Robert A. Kowalski

A logic-based calculus of events

We outline an approach for reasoning about events and time within a logic programming framework. The notion of event is taken to be more primitive than that of time and both are represented explicitly by means of Horn clauses augmented with negation by failure.The main intended applications are the updating of databases and narrative understanding. In contrast with conventional databases which assume that updates are made in the same order as the corresponding events occur in the real world, the explicit treatment of events allows us to deal with updates which provide new information about the past.Default reasoning on the basis of incomplete information is obtained as a consequence of using negation by failure. Default conclusions are automatically withdrawn if the addition of new information renders them inconsistent.Because events are differentiated from times, we can represent events with unknown times, as well as events which are partially ordered and concurrent.

The Semantics of Predicate Logic as a Programming Language

Sentences in first-order predicate logic can be usefully interpreted as programs. In this paper the operational and fixpoint semantics of predicate logic programs are defined, and the connections with the proof theory and model theory of logic are investigated. It is concluded that operational semantics is a part of proof theory and that fixpoint semantics is a special case of model-theoretic semantics.

An abstract, argumentation-theoretic approach to default reasoning

Abstract We present an abstract framework for default reasoning, which includes Theorist, default logic, logic programming, autoepistemic logic, non-monotonic modal logics, and certain instances of circumscription as special cases. The framework can be understood as a generalisation of Theorist. The generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions. An assumption can be defeated (or “attacked”) if its “contrary” can be proved, possibly with the aid of other conflicting assumptions. We show that, given such a framework, the standard semantics of most logics for default reasoning can be understood as sanctioning a set of assumptions, as an extension of a given theory, if and only if the set of assumptions is conflict-free (in the sense that it does not attack itself) and it attacks every assumption not in the set. We propose a more liberal, argumentation-theoretic semantics, based upon the notion of admissible extension in logic programming. We regard a set of assumptions, in general, as admissible if and only if it is conflict-free and defends itself (by attacking) every set of assumptions which attacks it. We identify conditions for the existence of extensions and for the equivalence of different semantics.

Algorithm = logic + control

The notion that computation = controlled deduction was first proposed by Pay Hayes [19] and more recently by Bibel [2] and Vaughn-Pratt [31]. A similar thesis that database systems should be regarded as consisting of a relational component, which defines the logic of the data, and a control component, which stores and retrieves it, has been successfully argued by Codd [10]. Hewitts argument [20] for the programming language PLANNER, though generally regarded as an argument against logic, can also be regarded as an argument for the thesis that algorithms be regarded as consisting of both logic and control components. In this paper we shall explore some of the useful consequences of that thesis.

The British Nationality Act as a logic program

The formalization of legislation and the development of computer systems to assist with legal problem solving provide a rich domain for developing and testing artificial-intelligence technology.

Linear resolution with selection function

Linear resolution with selection function (SL.resolution) is a restricted form of linear resolution. The main restriction is e~ected by a selection function which chooses fro:~ each clause a sit, gle literal to be resolved upon in that clause. This and other restrictions are adapted to linear resolution from Lovelands model elimination. We show that SL-resolution achieves a substantial reduction in the generation of redundant and irrelevant derivations and does so without significantly increasing the complexity o f simplest proofs. We base our argument for the increased efficiency of SL-resolution upon precise calculation of these quantities. A more far reaching advantage of SL-resolution is its suitability fo .~. ristic search. In particular, classification trees, subgoals, lemmas, and and/~./ search tret n all be used to increase the efficiency of flndino refutations. These considerations alone sug. r. :t the superiority of SL-resolution to theorem-proving procedures constructed solely for their I1euristie attraction. From comparison with other theorem-proving methods, we conjectur~ that best proof procedures for first order logic will be obtained by further elaboration of ~ ~.-resolution.

A Proof Procedure Using Connection Graphs

Various deficiencies of resolution systems are investigated and a new theorem-proving system designed to remedy those deficiencms is presented The system is notable for eliminating re- dundancies present in SL-resolutlon, for incorporating preprocessing procedures, for liberahzing the order in which subgoals can be activated, for incorporating multidirectmnal searches, and for giving immediate access to pairs of clauses which resolve Examples of how the new system copes with the defic2encies of other theorem-proving systems are chosen from the areas of predicate logic program- ming and language parsing. The paper emphasizes the historical development of the new system, beginning as a supplement to SL-resolution in the form of classificatmn trees and incorporating an analogue of the Waltz algorithm for picture Interpretation The paper ends with a discussion of the opportunities for using look-ahead to guide the search for proofs

Dialectic proof procedures for assumption-based, admissible argumentation

We present a family of dialectic proof procedures for the admissibility semantics of assumption-based argumentation. These proof procedures are defined for any conventional logic formulated as a collection of inference rules and show how any such logic can be extended to a dialectic argumentation system.The proof procedures find a set of assumptions, to defend a given belief, by starting from an initial set of assumptions that supports an argument for the belief and adding defending assumptions incrementally to counter-attack all attacks.The proof procedures share the same notion of winning strategy for a dispute and differ only in the search strategy they use for finding it. The novelty of our approach lies mainly in its use of backward reasoning to construct arguments and potential arguments, and the fact that the proponent and opponent can attack one another before an argument is completed. The definition of winning strategy can be implemented directly as a non-deterministic program, whose search strategy implements the search for defences.

The IFF proof procedure for abductive logic programming

Abstract In this paper, we outline a proof procedure which combines reasoning with defined predicates together with reasoning with undefined, abducible , predicates. Defined predicates are defined in if-and-only-if form. Abducible predicates are constrained by means of integrity constraints. Given an initial query, the task of the proof procedure is to construct a definition of the abducible predicates and a substitution for the variables in the query, such that both the resulting instance of the query and the integrity constraints are implied by the extended set of definitions. The iff proof procedure can be regarded as a hybrid of the proof procedure of Console et al. and the SLDNFA procedure of Denecker and De Schreye. It consists of a number of inference rules which, starting from the initial query, rewrite a formula into an equivalent formula. These rules are: 1) unfolding , which replaces an atom by its definition; 2) propagation , which resolves an atom with an implication; 3) splitting , which uses distributivity to represent a goal as a disjunction of conjunctions; 4) case analysis for an equality X = t in the conditions of an implication, which considers the two cases X = t and X ≠ t ; 5) factoring of two abducible atoms, which considers the two cases, where the atoms are identical and where they are different, 6) rewrite rules for equality , which simulate the unification algorithm; and 7) logical simplifications , such as A ∧ false ↔ false . The proof procedure is both sound and complete relative to the three-valued completion semantics. These soundness and completeness results improve previous results obtained for other proof procedures.

From logic programming towards multi-agent systems

In this paper we present an extension of logic programming (LP) that is suitable not only for the “rational” component of a single agent but also for the “reactive” component and that can encompass multi‐agent systems. We modify an earlier abductive proof procedure and embed it within an agent cycle. The proof procedure incorporates abduction, definitions and integrity constraints within a dynamic environment, where changes can be observed as inputs. The definitions allow rational planning behaviour and the integrity constraints allow reactive, condition‐action type behaviour. The agent cycle provides a resource‐bounded mechanism that allows the agent’s thinking to be interrupted for the agent to record and assimilate observations as input and execute actions as output, before resuming further thinking. We argue that these extensions of LP, accommodating multi‐theories embedded in a shared environment, provide the necessary multi‐agent functionality. We argue also that our work extends Shoham’s Agent0 and the BDI architecture.