are formulas of the form way, one can account for the behavior of object-oriented (¢, ¢)u, where ¢, ¢ are (sets of) closed first-order databases--something that most formalisms do not do. mulas and u is an atomic formula, called the name of In combination with F-logic [13], the structural aspects the transition. Intuitively, this formula says that u is of object-oriented systems can be accounted for as well. an update that transforms database ¢ into database ¢. The system that comes closest in spirit to T7¢ is Pro- For instance, if the atoms ins:q(t) and del:q(t) stand for log. Unfortunately, updates in Prolog are non-logical the insertion and deletion of the atom q(t), then they and, as a result, state-changing procedures are often the would be defined by an enumerable set of elementary most awkward of Prolog programs, and the most diffi- transitions consisting of the following formulas: cult to understand, debug, and maintain. Semantically Tn is closely related to Process Logic [11], but is differ- (D, D + {q(t)}) ins:q(t) (D, D - {q(t)}) del:q(t) ent from it in several important ways detailed in [2]. for every relational database, D.x Enumerable sets of Due to space limitation, many topics are merely elementary transitions are called transition bases. In sketched in this paper. Details appear in [2]. practice, these formulas would not be materialized all at once, but would be generated on demand by an algo- 2 Syntax rithm. We refer to [2] for a more detailed discussion of The syntax of Tn distinguishes two kinds of formulas: transition bases. As seen from the syntax, q-~e does not strictly distin- transaction formulas and elementary transitions. The guish between predicates that query the knowledge base former define composite transactions, and the latter de- and predicates that update it. As in classical logic, ev- fine elementary updates. ery predicate has a truth value; but in addition, every Transaction formulas, which extend first-order for- predicate may also have a side effect, by changing the mulas with a new connective, ®, called serial con- junction, are used to define transactions and formulate state of the knowledge base. This uniformity of repre- sentation is important in modeling methods (interface queries. Transaction formulas are defined as follows. An atomic transaction formula is an expression of the form functions encapsulated inside classes) in object-oriented databases, where one generally does not distinguish be- p(tl,...,t,~), where p E P is a predicate symbol, and tween information-retrieving and state-changing meth- tl,...,t,, are terms (as in classical predicate calculus). ods. Nevertheless, if desired, 7-Te can make such a dis- If ¢ and ¢ are transaction formulas, then so are ¢ V ¢, tinction by using different sorts of predicates, one for ¢^¢, ¢®¢, -,¢, (VX)¢, and (3X)¢, whereXisa updates and one for queries. variable. Thus, the expression a(X) V --,[b(X) c(X, Y) For instance, it is good programmingpractice to re- is a transaction formula. Intuitively, ¢®¢ means, "Do ¢, then do ¢." A dual connective, serial disjunction, is also serve a special set of predicates for certain basic updates. This paper uses just such a convention: for each predi- useful (Section 6.2): ¢ ~ ¢ is equivalent to --,(-~¢ ® -1¢). cate symbol p, we use another predicate symbol, ins:p, Serial conjunction provides a basic way to sequence to represent insertions of tuples into p. Likewise, we rep- transactions, where ¢ @¢ means "do ¢, then do ¢." resent deletions from p by the predicate del:p. Thus the In contrast, classical conjunction, "A", constrains the formula ins:p(a) ® ins:p(b) ~, ins:p(c) represents an up- non-determinism of a transaction. For instance, ¢ A ¢ dating transaction that inserts p(a) into the database, means, "do ¢ in a way compatible with doing ¢." This then p(b), and then p(c). use of "A" is further discussed in Section 6.2. Apart from this, "A" also has the traditional role of forming Blocks-World Example logic programs: in Tn, as in classical logic, any finite 3 set of rules is equivalent to a conjunction of all the rules Before presenting the semantics, we illustrate the syn- in the set.