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Positive Unit Hyperresolution Tableaux and Their Application to Minimal Model Generation
 Journal of Automated Reasoning
, 2000
"... . Minimal Herbrand models of sets of firstorder 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 bec ..."
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. Minimal Herbrand models of sets of firstorder 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 firstorder 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 depthfirst relying on a complement splitting expansion rule and on a form of backtracking involving constraints. A Prolog implementation, named MMSATCHMO, of this procedure is given and its performance on ben...
A Basis for Model Computation in Free Data Types
 IN CADE17, WORKSHOP ON MODEL COMPUTATION  PRINCIPLES, ALGORITHMNS, APPLICATIONS
, 2000
"... Abstract data types are specified by some equality logic under the assumption of term generatedness. They are called `free', if terms, built only by constructors, are semantically unique. This paper presents a calculus, intended to search for models of free data type specifications. A seman ..."
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Abstract data types are specified by some equality logic under the assumption of term generatedness. They are called `free', if terms, built only by constructors, are semantically unique. This paper presents a calculus, intended to search for models of free data type specifications. A semantical view is discussed, where the uniqueness of constructor terms is `hard wired'. This suggests an explicit reasoning about interpretations instead of performing real equality reasoning. The rules, which depend on signature, constructor definitions and axioms, are formulated as range restricted clauses. This allows to `perform' the calculus simply by calling a model generation prover, in particular the MGTP system. This approach
Tableaux + Constraints
, 2003
"... There is an increasing number of publications in which the analytic tableaux calculus is combined with technology based on constraint solving. Although the details, as well as the purpose of these combinations vary widely, the results are invariably referred to as "constraint tableaux" ..."
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There is an increasing number of publications in which the analytic tableaux calculus is combined with technology based on constraint solving. Although the details, as well as the purpose of these combinations vary widely, the results are invariably referred to as "constraint tableaux" or sometimes "constrained tableaux". We review some of the combinations and propose a more di#erentiated nomenclature.
Integrating Reactive and Reflective Reasoning by Generating Rational Models
, 1998
"... . We propose to model integrated reflective and reactive reasoning by massively parallel nonmonotonic model generation. To this end, a finite representation of models of normal logic programs is given, which is adapted to the interpretations typically produced by the meaning function TP . By simulat ..."
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. We propose to model integrated reflective and reactive reasoning by massively parallel nonmonotonic model generation. To this end, a finite representation of models of normal logic programs is given, which is adapted to the interpretations typically produced by the meaning function TP . By simulating TP on top of this representation, only finite representations of (possibly infinite) interpretations are processed. These representations are significantly shorter than by using related approaches. Our work overcomes typical problems of model generation and results in a tractable method, and, thereby, enables the integrated reflective and reactive reasoning we propose. 1 Introduction Intelligent behaviour covers both, reflex actions and wellconsidered actions. Reflex actions are triggered by fast reactive reasoning, which usually is defined to take only constant time (wrt the underlying database), and, hence, can solve only problems of restricted classes. For solving problems beyond s...