Abstract not found

In this paper we outline a theoretical framework for the combination of decision procedures for constraint satisfiability. We describe a general combination method which, given a procedure that decides constraint satisfiability with respect to a constraint theory T1 and one that decides constraint satisfiability with respect to a constraint theory T2, produces a procedure that (semi-)decides constraint satisfiability with respect to the union of T1 and T2. We provide a number of model-theoretic conditions on the constraint language and the component constraint theories for the method to be sound and complete, with special emphasis on the case in which the signatures of the component theories are non-disjoint. We also describe some general classes of theories to which our combination results apply, and relate our approach to some of the existing combination methods in the field.

Motivated by the problem of query answering over multiple structured commonsense theories, we exploit graph-based techniques to improve the efficiency of theorem proving for structured theories. Theories are organized into subtheories that are minimally connected by the literals they share. We present message-passing algorithms that reason over these theories using consequence finding, specializing our algorithms for the case of first-order resolution, and for batch and concurrent theorem proving. We provide an algorithm that restricts the interaction between subtheories by exploiting the polarity of literals. We attempt to minimize the reasoning within each individual partition by exploiting existing algorithms for focused incremental and general consequence finding. Finally, we propose an algorithm that compiles each subtheory into one in a reduced sublanguage. We have proven the soundness and completeness of all of these algorithms. 1

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In this paper we compare three approaches to polynomial time decidability for uniform word problems for quasivarieties. Two of the approaches, by Evans and Burris, respectively, are semantical, referring to certain embeddability and axiomatizability properties. The third approach is more proof-theoretic in nature, inspired by McAllester's concept of local inference. We define two closely related notions of locality for equational Horn theories and show that both the criteria by Evans and Burris lie in between these two concepts. In particular, the variant we call stable locality will be shown to subsume both Evans' and Burris' method.

In two earlier papers, the concept of "free amalgamation" has been introduced as a general methodology for interweaving solution structures for symbolic constraints, and it was shown how constraint solvers for two components can be lifted to a constraint solver for the free amalgam. Here we discuss a second general way for combining solution domains, called rational amalgamation. In praxis, rational amalgamation seems to be the preferred combination principle if the two solution structures to be combined are "rational" or "non-wellfounded" domains. It represents, e.g., the way how rational trees and rational lists are interwoven in the solution domain of Prolog III, and a variant has been used by W. Rounds for combining feature structures and hereditarily finite non-wellfounded sets. We show that rational amalgamation is a general combination principle, applicable to a large class of structures. As in the case of free amalgamation, constraint solvers for two component structures can be combined to a constraint solver for their rational amalgam. From this algorithmic point of view, rational amalgamation seems to be interesting since the combination technique for rational amalgamation avoids one source of non-determinism that is needed in the corresponding scheme for free amalgamation.

this paper. On the one hand, dening a semantics for the combined system may depend on methods and results from formal logic and universal algebra. On the other hand, an ecient combination of the actual constraint solvers often requires the possibility of communication and cooperation between the solvers.

Constraint Logic Programming languages on Finite Domains, CLP(FD), provide a declarative framework for Artificial Intelligence problems. However, in many real life cases, domains are not known and must be acquired or computed.

In recent years, techniques that had been developed for the combination of unification algorithms for equational theories were extended to combining constraint solvers. These techniques inherited an old deficit that was already present in the combination of equational theories which makes them rather unsuitable for practical use: The underlying combination algorithms are highly non-deterministic. This paper is concerned with the practical problem of how to optimise the combination method of Baader and Schulz. We present an optimisation method, called the deductive method, which uses specific algorithms for the components to reach certain decisions deterministically. We also give a strategy how to select an order of non-deterministic decisions. Run time tests of our implementation indicate that the optimised combination method yields combined decision procedures that are efficient enough to be used in practice.

In this paper we present a new method for combining ground decision procedures for rst-order theories over non-disjoint signatures.