Efficient Knowledge Base Management in DCSP

DCSP (Distributed Constraint Satisfaction Problem) has been a very important research area in AI (Artificial Intelligence). There are many application problems in distributed AI that can be formalized as DSCPs. With the increasing complexity and problem size of the application problems in AI, the required storage place in searching and the average searching time are increasing too. Thus, to use a limited storage place efficiently in solving DCSP becomes a very important problem, and it can help to reduce searching time as well. This paper provides an efficient knowledge base management approach based on general usage of hyper-resolution-rule in consistence algorithm. The approach minimizes the increasing of the knowledge base by eliminate sufficient constraint and false nogood. These eliminations do not change the completeness of the original knowledge base increased. The proofs are given as well. The example shows that this approach decrease both the new nogoods generated and the knowledge base greatly. Thus it decreases the required storage place and simplify the searching process.Comment: 11 page

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

Working with ARMs: Complexity Results on Atomic Representations of Herbrand Models

AbstractAn atomic representation of a Herbrand model (ARM) is a finite set of (not necessarily ground) atoms over a given Herbrand universe. Each ARM represents a possibly infinite Herbrand interpretation. This concept has emerged independently in different branches of computer science as a natural and useful generalization of the concept of finite Herbrand interpretation. It was shown that several recursively decidable problems on finite Herbrand models (or interpretations) remain decidable on ARMs.The following problems are essential when working with ARMs: Deciding the equivalence of two ARMs, deciding subsumption between ARMs, and evaluating clauses over ARMs. These problems were shown to be decidable, but their computational complexity has remained obscure so far. The previously published decision algorithms require exponential space. In this paper, we prove that all mentioned problems are coNP-complete

Resolution-based decision procedures for subclasses of first-order logic

This thesis studies decidable fragments of first-order logic which are relevant to the field of nonclassical logic and knowledge representation. We show that refinements of resolution based on suitable liftable orderings provide decision procedures for the subclasses E+, K, and DK of first-order logic. By the use of semantics-based translation methods we can embed the description logic ALB and extensions of the basic modal logic K into fragments of first-order logic. We describe various decision procedures based on ordering refinements and selection functions for these fragments and show that a polynomial simulation of tableaux-based decision procedures for these logics is possible. In the final part of the thesis we develop a benchmark suite and perform an empirical analysis of various modal theorem provers.Diese Arbeit untersucht entscheidbare Fragmente der Logik erster Stufe, die mit nicht-klassischen Logiken und Wissensrepräsentationsformalismen im Zusammenhang stehen. Wir zeigen, daß Entscheidungsverfahren für die Teilklassen E+, K, und DK der Logik erster Stufe unter Verwendung von Resolution eingeschränkt durch geeignete liftbare Ordnungen realisiert werden können. Durch Anwendung von semantikbasierten Übersetzungsverfahren lassen sich die Beschreibungslogik ALB und Erweiterungen der Basismodallogik K in Teilklassen der Logik erster Stufe einbetten. Wir stellen eine Reihe von Entscheidungsverfahren auf der Basis von Resolution eingeschränkt durch liftbare Ordnungen und Selektionsfunktionen für diese Logiken vor und zeigen, daß eine polynomielle Simulation von tableaux-basierten Entscheidungsverfahren für diese Logiken möglich ist. Im abschließenden Teil der Arbeit führen wir eine empirische Untersuchung der Performanz verschiedener modallogischer Theorembeweiser durch