Super Logic Programs

The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper, we specialize it to a class of theories called `super logic programs'. We argue that these programs form a natural generalization of standard logic programs. In particular, they allow disjunctions and default negation of arbibrary positive objective formulas. Our main results are two new and powerful characterizations of the static semant ics of these programs, one syntactic, and one model-theoretic. The syntactic fixed point characterization is much simpler than the fixed point construction of the static semantics for arbitrary AELB theories. The model-theoretic characterization via Kripke models allows one to construct finite representations of the inherently infinite static expansions. Both characterizations can be used as the basis of algorithms for query answering under the static semantics. We describe a query-answering interpreter for super programs which we developed based on the model-theoretic characterization and which is available on the web.Comment: 47 pages, revised version of the paper submitted 10/200

Combining Enumeration and Deductive Techniques in order to Increase the Class of Constructible Infinite Models

AbstractA new method for building infinite models for first-order formulae is presented. The method combines enumeration techniques with existing deductive (in a broad sense) ones. Its soundness and completeness w.r.t. the class of models that can be represented by equational constraints are proven. This shows that the use of enumeration techniques strictly increases the power of existing methods for building Herbrand models that are not complete in this sense. Some strategies are proposed to reduce the search space. We give examples and show how to use this approach for building interactively a model of a formula introduced by Goldfarb in his proof of the undecidability of the Gödel class with identity. This formula is satisfiable but has no finite model

Positive Unit Hyperresolution Tableaux and Their Application to Minimal Model Generation

Minimal Herbrand models of sets of first-order clauses are useful in several areas of computer science, e.g. automated theorem proving, program verification, logic programming, databases, and artificial intelligence. In most cases, the conventional model generation algorithms are inappropriate because they generate nonminimal Herbrand models and can be inefficient. This article describes an approach for generating the minimal Herbrand models of sets of first-order clauses. The approach builds upon positive unit hyperresolution (PUHR) tableaux, that are in general smaller than conventional tableaux. PUHR tableaux formalize the approach initially introduced with the theorem prover SATCHMO. Two minimal model generation procedures are described. The first one expands PUHR tableaux depth-first relying on a complement splitting expansion rule and on a form of backtracking involving constraints. A Prolog implementation, named MM-SATCHMO, of this procedure is given and its performance on benchmark suites is reported. The second minimal model generation procedure performs a breadth-first, constrained expansion of PUHR (complement) tableaux. Both procedures are optimal in the sense that each minimal model is constructed only once, and the construction of nonminimal models is interrupted as soon as possible. They are complete in the following sense The depth-first minimal model generation procedure computes all minimal Herbrand models of the considered clauses provided these models are all finite. The breadth-first minimal model generation procedure computes all finite minimal Herbrand models of the set of clauses under consideration. The proposed procedures are compared with related work in terms of both principles and performance on benchmark problems

Minimal Model Generation with Positive Unit Hyper-Resolution Tableaux

Herbrand models for clausal theories are useful in several areas of computer science. In most cases, however, the conventional model generation algorithms are inappropriate because they generate nonminimal Herbrand models and can be inefficient. This article describes a novel approach for generating minimal Herbrand models of clausal theories. The approach builds upon positive unit hyper-resolution (PUHR) tableaux, that are in general smaller than conventional tableaux. To generate only minimal Herbrand models, a complement splitting expansion rule and a specific search strategy are applied. The proposed procedure is optimal in the sense that each minimal model is generated only once, and nonminimal models are rejected before their complete construction. First measurements on an implementation point to the efficiency of the procedure

Minimal Model Generation with Positive Unit Hyper-Resolution Tableaux

. Herbrand models for clausal theories are useful in several areas of computer science. In most cases, however, the conventional model generation algorithms are inappropriate because they generate nonminimal Herbrand models and can be inefficient. This article describes a novel approach for generating minimal Herbrand models of clausal theories. The approach builds upon positive unit hyper-resolution (PUHR) tableaux, that are in general smaller than conventional tableaux. To generate only minimal Herbrand models, a complement splitting expansion rule and a specific search strategy are applied. The proposed procedure is optimal in the sense that each minimal model is generated only once, and nonminimal models are rejected before their complete construction. First measurements on an implementation point to its efficiency. 1 Introduction: Generating Herbrand models of clausal theories is useful in several areas of computer science. In automated theorem proving, models can assist in makin..