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Controlled Integrations of the Cut Rule into Connection Tableau Calculi
"... In this paper techniques are developed and compared which increase the inferential power of tableau systems for classical firstorder logic. The mechanisms are formulated in the framework of connection tableaux, which is an amalgamation of the connection method and the tableau calculus, and a genera ..."
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Cited by 61 (3 self)
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In this paper techniques are developed and compared which increase the inferential power of tableau systems for classical firstorder logic. The mechanisms are formulated in the framework of connection tableaux, which is an amalgamation of the connection method and the tableau calculus, and a generalization of model elimination. Since connection tableau calculi are among the weakest proof systems with respect to proof compactness, and the (backward) cut rule is not suitable for the firstorder case, we study alternative methods for shortening proofs. The techniques we investigate are the folding up and the folding down operation. Folding up represents an efficient way of supporting the basic calculus, which is topdown oriented, with lemmata derived in a bottomup manner. It is shown that both techniques can also be viewed as controlled integrations of the cut rule. In order to remedy the additional redundancy imported into tableau proof procedures by the new inference rules, we develop and apply an extension of the regularity condition on tableaux and the mechanism of antilemmata which realizes a subsumption concept on tableaux. Using the framework of the theorem prover SETHEO, we have implemented three new proof procedures which overcome the deductive weakness of cutfree tableau systems. Experimental results demonstrate the superiority of the systems with folding up over the cutfree variant and the one with folding down.
Consolution as a Framework for Comparing Calculi
 JOURNAL OF SYMBOLIC COMPUTATION
, 1994
"... In this paper, stepwise and nearly stepwise simulation results for a number of firstorder proof calculi are presented and an overview is given that illustrates the relations between these calculi. For this purpose, we modify the consolution calculus in such a way that it can be instantiated to reso ..."
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Cited by 14 (10 self)
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In this paper, stepwise and nearly stepwise simulation results for a number of firstorder proof calculi are presented and an overview is given that illustrates the relations between these calculi. For this purpose, we modify the consolution calculus in such a way that it can be instantiated to resolution, tableaux model elimination, a connection method and Loveland's model elimination.
Autarky pruning in propositional model elimination reduces failure redundancy
 Journal of Automated Reasoning
, 1999
"... Goalsensitive resolution methods, such as Model Elimination, have been observed to have a higher degree of search redundancy than modelsearch methods, Therefore, resolution methods have not been seen in high performance propositional satis ability testers. A method to reduce search redundancy in g ..."
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Cited by 12 (3 self)
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Goalsensitive resolution methods, such as Model Elimination, have been observed to have a higher degree of search redundancy than modelsearch methods, Therefore, resolution methods have not been seen in high performance propositional satis ability testers. A method to reduce search redundancy in goalsensitive resolution methods is introduced. The idea at the heart of the method is to attempt to construct a refutation and a model simultaneously and incrementally, based on subsearch outcomes. The method exploits the concept of \autarky", which can be informally described as a \selfsu cient " model for some clauses, but which does not a ect the remaining clauses of the formula. Incorporating this method into Model Elimination leads to an algorithm called Modoc. Modoc is shown, both analytically and experimentally, to be faster than Model Elimination by an exponential factor. Modoc, unlike Model Elimination, is able to nd a model if it fails to nd a refutation, essentially by combining autarkies. Unlike the pruning strategies of most re nements of resolution, autarkyrelated pruning does not prune any successful refutation; it only prunes attempts that ultimately will be unsuccessful; consequently, it will not force the underlying Modoc search to nd an unnecessarily long refutation. To prove correctness and other properties, a game characterization of refutation search isintroduced, which demonstrates
A Propositional Theorem Prover to Solve Planning and Other Problems
 Annals of Mathematics and Artificial Intelligence
, 1998
"... Classical STRIPSstyle planning problems are formulated as theorems to be proven from a new point of view. The result for a refutationbased theorem prover may be a propositional formula that is to be proven unsatisfiable. This formula is identical to the formula that may be derived directly by vari ..."
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Cited by 10 (4 self)
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Classical STRIPSstyle planning problems are formulated as theorems to be proven from a new point of view. The result for a refutationbased theorem prover may be a propositional formula that is to be proven unsatisfiable. This formula is identical to the formula that may be derived directly by various "sat compilers", but the theoremproving view provides valuable additional information not in the formula: namely, the theorem to be proven. Traditional satisfiability methods, most of which are based on model search, are unable to exploit this additional information. However, a new algorithm, called "Modoc", is able to exploit this information and has achieved performance comparable or superior to the fastest known satisfiability methods, including stochastic search methods, on planning problems that have been reported by other researchers, as well as formulas derived from other applications. Unlike most theorem provers, Modoc performs well on both satisfiable and unsatisfiable formulas...
Lemma and Cut Strategies for Propositional Model Elimination
 Annals of Mathematics and Artificial Intelligence
, 1999
"... This paper describes new "lemma" and "cut" strategies that are efficient to apply in the setting of propositional Model Elimination. It builds upon the Cliteral strategy proposed by Shostak, and studied further by Letz, Mayr and Goller. Previous strategies for managing lemmas and Cliterals in Mode ..."
