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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 65 (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.
Parallel cooperative propositional theorem proving
 Annals of Mathematics and Artificial Intelligence
, 1998
"... A parallel satis ability testing algorithm called Parallel Modoc is presented. Parallel Modoc is based on Modoc, which is based on propositional Model Elimination with an added capability to prune away certain branches that cannot lead to a successful subrefutation. The pruning information is encod ..."
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Cited by 13 (3 self)
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A parallel satis ability testing algorithm called Parallel Modoc is presented. Parallel Modoc is based on Modoc, which is based on propositional Model Elimination with an added capability to prune away certain branches that cannot lead to a successful subrefutation. The pruning information is encoded in a partial truth assignment called an autarky. Parallel Modoc executes multiple instances of Modoc as separate processes and allows processes to cooperate by sharing lemmas and autarkies as they are found. When a Modoc process nds a new autarky or a new lemma, it makes the information available to other Modoc processes via a \blackboard&quot;. Combining autarkies generally is not straightforward because two autarkies found by two separate processes may have con icting assignments. The paper presents an algorithm to combine two arbitrary autarkies to form a larger autarky. Experimental results show that for many of the formulas, Parallel Modoc achieves speedup greater than the number of processors. Formulas that could not be solved in an hour by Modoc were often solved by Parallel Modoc in the order of minutes, and in some cases, in seconds.
A Heterogeneous Parallel Deduction System
 In Proc. FGCS'92 Workshop W3
, 1992
"... This paper describes the architecture, implementation and performance, of a heterogeneous parallel deduction system (HPDS). The HPDS uses multiple deduction components, each of which attempts to find a refutation of the same input set, but using different deduction formats. The components cooperate ..."
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Cited by 12 (2 self)
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This paper describes the architecture, implementation and performance, of a heterogeneous parallel deduction system (HPDS). The HPDS uses multiple deduction components, each of which attempts to find a refutation of the same input set, but using different deduction formats. The components cooperate by distributing clauses they generate to other components. The HPDS has been implemented in PrologDLinda. PrologDLinda provides appropriate data transfer and synchronisation facilities for implementing parallel deduction systems. The performance of the HPDS has been investigated. Parallel Deduction Systems A parallel deduction system is one in which multiple deduction components run in parallel on separate processors. This is distinct from those deduction systems which run multiple deduction components alternately, such as the unit preference system [Wos, Carlson & Robinson#G.A.,#1964], and those which are only conceptually parallel systems. Parallel deduction systems can be categorised ...
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 an ..."
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Cited by 9 (6 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 "selfsuf ..."
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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...
A Hole in Goal Trees: Some Guidance from Resolution Theory
, 1973
"... A hole in goal trees: some guidance from resolution theory ..."
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Cited by 8 (1 self)
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A hole in goal trees: some guidance from resolution theory
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 8 (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...
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...
LinearInput Subset Analysis
 11th International Conference on Automated Deduction
, 1992
"... Abstract. There are syntactically identifiable situations in which reduction does not occur in chain format linear deduction systems, i.e. situations in which linearinput subdeductions are performed. Three methods of detecting these situations are described in this paper. The first method (Horn sub ..."
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Cited by 4 (2 self)
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Abstract. There are syntactically identifiable situations in which reduction does not occur in chain format linear deduction systems, i.e. situations in which linearinput subdeductions are performed. Three methods of detecting these situations are described in this paper. The first method (Horn subset analysis) focuses on Horn input chains while the second (LISS analysis) and third (LISL analysis) are successive generalisations of the first method. A significant benefit that may be derived from detecting linearinput subdeductions is the applicability of a truth value deletion strategy in such subdeductions. The completeness of the deletion strategy is proved, and its efficacy indicated. 1.