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11
Otter: The CADE13 Competition Incarnations
 JOURNAL OF AUTOMATED REASONING
, 1997
"... This article discusses the two incarnations of Otter entered in the CADE13 Automated Theorem Proving Competition. Also presented are some historical background, a summary of applications that have led to new results in mathematics and logic, and a general discussion of Otter. ..."
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Cited by 44 (3 self)
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This article discusses the two incarnations of Otter entered in the CADE13 Automated Theorem Proving Competition. Also presented are some historical background, a summary of applications that have led to new results in mathematics and logic, and a general discussion of Otter.
A connection based proof method for intuitionistic logic
 TH WORKSHOP ON THEOREM PROVING WITH ANALYTIC TABLEAUX AND RELATED METHODS, LNAI 918
, 1995
"... We present a proof method for intuitionistic logic based on Wallen’s matrix characterization. Our approach combines the connection calculus and the sequent calculus. The search technique is based on notions of paths and connections and thus avoids redundancies in the search space. During the proof s ..."
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Cited by 29 (19 self)
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We present a proof method for intuitionistic logic based on Wallen’s matrix characterization. Our approach combines the connection calculus and the sequent calculus. The search technique is based on notions of paths and connections and thus avoids redundancies in the search space. During the proof search the computed firstorder and intuitionistic substitutions are used to simultaneously construct a sequent proof which is more human oriented than the matrix proof. This allows to use our method within interactive proof environments. Furthermore we can consider local substitutions instead of global ones and treat substitutions occurring in different branches of the sequent proof independently. This reduces the number of extra copies of formulae to be considered.
On transforming intuitionistic matrix proofs into standardsequent proofs
 TABLEAUX–95, LNAI 918
, 1995
"... We present a procedure transforming intuitionistic matrix proofs into proofs within the intuitionistic standard sequent calculus. The transformation is based on L. Wallen’s proof justifying his matrix characterization for the validity of intuitionistic formulae. Since this proof makes use of Fitting ..."
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Cited by 26 (15 self)
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We present a procedure transforming intuitionistic matrix proofs into proofs within the intuitionistic standard sequent calculus. The transformation is based on L. Wallen’s proof justifying his matrix characterization for the validity of intuitionistic formulae. Since this proof makes use of Fitting‘s nonstandard sequent calculus our procedure consists of two steps. First a nonstandard sequent proof will be extracted from a given matrix proof. Secondly we transform each nonstandard proof into a standard proof in a structure preserving way. To simplify the latter step we introduce an extended standard calculus which is shown to be sound and complete.
Experiments in automated deduction with condensed detachment
 in Proceedings of the Eleventh International Conference on Automated Deduction (CADE11), Lecture Notes in Artificial Intelligence
, 1992
"... This paper contains the results of experiments with several search strategies on 112 problems involving condensed detachment. The problems are taken from nine di erent logic calculi: three versions of the twovalued sentential calculus, the manyvalued sentential calculus, the implicational calculus ..."
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Cited by 23 (8 self)
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This paper contains the results of experiments with several search strategies on 112 problems involving condensed detachment. The problems are taken from nine di erent logic calculi: three versions of the twovalued sentential calculus, the manyvalued sentential calculus, the implicational calculus, the equivalential calculus, the R calculus, the left group calculus, and the right group calculus. Each problem was given to the theorem prover Otter and was run with at least three strategies: (1) a basic strategy, (2) a strategy with a more re ned method for selecting clauses on which to focus, and (3) a strategy that uses the re ned selection mechanism and deletes deduced formulas according to some simple rules. Two new features of Otter are also presented: the re ned method for selecting the next formula on which to focus, and a method for controlling memory usage. 1
Tstringunification: unifying prefixes in nonclassical proof methods
 5 TH TABLEAUX WORKSHOP, LNAI 1071
, 1996
"... For an efficient proof search in nonclassical logics, particular in intuitionistic and modal logics, two similar approaches have been established: Wallen’s matrix characterization and Ohlbach’s resolution calculus. Beside the usual termunification both methods require a specialized stringunificat ..."
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Cited by 23 (12 self)
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For an efficient proof search in nonclassical logics, particular in intuitionistic and modal logics, two similar approaches have been established: Wallen’s matrix characterization and Ohlbach’s resolution calculus. Beside the usual termunification both methods require a specialized stringunification to unify the socalled prefixes of atomic formulae (in Wallen’s notation) or worldpaths (in Ohlbach’s notation). For this purpose we present an efficient algorithm, called TStringUnification, which computes a minimal set of most general unifiers. By transforming systems of equations we obtain an elegant unification procedure, which is applicable to the intuitionistic logic J and the modal logic S4. With some modifications we are able to treat the modal logics D, K, D4, K4, S5, and T. We explain our method by an intuitive graphical presentation, prove correctness, completeness, minimality, and termination and investigate its complexity.
