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19
Logic and databases: a deductive approach
 ACM Computing Surveys
, 1984
"... 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 ..."
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Cited by 143 (2 self)
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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
Strategies for Temporal Resolution
, 1995
"... Verifying that a temporal logic specification satisfies a temporal property requires some form of theorem proving. However, although proof procedures exist for such logics, many are either unsuitable for automatic implementation or only deal with small fragments of the logic. In this thesis the algo ..."
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Cited by 93 (42 self)
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Verifying that a temporal logic specification satisfies a temporal property requires some form of theorem proving. However, although proof procedures exist for such logics, many are either unsuitable for automatic implementation or only deal with small fragments of the logic. In this thesis the algorithms for, and strategies to guide, a fully automated temporal resolution theorem prover are given, proved correct and evaluated. An approach to applying resolution, a proof method for classical logics suited to mechanisation, to temporal logics has been developed by Fisher. The method involves translation to a normal form, classical style resolution within states and temporal resolution over states. It has only one temporal resolution rule and is therefore particularly suitable as the basis of an automated temporal resolution theorem prover. As the application of the temporal resolution rule is the most costly part of the method, involving search amongst graphs, different algorithms on w...
PartitionBased Logical Reasoning for FirstOrder and Propositional Theories
 Artificial Intelligence
, 2000
"... In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and firstorder logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is twofold. First, we are concerned with ..."
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Cited by 52 (8 self)
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In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and firstorder logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is twofold. 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 messagepassing and using backward messagepassing 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 messagepassing ...
Resolution strategies as decision procedures
 J. ACM
, 1976
"... ABSTRACT. The resolution principle, an automatic inference technique, is studied as a possible decision procedure for certain classes of firstorder formulas It is shown that most previous resolution strategies do not decide satlsfiabihty even for "simple " solvable classes Two new resolut ..."
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Cited by 30 (0 self)
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ABSTRACT. The resolution principle, an automatic inference technique, is studied as a possible decision procedure for certain classes of firstorder 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 firstorder 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
Deduction Systems Based on Resolution
, 1991
"... 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 entailmen ..."
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Cited by 19 (0 self)
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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 for Logic Programming
, 1994
"... 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 intell ..."
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Cited by 4 (0 self)
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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 SLDresolution, 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. (SLresolution actually is a derivative of the Model Elimination procedure, which was developed independently of resolution.) We then consider logic programming itself, reviewing SLDresolution and then describing a general criterion for ...
Emergent Tendencies in MultiAgentbased Simulations using Constraintbased Methods to Effect Practical Proofs over Finite Subsets of Simulation Outcomes
, 2001
"... xiii Declaration, xiv The Author, xv Acknowledgements, xv 1 Chapter 1  ..."
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Cited by 3 (3 self)
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xiii Declaration, xiv The Author, xv Acknowledgements, xv 1 Chapter 1 
The Subsumption Theorem for Several Forms of Resolution
 In Proc. CSN95
, 1996
"... 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 th ..."
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Cited by 3 (1 self)
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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 refutationcompleteness: the one can be proved from the other. The same is true for linear resolution. For input resolution, t...
Linear and UnitResulting Refutations for Horn Theories
 Journal of Automated Reasoning
, 1995
"... . 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 SLDresolution) and unitresulting (i.e. the resolvents are unit clauses). This is not trivial since altho ..."
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Cited by 2 (0 self)
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. 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 SLDresolution) and unitresulting (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 KnuthBendix 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 wellknown linear paramodulation calculus for the combined theory of equality and strict orderings. The met...