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Application of theorem proving to problem solving
, 1969
"... This paper shows how an extension of the resolution proof procedure can be used to construct problem solutions. The extended proof procedure can solve problems involving state transformations. The paper explores several alternate problem representations and provides a discussion of solutions to samp ..."
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Cited by 222 (1 self)
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This paper shows how an extension of the resolution proof procedure can be used to construct problem solutions. The extended proof procedure can solve problems involving state transformations. The paper explores several alternate problem representations and provides a discussion of solutions to sample problems including the "Monkey and Bananas " puzzle and the 'Tower of Hanoi " puzzle. The paper exhibits solutions to these problems obtained by QA3, a computer program bused on these theoremproving methods. In addition, the paper shows how QA3 can write simple computer programs and can solve practical problems for a simple robot. Key Words: Theorem proving, resolution, problem solving, automatic programming, program writing, robots, state transformations, question answering. Automatic theorem proving by the resolution proof procedure § represents perhaps the most powerful known method for automatically determining the validity of a statement of firstorder logic. In an earlier paper Green and Raphael" illustrated how an extended resolution procedure can be used as a question answerer—e.g., if the statement (3x)P(x) can be shown to follow from a set of axioms by the resolution proof procedure, then the extended proof procedure will find or construct an x that satisfies P(x). This earlier paper (1) showed how one can axiomatize simple questionanswering subjects, (2) described a questionanswering program called QA2 based on this procedure, and (3) presented examples of simple questionanswering dialogues with QA2. In a more recent paper " the author (1) presents the answer construction method in detail and proves its correctness, (2) describes the latest version of the program, QA3, and (3) introduces statetransformation methods into the constructive proof formalism. In addition to the questionanswering applications illustrated in these earlier papers, QA3 has been used as an SRI robot 4 problem solver and as an automatic
Using firstorder logic to reason about policies
 In Proc. 16th IEEE Computer Security Foundations Workshop (CSFW’03
, 2003
"... A policy describes the conditions under which an action is permitted or forbidden. We show that a fragment of (multisorted) firstorder logic can be used to represent and reason about policies. Because we use firstorder logic, policies have a clear syntax and semantics. We show that further restri ..."
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Cited by 77 (5 self)
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A policy describes the conditions under which an action is permitted or forbidden. We show that a fragment of (multisorted) firstorder logic can be used to represent and reason about policies. Because we use firstorder logic, policies have a clear syntax and semantics. We show that further restricting the fragment results in a language that is still quite expressive yet is also tractable. More precisely, questions about entailment, such as ‘May Alice access the file?’, can be answered in time that is a loworder polynomial (indeed, almost linear in some cases), as can questions about the consistency of policy sets.
The Applications of Theorem Proving to QuestionAnswering Systems
, 1969
"... This paper shows how a questionanswering system can use firstorder logic as its language and an automatic theorem prover, based upon the resolution inference principle, as its deductive mechanism. The resolution proof procedure is extended to a constructive proof procedure. An answer construction ..."
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Cited by 26 (0 self)
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This paper shows how a questionanswering system can use firstorder logic as its language and an automatic theorem prover, based upon the resolution inference principle, as its deductive mechanism. The resolution proof procedure is extended to a constructive proof procedure. An answer construction algorithm is given whereby the system is able not only to produce yes or no answers but also to find or construct an object satisfying a specified condition. A working computer program, QA3, based on these ideas, is described. The performance of the program, illustrated by extended examples, compares favorably with several other questionanswering programs. Methods are presented for solving state transformation problems. In addition to questionanswering, the program can do automatic programming
33 Basic Test Problems: A Practical Evaluation of Some Paramodulation Strategies
, 1996
"... Introduction Many researchers who study the theoretical aspects of inference systems believe that if inference rule A is complete and more restrictive than inference rule B, then the use of A will lead more quickly to proofs than will the use of B. The literature contains statements of the sort "ou ..."
