Automated proofs of the moufang identities in alternative rings
Identifieur interne : 000058 ( Istex/Corpus ); précédent : 000057; suivant : 000059Automated proofs of the moufang identities in alternative rings
Auteurs : Siva Anantharaman ; Jieh HsiangSource :
- Journal of Automated Reasoning [ 0168-7433 ] ; 1990-03-01.
English descriptors
- KwdEn :
- Teeft :
- Alternative ring, Alternative rings, Anantharaman, Auxiliary functions, Cancellation, Cancellation inferences, Cancellation laws, Critical pair, Critical pairs, Equational, Equational theorem, Final step, Hand side, Ineqn, Inequality, Inference mechanism, Input equations, Moufang, Moufang identities, Moufang identity, Orientable, Orientable instance, Prover, Right cancellable, Right hand side, Right hand sides, Right moufang identity, Runtime, Sbr2, Search mechanism, Search space, Simplification, Simplification steps, Siva, Siva anantharaman, Subterm, Superposing, Superposition, Symbolic computation, Term structure, Unfailing completion.
Abstract
Abstract: In this paper we present automatic proofs of the Moufang identities in alternative rings. Our approach is based on the term rewriting (Knuth-Bendix completion) method, enforced with various features. Our proofs seem to be the first computer proofs of these problems done by a general purpose theorem prover. We also present a direct proof of a certain property of alternative rings without employing any auxiliary functions. To our knowledge our computer proof seems to be the first direct proof of this property, by human or by a computer.
Url:
DOI: 10.1007/BF00302643
Links to Exploration step
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<Para>In this paper we present automatic proofs of the Moufang identities in alternative rings. Our approach is based on the term rewriting (Knuth-Bendix completion) method, enforced with various features. Our proofs seem to be the first computer proofs of these problems done by a general purpose theorem prover. We also present a <Emphasis Type="Italic">direct</Emphasis>
proof of a certain property of alternative rings without employing any auxiliary functions. To our knowledge our computer proof seems to be the first direct proof of this property, by human or by a computer.</Para>
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<KeywordGroup Language="En"><Heading>Key words</Heading>
<Keyword>Automated theorem proving</Keyword>
<Keyword>equational logic</Keyword>
<Keyword>Knuth-Bendix completion</Keyword>
<Keyword>term rewriting</Keyword>
<Keyword>Moufang identities</Keyword>
<Keyword>alternative rings</Keyword>
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<ArticleNote Type="Misc"><SimplePara>On leave from the Department of Computer Science, UNYY at Stony Brook, New York. Research supported in part by NSF grants CCR-8805734, INT-8715231, and CCR-8901322.</SimplePara>
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<name type="personal"><namePart type="given">Siva</namePart>
<namePart type="family">Anantharaman</namePart>
<affiliation>LIFO, Dépt. Math-Info., Université d'Orléans, 45067, Orléans Cedex 02, France</affiliation>
<affiliation>E-mail: siva@univ-orleans.fr</affiliation>
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<name type="personal"><namePart type="given">Jieh</namePart>
<namePart type="family">Hsiang</namePart>
<affiliation>Department of Computer Science, National Taiwan University, Taipei, Taiwan, Republic of China</affiliation>
<affiliation>E-mail: hsiang@sbcs.sunysb.edu</affiliation>
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<abstract lang="en">Abstract: In this paper we present automatic proofs of the Moufang identities in alternative rings. Our approach is based on the term rewriting (Knuth-Bendix completion) method, enforced with various features. Our proofs seem to be the first computer proofs of these problems done by a general purpose theorem prover. We also present a direct proof of a certain property of alternative rings without employing any auxiliary functions. To our knowledge our computer proof seems to be the first direct proof of this property, by human or by a computer.</abstract>
<note>Problem Corner</note>
<subject lang="en"><genre>Key words</genre>
<topic>Automated theorem proving</topic>
<topic>equational logic</topic>
<topic>Knuth-Bendix completion</topic>
<topic>term rewriting</topic>
<topic>Moufang identities</topic>
<topic>alternative rings</topic>
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<relatedItem type="host"><titleInfo><title>Journal of Automated Reasoning</title>
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<titleInfo type="abbreviated"><title>J Autom Reasoning</title>
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<topic>Symbolic and Algebraic Manipulation</topic>
<topic>Artificial Intelligence (incl. Robotics)</topic>
<topic>Mathematical Logic and Foundations</topic>
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<identifier type="ISSN">0168-7433</identifier>
<identifier type="eISSN">1573-0670</identifier>
<identifier type="JournalID">10817</identifier>
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