Inductive proof search modulo
Identifieur interne : 003942 ( Main/Exploration ); précédent : 003941; suivant : 003943Inductive proof search modulo
Auteurs : Fabrice Nahon [France] ; Claude Kirchner [France] ; Hélène Kirchner [France] ; Paul Brauner [France]Source :
- Annals of Mathematics and Artificial Intelligence [ 1012-2443 ] ; 2009-02-01.
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Abstract
Abstract: We present an original narrowing-based proof search method for inductive theorems in equational rewrite theories given by a rewrite system $\mathcal{R}$ and a set E of equalities. It has the specificity to be grounded on deduction modulo and to rely on narrowing to provide both induction variables and instantiation schemas. Whenever the equational rewrite system $(\mathcal{R},E)$ has good properties of termination, sufficient completeness, and when E is constructor and variable preserving, narrowing at defined-innermost positions leads to consider only unifiers which are constructor substitutions. This is especially interesting for associative and associative-commutative theories for which the general proof search system is refined. The method is shown to be sound and refutationally correct and complete. A major feature of our approach is to provide a constructive proof in deduction modulo for each successful instance of the proof search procedure.
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DOI: 10.1007/s10472-009-9154-5
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xml:lang="fr">France</country><wicri:regionArea>LORIA and University of Nancy, Nancy</wicri:regionArea><placeName><region type="region">Grand Est</region><region type="old region">Lorraine (région)</region><settlement type="city">Nancy</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Annals of Mathematics and Artificial Intelligence</title><title level="j" type="abbrev">Ann Math Artif Intell</title><idno type="ISSN">1012-2443</idno><idno type="eISSN">1573-7470</idno><imprint><publisher>Springer Netherlands</publisher><pubPlace>Dordrecht</pubPlace><date type="published" when="2009-02-01">2009-02-01</date><biblScope unit="volume">55</biblScope><biblScope unit="issue">1-2</biblScope><biblScope unit="page" from="123">123</biblScope><biblScope unit="page" to="154">154</biblScope></imprint><idno 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It has the specificity to be grounded on deduction modulo and to rely on narrowing to provide both induction variables and instantiation schemas. Whenever the equational rewrite system $(\mathcal{R},E)$ has good properties of termination, sufficient completeness, and when E is constructor and variable preserving, narrowing at defined-innermost positions leads to consider only unifiers which are constructor substitutions. This is especially interesting for associative and associative-commutative theories for which the general proof search system is refined. The method is shown to be sound and refutationally correct and complete. A major feature of our approach is to provide a constructive proof in deduction modulo for each successful instance of the proof search procedure.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Aquitaine</li><li>Grand Est</li><li>Lorraine (région)</li><li>Nouvelle-Aquitaine</li></region><settlement><li>Bordeaux</li><li>Nancy</li></settlement></list><tree><country name="France"><noRegion><name sortKey="Nahon, Fabrice" sort="Nahon, Fabrice" uniqKey="Nahon F" first="Fabrice" last="Nahon">Fabrice Nahon</name></noRegion><name sortKey="Brauner, Paul" sort="Brauner, Paul" uniqKey="Brauner P" first="Paul" last="Brauner">Paul Brauner</name><name sortKey="Brauner, Paul" sort="Brauner, Paul" uniqKey="Brauner P" first="Paul" last="Brauner">Paul Brauner</name><name sortKey="Kirchner, Claude" sort="Kirchner, Claude" uniqKey="Kirchner C" first="Claude" last="Kirchner">Claude Kirchner</name><name sortKey="Kirchner, Claude" sort="Kirchner, Claude" uniqKey="Kirchner C" first="Claude" last="Kirchner">Claude Kirchner</name><name sortKey="Kirchner, Helene" sort="Kirchner, Helene" uniqKey="Kirchner H" first="Hélène" last="Kirchner">Hélène Kirchner</name><name sortKey="Kirchner, Helene" sort="Kirchner, Helene" uniqKey="Kirchner H" first="Hélène" last="Kirchner">Hélène Kirchner</name><name sortKey="Nahon, Fabrice" sort="Nahon, Fabrice" uniqKey="Nahon F" first="Fabrice" last="Nahon">Fabrice Nahon</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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