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Cited by 8 (5 self)
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This paper describes new "lemma" and "cut" strategies that are efficient to apply in the setting of propositional Model Elimination. It builds upon the Cliteral strategy proposed by Shostak, and studied further by Letz, Mayr and Goller. Previous strategies for managing lemmas and Cliterals in Model Elimination were oriented toward firstorder theorem proving. The original "cumulative" strategy remembers lemmas forever, and was found to be too inefficient. The previously reported Cliteral and unit lemma strategies, such as "strong regularity", forget them unnecessarily soon in the propositional domain. An intermediate strategy, called "quasipersistent" lemmas, is introduced. Supplementing this strategy, methods for "eager" lemmas, and two forms of controlled cut provide further efficiencies. The techniques have been incorporated into Modoc, which is an implementation of Model Elimination, extended with a new pruning method that is designed to eliminate certain refutation attempts th...
Simultaneous Construction of Refutations and Models for Propositional Formulas
, 1995
"... Methodology is developed to attempt to construct simultaneously either a refutation or a model for a propositional formula in conjunctive normal form. The method exploits the concept of "autarky", which was introduced by Monien and Speckenmeyer. Informally, an autarky is a "selfsufficient" model ..."
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Cited by 8 (5 self)
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Methodology is developed to attempt to construct simultaneously either a refutation or a model for a propositional formula in conjunctive normal form. The method exploits the concept of "autarky", which was introduced by Monien and Speckenmeyer. Informally, an autarky is a "selfsufficient" model for some clauses, but which does not affect the remaining clauses of the formula. Whereas their work was oriented toward finding a model, our method has as its primary goal to find a refutation in the style of model elimination. It also finds a model if it fails to find a refutation, essentially by combining autarkies. However, the autarkyrelated processing is integrated with the refutation search, and can greatly improve the efficiency of that search even when a refutation does exist. Unlike the pruning strategies of most refinements of resolution, autarkyrelated pruning does not prune any successful refutation; it only prunes attempts that ultimately will be unsuccessful; conseque...
The Partial Rehabilitation of Propositional Resolution
, 1996
"... Resolution has not been an effective tool for deciding satisfiability of propositional CNF formulas, due to explosion of the search space, particularly when the formula is satisfiable. A new pruning method is described, which is designed to eliminate certain refutation attempts that cannot succeed. ..."
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Cited by 6 (3 self)
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Resolution has not been an effective tool for deciding satisfiability of propositional CNF formulas, due to explosion of the search space, particularly when the formula is satisfiable. A new pruning method is described, which is designed to eliminate certain refutation attempts that cannot succeed. The method exploits the concept of "autarky", which was introduced by Monien and Speckenmeyer. New forms of lemma creation are also introduced, which eliminate the need to carry out refutation attempts that must succeed. The resulting algorithm, called "Modoc", is a modification of propositional model elimination. Informally, an autarky is a "selfsufficient" model for some clauses, but which does not affect the remaining clauses of the formula. Whereas Monien and Speckenmeyer's work was oriented toward finding a model, our method has as its primary goal to find a refutation in the style of model elimination. However, Modoc finds a model if it fails to find a refutation, essentially by combi...
Complexity analysis of propositional resolution with autarky pruning
 Discrete Applied Mathematics
, 2000
"... An algorithm called \Modoc", which has been introduced elsewhere, enhances propositional model elimination with autarky pruning, and other features. The model elimination method is based on linear resolution, and is designed to produce refutations of formulas in conjunctive normal form (CNF). I ..."
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Cited by 2 (2 self)
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An algorithm called \Modoc", which has been introduced elsewhere, enhances propositional model elimination with autarky pruning, and other features. The model elimination method is based on linear resolution, and is designed to produce refutations of formulas in conjunctive normal form (CNF). Informally, an autarky is a \selfsu cient " model for some clauses, but which does not a ect the remaining clauses of the formula. Modoc nds a model if it fails to nd a refutation, essentially by combining autarkies. Although the original motivation for autarky pruning was to extract a model when the refutation attempt failed, practical experience has shown that it also greatly increases the performance, by reducing the amount of search redundancy. This paper presents a worstcase analysis of Modoc as a function of the number of propositional variables in the formula. The analysis sheds light on why autarky pruning improves the performance, compared to \standard " model elimination. A worstcase analysis of the original algorithm of Davis, Putnam, Loveland and Logemann (DPLL) is also presented. The Modoc analysis yields a worstcase upper bound that is not as strong as the best known upper bound for modelsearching satis ability methods, on general propositional CNF. However, it is the rst time a nontrivial upper bound on nonHorn formulas has been shown for any resolutionbased refutation procedure.
Editor Logic and Semantic Networks
"... An extended form of semantic network is defined, which can be regarded as a syntactic variant of the clausal form of logic. By virtue of its relationship with logic, the extended semantic network is provided with a precise semantics, inference rules, and a procedural interpretation. On the other han ..."
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An extended form of semantic network is defined, which can be regarded as a syntactic variant of the clausal form of logic. By virtue of its relationship with logic, the extended semantic network is provided with a precise semantics, inference rules, and a procedural interpretation. On the other hand, by regarding semantic networks as an abstract data structure for the representation of clauses, we provide a theoremprover with a potentially useful indexing scheme and pathfollowing strategy for guiding the search for a proof. Key Words and Phrases: logic, semantic networks, theoremproving, indexing, resolution, deduction, logic programming