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Cited by 24 (5 self)
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Introduction Many researchers who study the theoretical aspects of inference systems believe that if inference rule A is complete and more restrictive than inference rule B, then the use of A will lead more quickly to proofs than will the use of B. The literature contains statements of the sort "our rule is complete and it heavily prunes the search space; therefore it is efficient". 2 These positions are highly questionable and indicate that the authors have little or no experience with the practical use of automated inference systems. Restrictive rules (1) can block short, easytofind proofs, (2) can block proofs involving simple clauses, the type of clause on which many practical searches focus, (3) can require weakening of redundancy control such as subsumption and demodulation, and (4) can require the use of complex checks in deciding whether such rules should be applied. The only way to determ
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...
ZResolution: TheoremProving with Compiled Axioms
 Journal of the ACM
, 1973
"... ABSTRACT. An improved procedure for resolution theorem proving, called Zresolution, is described. The basic idea of Zresolution is to "compile " some of the axioms in a deductive problem. This means to automatically transform the selected axioms into a computer program which carries out the infere ..."
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Cited by 7 (0 self)
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ABSTRACT. An improved procedure for resolution theorem proving, called Zresolution, is described. The basic idea of Zresolution is to "compile " some of the axioms in a deductive problem. This means to automatically transform the selected axioms into a computer program which carries out the inference rules indicated by the axioms. This Is done automatically by another program called the speciahzer. The advantage of doing this is that the compiled axioms run faster, just as a compiled program runs faster than an interpreted program. A proof is given that the inference rule used m Zresolution is complete, provided that the axioms "compiled " have certain properties
Experiments With Subdivision of Search in Distributed Theorem Proving
 Proc. of PASCO97
, 1997
"... We introduce the distributed theorem prover Peersmcd for networks of workstations. Peersmcd is the parallelization of the Argonne prover EQP, according to our ClauseDiffusion methodology for distributed deduction. The new features of Peersmcd include the AGO (AncestorGraph Oriented) heuristic c ..."
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Cited by 6 (2 self)
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We introduce the distributed theorem prover Peersmcd for networks of workstations. Peersmcd is the parallelization of the Argonne prover EQP, according to our ClauseDiffusion methodology for distributed deduction. The new features of Peersmcd include the AGO (AncestorGraph Oriented) heuristic criteria for subdividing the search space among parallel processes. We report the performance of Peersmcd on several experiments, including problems which require days of sequential computation. In these experiments Peersmcd achieves considerable, sometime superlinear, speedup over EQP. We analyze these results by examining several statistics produced by the provers. The analysis shows that the AGO criteria partitions the search space effectively, enabling Peersmcd to achieve superlinear speedup by parallel search. 1 Introduction Distributed deduction is concerned with the problem of proving difficult theorems by distributing the work among networked computers. The motivation is to st...
Steps Toward a Computational Metaphysics
 Journal of Philosophical Logic
, 2007
"... In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this objects is implemented in prover9 (a firstorder automated reasoning system which is the successor to otter). Afte ..."
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Cited by 6 (4 self)
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In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this objects is implemented in prover9 (a firstorder automated reasoning system which is the successor to otter). After reviewing the secondorder, axiomatic theory of abstract objects, we show (1)howtorepresentafragmentofthattheoryinprover9’s firstorder syntax, and (2) how prover9 then finds proofs of interesting theorems of metaphysics, such as that every possible world is maximal. We conclude the paper by discussing some issues for further research. 1.
Logic Control via Automatic Theorem Proving: COCOLOG Fragments Implemented in Blitzensturm 5.0
, 1993
"... The COCOLOG system is a partially ordered family of first order logical theories that describe the controlled evolution of the state of a given partially observered finite machine M. Following the review of the general theory of COCOLOG, the notion of Markovian fragments MTh k ,k 1, of full COCOLOG ..."
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Cited by 5 (5 self)
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The COCOLOG system is a partially ordered family of first order logical theories that describe the controlled evolution of the state of a given partially observered finite machine M. Following the review of the general theory of COCOLOG, the notion of Markovian fragments MTh k ,k 1, of full COCOLOG theories Th k is presented. These fragments enjoy the property of having axiom set of fixed size over time. MTh k and Th k have the virtually same state estimation and control power. Next, a newly developed automatic theorem proving software called Blitzenstrum is described and some applications Blitzenstrum 5.0 to the logic control of a stylized elevator problem are presented.