Converting nonclassical matrix proofs into sequentstyle systems
 CADE13, LNAI 1104
, 1996
"... Abstract. We present a uniform algorithm for transforming matrix proofs in classical, constructive, and modal logics into sequent style proofs. Making use of a similarity between matrix methods and Fitting’s prefixed tableaus we first develop a procedure for extracting a prefixed sequent proof from ..."
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Cited by 14 (8 self)
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Abstract. We present a uniform algorithm for transforming matrix proofs in classical, constructive, and modal logics into sequent style proofs. Making use of a similarity between matrix methods and Fitting’s prefixed tableaus we first develop a procedure for extracting a prefixed sequent proof from a given matrix proof. By considering the additional restrictions on the order of rule applications we then extend this procedure into an algorithm which generates a conventional sequent proof. Our algorithm is based on unified representations of matrix characterizations for various logics as well as of prefixed and usual sequent calculi. The peculiarities of a logic are encoded by certain parameters which are summarized in tables to be consulted by the algorithm. 1
Automated Reasoning and Bledsoe's Dream for the Field
"... In one sense, this article is a personal tribute to Woody Bledsoe. As such, the style will in general be that of private correspondence. However, since this article is also a compendium of experiments with an automated reasoning program, researchers interested in automated reasoning, mathematics, an ..."
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Cited by 7 (6 self)
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In one sense, this article is a personal tribute to Woody Bledsoe. As such, the style will in general be that of private correspondence. However, since this article is also a compendium of experiments with an automated reasoning program, researchers interested in automated reasoning, mathematics, and logic will find pertinent material here. The results of those experiments strongly suggest that research frequently benefits greatly from the use of an automated reasoning program. As evidence, I select from those results some proofs that are better than one can find in the literature, and focus on some theorems that, until now, had never been proved with an automated reasoning program, theorems that Hilbert, Church, and various logicians thought significant. To add spice to the article, I present challenges for reasoning programs, including questions that are still open. 1 This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Depa...
A New Method for Automated Finite Model Building Exploiting Failures and Symmetries
, 1998
"... . A method for building finite models is proposed. It combines enumeration of the set of interpretations on a finite domain with strategies in order to prune significantly the search space. The main new ideas underlying our method are to benefit from symmetries and from the information extracted fro ..."
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Cited by 6 (2 self)
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. A method for building finite models is proposed. It combines enumeration of the set of interpretations on a finite domain with strategies in order to prune significantly the search space. The main new ideas underlying our method are to benefit from symmetries and from the information extracted from the structure of the problem and from failures of model verification tests. The algorithms formalizing the approach are given and the standard properties (termination, completeness, and soundness) are proven. The method can deal with firstorder logic with equality. In contrast to existing ones, it does not require to transform the initial problem into a normal form and can be easily extended to other logics. Experimental results and comparisons with related works are reported. 1. Introduction The capital importance of the notion of "model" in Logic was naturally inherited by Automated Deduction, where, since the very beginning, the use of models has been recognized as an useful technique...
Evolving Combinators
 In Proceedings of the 14th International Conference on Automated Deduction, volume
, 1996
"... One of the many abilities that distinguish a mathematician from an automated deduction system is to be able to offer appropriate expressions based on intuition and experience that are substituted for existentially quantified variables so as to simplify the problem at hand substantially. We propose t ..."
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Cited by 4 (2 self)
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One of the many abilities that distinguish a mathematician from an automated deduction system is to be able to offer appropriate expressions based on intuition and experience that are substituted for existentially quantified variables so as to simplify the problem at hand substantially. We propose to simulate this ability with a technique called genetic programming for use in automated deduction. We apply this approach to problems of combinatory logic. Our experimental results show that the approach is viable and actually produces very promising results. A comparison with the renowned theorem prover Otter underlines the achievements. This work was supported by the Deutsche Forschungsgemeinschaft (DFG). 2 1 INTRODUCTION 1 Introduction Automated deduction systems have gained remarkable powerfulness in recent years. Nevertheless, they still lack a number of abilities that distinguish a good mathematician. One of these abilities is to use intuition and experience to suggest a solution...