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Modeling Belief in Dynamic Systems, Part II: Revision and Update

Journal of Artificial Intelligence Research

The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper (Friedman & Halpern, 1997), we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the principles underlying them. In particular, it shows that Katsuno and Mendelzon's notion of belief update (Katsuno & Mendelzon, 1991a) depends on several strong assumptions that may limit its applicability in artificial intelligence. Finally, our analysis allow us to identify a notion of minimal change that underlies a broad range of belief change operations including revision and update.


Cooperation between Top-Down and Bottom-Up Theorem Provers

arXiv.org Artificial Intelligence

Top-down and bottom-up theorem proving approaches each have specific advantages and disadvantages. Bottom-up provers profit from strong redundancy control but suffer from the lack of goal-orientation, whereas top-down provers are goal-oriented but often have weak calculi when their proof lengths are considered. In order to integrate both approaches, we try to achieve cooperation between a top-down and a bottom-up prover in two different ways: The first technique aims at supporting a bottom-up with a top-down prover. A top-down prover generates subgoal clauses, they are then processed by a bottom-up prover. The second technique deals with the use of bottom-up generated lemmas in a top-down prover. We apply our concept to the areas of model elimination and superposition. We discuss the ability of our techniques to shorten proofs as well as to reorder the search space in an appropriate manner. Furthermore, in order to identify subgoal clauses and lemmas which are actually relevant for the proof task, we develop methods for a relevancy-based filtering. Experiments with the provers SETHEO and SPASS performed in the problem library TPTP reveal the high potential of our cooperation approaches.


Achieving compositionality of the stable model semantics for Smodels programs

arXiv.org Artificial Intelligence

In this paper, a Gaifman-Shapiro-style module architecture is tailored to the case of Smodels programs under the stable model semantics. The composition of Smodels program modules is suitably limited by module conditions which ensure the compatibility of the module system with stable models. Hence the semantics of an entire Smodels program depends directly on stable models assigned to its modules. This result is formalized as a module theorem which truly strengthens Lifschitz and Turner's splitting-set theorem for the class of Smodels programs. To streamline generalizations in the future, the module theorem is first proved for normal programs and then extended to cover Smodels programs using a translation from the latter class of programs to the former class. Moreover, the respective notion of module-level equivalence, namely modular equivalence, is shown to be a proper congruence relation: it is preserved under substitutions of modules that are modularly equivalent. Principles for program decomposition are also addressed. The strongly connected components of the respective dependency graph can be exploited in order to extract a module structure when there is no explicit a priori knowledge about the modules of a program. The paper includes a practical demonstration of tools that have been developed for automated (de)composition of Smodels programs. To appear in Theory and Practice of Logic Programming.


A Temporal Description Logic for Reasoning about Actions and Plans

Journal of Artificial Intelligence Research

A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed by temporally relating actions and world states. The temporal languages are members of the family of Description Logics, which are characterized by high expressivity combined with good computational properties. The subsumption problem for a class of temporal Description Logics is investigated and sound and complete decision procedures are given. The basic language TL-F is considered first: it is the composition of a temporal logic TL -- able to express interval temporal networks -- together with the non-temporal logic F -- a Feature Description Logic. It is proven that subsumption in this language is an NP-complete problem. Then it is shown how to reason with the more expressive languages TLU-FU and TL-ALCF. The former adds disjunction both at the temporal and non-temporal sides of the language, the latter extends the non-temporal side with set-valued features (i.e., roles) and a propositionally complete language.


The Divide-and-Conquer Subgoal-Ordering Algorithm for Speeding up Logic Inference

Journal of Artificial Intelligence Research

It is common to view programs as a combination of logic and control: the logic part defines what the program must do, the control part -- how to do it. The Logic Programming paradigm was developed with the intention of separating the logic from the control. Recently, extensive research has been conducted on automatic generation of control for logic programs. Only a few of these works considered the issue of automatic generation of control for improving the efficiency of logic programs. In this paper we present a novel algorithm for automatic finding of lowest-cost subgoal orderings. The algorithm works using the divide-and-conquer strategy. The given set of subgoals is partitioned into smaller sets, based on co-occurrence of free variables. The subsets are ordered recursively and merged, yielding a provably optimal order. We experimentally demonstrate the utility of the algorithm by testing it in several domains, and discuss the possibilities of its cooperation with other existing methods.