Structural Sharing and Efficient Proof-Search in Propositional Intuitionistic Logic
Identifieur interne : 002583 ( Crin/Corpus ); précédent : 002582; suivant : 002584Structural Sharing and Efficient Proof-Search in Propositional Intuitionistic Logic
Auteurs : Didier Galmiche ; Dominique Larchey-WendlingSource :
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Abstract
In this paper, we present a new system for proof-search in propositional intuitionistic logic from which an efficient implementation based on structural sharing is naturally derived. The way to solve the problem of formula duplication is not based on logical solutions but on an appropriate representation of sequents with a direct impact on sharing and therefore on the implementation. Then, the proof-search is based on a finer control of the resources and has a {\cal O}(n\log n)-space complexity. The system has the subformula property and leads to an algorithm that, for a given sequent, constructs a proof or generates a counter-model.
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" wicri:score="668">Structural Sharing and Efficient Proof-Search in Propositional Intuitionistic Logic</title></titleStmt><publicationStmt><idno type="RBID">CRIN:galmiche99g</idno><date when="1999" year="1999">1999</date><idno type="wicri:Area/Crin/Corpus">002583</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Structural Sharing and Efficient Proof-Search in Propositional Intuitionistic Logic</title><author><name sortKey="Galmiche, Didier" sort="Galmiche, Didier" uniqKey="Galmiche D" first="Didier" last="Galmiche">Didier Galmiche</name></author><author><name sortKey="Larchey Wendling, Dominique" sort="Larchey Wendling, Dominique" uniqKey="Larchey Wendling D" first="Dominique" last="Larchey-Wendling">Dominique Larchey-Wendling</name></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Counter-Models</term><term>Intuitionistic Logic</term><term>Proof-Search</term><term>Proofs</term><term>Structural Sharing</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en" wicri:score="2269">In this paper, we present a new system for proof-search in propositional intuitionistic logic from which an efficient implementation based on structural sharing is naturally derived. The way to solve the problem of formula duplication is not based on logical solutions but on an appropriate representation of sequents with a direct impact on sharing and therefore on the implementation. Then, the proof-search is based on a finer control of the resources and has a {\cal O}(n\log n)-space complexity. The system has the subformula property and leads to an algorithm that, for a given sequent, constructs a proof or generates a counter-model.</div></front></TEI><BibTex type="inproceedings"><ref>galmiche99g</ref><crinnumber>99-R-112</crinnumber><category>3</category><equipe>TYPES</equipe><author><e>Galmiche, Didier</e><e>Larchey-Wendling, Dominique</e></author><title>Structural Sharing and Efficient Proof-Search in Propositional Intuitionistic Logic</title><booktitle>{Asian Computing Science Conference - ASIAN'99, Phuket, Thailand}</booktitle><year>1999</year><editor>P.S. Thiagarajan, R. Yap</editor><volume>1742</volume><series>Lecture Notes in Computer Science</series><pages>101-112</pages><month>Dec</month><publisher>Springer Verlag</publisher><keywords><e>Proof-Search</e><e>Intuitionistic Logic</e><e>Structural Sharing</e><e>Proofs</e><e>Counter-Models</e></keywords><abstract>In this paper, we present a new system for proof-search in propositional intuitionistic logic from which an efficient implementation based on structural sharing is naturally derived. The way to solve the problem of formula duplication is not based on logical solutions but on an appropriate representation of sequents with a direct impact on sharing and therefore on the implementation. Then, the proof-search is based on a finer control of the resources and has a {\cal O}(n\log n)-space complexity. The system has the subformula property and leads to an algorithm that, for a given sequent, constructs a proof or generates a counter-model.</abstract></BibTex></record>Pour manipuler ce document sous Unix (Dilib)
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