The purpose of this paper is to show that logic provides a convenient formalism for studying classical database problems. There are two main parts to the paper, devoted respectively to conventional databases and deductive databases. In the first part, we focus on query languages, integrity modeling and maintenance, query optimization, and data

In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and first-order logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is two-fold. First, we are concerned with how to reason e#ectively with multiple knowledge bases that have overlap in content. Second, we are concerned with improving the e#ciency of reasoning over a set of logical axioms by partitioning the set with respect to some detectable structure, and reasoning over individual partitions. Many of the reasoning procedures we present are based on the idea of passing messages between partitions. We present algorithms for reasoning using forward message-passing and using backward message-passing with partitions of logical axioms. Associated with each partition is a reasoning procedure. We characterize a class of reasoning procedures that ensures completeness and soundness of our message-passing ...

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ABSTRACT. The resolution principle, an automatic inference technique, is studied as a possible decision procedure for certain classes of first-order formulas It is shown that most previous resolution strategies do not decide satlsfiabihty even for "simple " solvable classes Two new resolution procedures are described and are shown to be complete (1 e semidecislon procedures) In the general case and, m addition, to be decision procedures for successively wider classes of first-order formulas These include many previously studied solvable classes The proofs that a complete resolutmn procedure will always halt (without producing the empty clause) when apphed to satisfiable formulas in certain classes provide new, and in some cases more enlightening, demonstrations of the solvablhty of these classes A technique for constructing a model for a formula shown satisfiable in this way is also described

A general theory of deduction systems is presented. The theory is illustrated with deduction systems based on the resolution calculus, in particular with clause graphs. This theory distinguishes four constituents of a deduction system: ffl the logic, which establishes a notion of semantic entailment; ffl the calculus, whose rules of inference provide the syntactic counterpart of entailment; ffl the logical state transition system, which determines the representation of formulae or sets of formulae together with their interrelationships, and also may allow additional operations reducing the search space; ffl the control, which comprises the criteria used to choose the most promising from among all applicable inference steps. Much of the standard material on resolution is presented in this framework. For the last two levels many alternatives are discussed. Appropriately adjusted notions of soundness, completeness, confluence, and Noetherianness are introduced in order to characterize...

Proof procedures are an essential part of logic applied to artificial intelligence tasks, and form the basis for logic programming languages. As such, many of the chapters throughout this handbook utilize, or study, proof procedures. The study of proof procedures that are useful in artificial intelligence would require a large book so we focus on proof procedures that relate to logic programming. We begin with the resolution procedures that influenced the definition of SLD-resolution, the procedure upon which Prolog is built. Starting with the general resolution procedure we move through linear resolution to a very restricted linear resolution, SLresolution, which actually is not a resolution restriction, but a variant using an augmented logical form. (SL-resolution actually is a derivative of the Model Elimination procedure, which was developed independently of resolution.) We then consider logic programming itself, reviewing SLD-resolution and then describing a general criterion for ...

xiii Declaration, xiv The Author, xv Acknowledgements, xv 1 Chapter 1 -

The Subsumption Theorem is the following completeness result for resolution: if # is a set of clauses and C is a clause, then # logically implies C i# C is a tautology, or there exists a clause D which subsumes C, and which can be derived from # by some form of resolution. Di#erentversions of this theorem exist, depending on the kind of resolution we use. It provides a more #direct" form of completeness than the better known refutationcompleteness, which often makes the Subsumption Theorem better suited for theoretical research. In this paper weinvestigate for which forms of resolution the theorem holds, and for which it does not. We collect results earlier obtained by others, and contribute some results of our own. The main results of the paper are as follows. For #unconstrained" resolution, the Subsumption Theorem holds, and is equivalent to the refutation-completeness: the one can be proved from the other. The same is true for linear resolution. For input resolution, t...

. We present a new transformation method by which a given Horn theory is transformed in such a way that resolution derivations can be carried out which are both linear (in the sense of Prologs SLD-resolution) and unit-resulting (i.e. the resolvents are unit clauses). This is not trivial since although both strategies alone are complete, their na ve combination is not. Completeness is recovered by our method through a completion procedure in the spirit of Knuth-Bendix completion, however with different ordering criteria. A powerful redundancy criterion helps to find a finite system quite often. The transformed theory can be used in combination with linear calculi such as e.g. (theory) model elimination to yield sound, complete and efficient calculi for full first order clause logic over the given Horn theory. As an example application, our method discovers a generalization of the well-known linear paramodulation calculus for the combined theory of equality and strict orderings. The met...

ABSTRACT. Paramodulation can be used in conjunction with resolution for proving theoreIm in first-order logic with equality. Unit, input, and linear refutations using paramodulation and resolution are defined for theories with equality. It is proved that (a) if a set S of clauses has an input refutation, then S together with its unit factors and functionally reflexive axioms has a unit refutation; and (b) if C is a clause in an E-unsatisfiable set S of clauses including {x = x} and the functionally reflexive axioms and if (S- {C} ) is E-satisfiable, then S has a linear re-futation with top clause C. ("E-unsatisfiable " is called "R-unsatisfiable " by some authors.) The refutation completeness theorem proved by Wos and Robinson for paramodulation with set of support is a corollary of our result (b). Our result (b) provides a link between heuristk programs and theorem-proving programs for first-order theories with equality.