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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 43 (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.
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
Searching for Circles of Pure Proofs
, 1995
"... hen given a set of properties or conditions (say, three) that are claimed to be equivalent, the claim e s can be verified by supplying what we call a circle of proofs. In the case in point, one proves th econd property or condition from the first, the third from the second, and the first from the ..."
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Cited by 14 (9 self)
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hen given a set of properties or conditions (say, three) that are claimed to be equivalent, the claim e s can be verified by supplying what we call a circle of proofs. In the case in point, one proves th econd property or condition from the first, the third from the second, and the first from the third. If r s the proof that 1 implies 2 does not rely on 3, then we say that the proof is pure with respect to 3, o imply say the proof is pure. If one can renumber the three properties or conditions in such a way that t one can find a circle of three pure proofstechnically, each proof pure with respect to the condition hat is neither the hypothesis nor the conclusionthen we say that a circle of pure proofs has been n s found. Here we study the specific question of the existence of a circle of pure proofs for the thirtee hortest single axioms for equivalential calculus, subject to the requirement that condensed detachment t be used as the rule of inference. For an indication of ...
The Hot List Strategy
, 1997
"... Experimentation strongly suggests that, for attacking deep questions and hard problems with the assistance of an automated reasoning program, the more effective paradigms rely on the retention of deduced information. A significant obstacle ordinarily presented by such a paradigm is the deduction and ..."
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Cited by 9 (4 self)
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Experimentation strongly suggests that, for attacking deep questions and hard problems with the assistance of an automated reasoning program, the more effective paradigms rely on the retention of deduced information. A significant obstacle ordinarily presented by such a paradigm is the deduction and retention of one or more needed conclusions whose complexity sharply delays their consideration. To mitigate the severity of the cited obstacle, I formulated and feature in this article the hot list strategy. The hot list strategy asks the researcher to choose, usually from among the input statements characterizing the problem under study, one or more statements that are conjectured to play a key role for assignment completion. The chosen statementsconjectured to merit revisiting, again and againare placed in an input list of statements, called the hot list. When an automated reasoning program has decided to retain a new conclusion Cbefore any other statement is chosen to initiat...
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...
Automated Deduction in Equational Logic and Geometry
, 1995
"... Algebras, pages 263 297. Pergamon Press, Oxford, U.K., 1970. [24] K. Kunen. Single axioms for groups. J. Automated Reasoning, 9(3):291308, 1992. [25] H. Lakser, R. Padmanabhan, and C. R. Platt. Subdirect decomposition of P/lonka sums. Duke Math. J., 39(3):485488, 1972. [26] A. I. Mal'cev. ..."
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Algebras, pages 263 297. Pergamon Press, Oxford, U.K., 1970. [24] K. Kunen. Single axioms for groups. J. Automated Reasoning, 9(3):291308, 1992. [25] H. Lakser, R. Padmanabhan, and C. R. Platt. Subdirect decomposition of P/lonka sums. Duke Math. J., 39(3):485488, 1972. [26] A. I. Mal'cev. Uber die Einbettung von assoziativen Systemen Gruppen I. Mat. Sbornik, 6(48):331336, 1939. [27] B. Mazur. Arithmetic on curves. Bull. AMS, 14:207259, 1986. [28] J. McCharen, R. Overbeek, and L. Wos. Complexity and related enhancements for automated theoremproving programs. Computers and Math. Applic., 2:116, 1976. [29] J. McCharen, R. Overbeek, and L. Wos. Problems and experiments for and with automated theoremproving programs. IEEE Trans. on Computers, C25(8):773782, August 1976. [30] W. McCune. Automated discovery of new axiomatizations of the left group and right group calculi. J. Automated Reasoning, 9(1):124, 1992. [31] W. McCune. Single axioms for groups and Abelian g...
Automated reasoning: Real uses and . . .
"... An automated reasoning program has provided invaluable assistance in answering certain previously open questions in mathematics and in formal logic. These questions would not have been answered, at least by those who obtained the results, were it not for the program's contribution. Others have used ..."
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An automated reasoning program has provided invaluable assistance in answering certain previously open questions in mathematics and in formal logic. These questions would not have been answered, at least by those who obtained the results, were it not for the program's contribution. Others have used such a program to design logic circuits, many of which proved superior (with respect to transistor count) to the existing designs, and to validate the design of other circuits. These successes establish the value of an automated reasoning program for research and suggest the value for practical applications. We thus conclude that the field of automated reasoning is on the verge of becoming one of the more significant branches of computer science. Further, we conclude that the field has already advanced from stage 1, that of potential usefulness, to stage 2, that of actual usefulness. To pass to stage 3, that of wide acceptance and use, requires, among other things, easy access to an automated reasoning program and an understanding of the various aspects of automated reasoning. In fact, an automated reasoning program is available that is portable and can be run on relatively inexpensive machines. Moreover, a system exists for producing a reasoning program tailored to given specifications. As for the requirement of understanding the aspects of automated reasoning, much research remainsâ€”research aided by access to a reasoning program. A large obstacle has thus been removed, permitting many to experiment with and find uses for a computer program that can be relied upon as a most valuable automated reasoning assistant.
Elsevier Logic and artificial intelligence
, 1989
"... Nilsson, N.J., Logic and artificial intelligence, Artificial Intelligence 47 (1990) 3156. The theoretical foundations of the logical approach to artificial intelligence are presented. Logical languages are widely used for expressing the declarative knowledge needed in artificial intelligence system ..."
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Nilsson, N.J., Logic and artificial intelligence, Artificial Intelligence 47 (1990) 3156. The theoretical foundations of the logical approach to artificial intelligence are presented. Logical languages are widely used for expressing the declarative knowledge needed in artificial intelligence systems. Symbolic logic also provides a clear semantics for knowledge representation languages and a methodology for analyzing and comparing deductive inference techniques. Several observations gained from experience with the approach are discussed. Finally, we confront some challenging problems for artificial intelligence and describe what is being done in an attempt to solve them. 1.