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27
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 ...
SCOTT: A ModelGuided Theorem Prover
 In Proceedings IJCAI93
, 1993
"... SCOTT (Semantically Constrained Otter) is a resolutionbased automatic theorem prover for first order logic. It is based on the high performance prover OTTER by W. McCune and also incorporates a model generator. This finds finite models which SCOTT is able to use in a variety of ways to direct ..."
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Cited by 32 (2 self)
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SCOTT (Semantically Constrained Otter) is a resolutionbased automatic theorem prover for first order logic. It is based on the high performance prover OTTER by W. McCune and also incorporates a model generator. This finds finite models which SCOTT is able to use in a variety of ways to direct its proof search. Clauses generated by the prover are in turn used as axioms of theories to be modelled. Thus prover and model generator inform each other dynamically. This paper describes the algorithm and some sample results. SCOTT (Semantically Constrained Otter) is a resolution based automatic theorem prover for first order logic. So much is hardly revolutionary. What is new in SCOTT is the way in which it blends traditional theorem proving methods, best seen as purely syntactic, with techniques for semantic investigation more usually associated with constraint satisfaction problems. Thus it bridges two aspects of the science of reasoning. It was made by marrying an existing high...
A Method for Building Models Automatically. Experiments with an extension of OTTER
 In Proceedings of CADE12
, 1994
"... . A previous work on Herbrand model construction is extended in two ways. The first extension increases the capabilities of the method, by extending one of its key rules. The second, more important one, defines a new method for simultaneous search of refutations and models for set of equational clau ..."
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Cited by 28 (14 self)
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. A previous work on Herbrand model construction is extended in two ways. The first extension increases the capabilities of the method, by extending one of its key rules. The second, more important one, defines a new method for simultaneous search of refutations and models for set of equational clauses. The essential properties of the new method are given. The main theoretical result of the paper is the characterization of conditions assuring that models can be built. Both methods (for equational and non equational clauses) have been implemented as an extension of OTTER. Several running examples are given, in particular a new automatic solution of the ternary algebra problem first solved by Winker. The examples emphasize the unified approach to model building allowed by the ideas underlying our method and the usefulness of using constrained clauses. Several problems open by the present work are the main lines of future work. 1 Introduction It is trivial to say that the use of models o...
Practical PartitionBased Theorem Proving for Large Knowledge Bases
, 2003
"... Query answering over commonsense knowledge bases typically employs a firstorder logic theorem prover. While firstorder inference is intractable in general, provers can often be handtuned to answer queries with reasonable performance in practice. ..."
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Cited by 26 (4 self)
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Query answering over commonsense knowledge bases typically employs a firstorder logic theorem prover. While firstorder inference is intractable in general, provers can often be handtuned to answer queries with reasonable performance in practice.
Ordered Semantic HyperLinking
, 1994
"... We propose a method for combining the clause linking theorem proving method with theorem proving methods based on orderings. This may be useful for incorporating termrewriting based approaches into clause linking. In this way, some of the propositional inefficiencies of orderingbased approaches ..."
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Cited by 24 (3 self)
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We propose a method for combining the clause linking theorem proving method with theorem proving methods based on orderings. This may be useful for incorporating termrewriting based approaches into clause linking. In this way, some of the propositional inefficiencies of orderingbased approaches may be overcome, while at the same time incorporating the advantages of ordering methods into clause linking. The combination also provides a natural way to combine resolution on nonground clauses, with the clause linking method, which is essentially a ground method. We describe the method, prove completeness, and show that the enumeration part of clause linking with semantics can be reduced to polynomial time in certain cases. We analyze the complexity of the proposed method, and also give some plausibility arguments concerning its expected performance. 1 Introduction There are at least two basic approaches to the study of automated deduction. One approach concentrates on solving...
The Search Efficiency of Theorem Proving Strategies: An Analytical Comparison
, 1994
"... We analyze the search efficiency of a number of common refutational theorem proving strategies for firstorder logic. Search efficiency is concerned with the total number of proofs and partial proofs generated, rather than with the sizes of the proofs. We show that most common strategies produce sea ..."
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Cited by 22 (3 self)
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We analyze the search efficiency of a number of common refutational theorem proving strategies for firstorder logic. Search efficiency is concerned with the total number of proofs and partial proofs generated, rather than with the sizes of the proofs. We show that most common strategies produce search spaces of exponential size even on simple sets of clauses, or else are not sensitive to the goal. However, clause linking, which uses a reduction to propositional calculus, has behavior that is more favorable in some respects, a property that it shares with methods that cache subgoals. A strategy which is of interest for termrewriting based theorem proving is the Aordering strategy, and we discuss it in some detail. We show some advantages of Aordering over other strategies, which may help to explain its efficiency in practice. We also point out some of its combinatorial inefficiencies, especially in relation to goalsensitivity and irrelevant clauses. In addition, SLDreso...
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...
Decision Procedures using Model Building techniques
 In Computer Science Logic (9th Int. Workshop CSL'95
, 1996
"... . Few year ago we have developed an Automated Deduction approach to model building. The method, called RAMC 1 looks simultaneously for inconsistencies and models for a given formula. The capabilities of RAMC have been extended both for model building and for unsatisfiability detection by including ..."
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Cited by 18 (4 self)
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. Few year ago we have developed an Automated Deduction approach to model building. The method, called RAMC 1 looks simultaneously for inconsistencies and models for a given formula. The capabilities of RAMC have been extended both for model building and for unsatisfiability detection by including in it the use of semantic strategies. In the present work we go further in this direction and define more general and powerful semantic rules. These rules are an extension of Slagle 's semantic resolution. The robustness of our approach is evidenced by proving that the method is also a decision procedure for a wide range of classes decidable by semantic resolution and in particular by hyperresolution. Moreover, the method builds models for satisfiable formulae in these classes, in particular, for satisfiable formulae that do not have any finite model. 1 Introduction Model building and model checking are extremely important topics in Logic and Computer Science. Few years ago we have develop...
Extending Semantic Resolution via Automated Model Building: applications
 In Proceeding of IJCAI'95
, 1995
"... An extension of semantic resolution is proposed. It is also an extension of the set of support as it can be considered as a particular case of semantic resolution. It is proved sound and refutationally complete. The extension is based on our former method for model building. The approach uses constr ..."
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Cited by 16 (9 self)
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An extension of semantic resolution is proposed. It is also an extension of the set of support as it can be considered as a particular case of semantic resolution. It is proved sound and refutationally complete. The extension is based on our former method for model building. The approach uses constrained clauses (or cclauses), i.e. couples [[clause : constraint]]. Two important new features are introduced with respect to semantic resolution. Firstly, the method builds its own (finite or infinite) models to guide the search or to stop it if the initial set of clauses is satisfiable. Secondly, instead of evaluating a clause in an interpretation it imposes conditions (coded in its rules) to force a cclause not to be evaluated to true in the interpretation it builds. The extension is limited in this paper to binary resolution but generalizing it to naryresolution should be straightforward. The prover implementing our method is an extension of OTTER and compares advantageously with it ...