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.


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.


A remark on higher order RUE-resolution with EXTRUE

arXiv.org Artificial Intelligence

We show that a prominent counterexample for the completeness of first order RUE-resolution does not apply to the higher order RUE-resolution approach EXTRUE.


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.


On Reachability, Relevance, and Resolution in the Planning as Satisfiability Approach

Journal of Artificial Intelligence Research

In recent years, there is a growing awareness of the importance of reachability and relevance-based pruning techniques for planning, but little work specifically targets these techniques. In this paper, we compare the ability of two classes of algorithms to propagate and discover reachability and relevance constraints in classical planning problems. The first class of algorithms operates on SAT encoded planning problems obtained using the linear and Graphplan encoding schemes. It applies unit-propagation and more general resolution steps (involving larger clauses) to these plan encodings. The second class operates at the plan level and contains two families of pruning algorithms: Reachable-k and Relevant-k. Reachable-k provides a coherent description of a number of existing forward pruning techniques used in numerous algorithms, while Relevant-k captures different grades of backward pruning. Our results shed light on the ability of different plan-encoding schemes to propagate information forward and backward and on the relative merit of plan-level and SAT-level pruning methods.