Case Study : Additive Linear Logic and Lattices
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Auteurs : Jean-Yves MarionSource :
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Abstract
We investigate sequent calculus where contexts, called additive contexts, are governed by the operations of a non-distributive lattice. We present a sequent calculus ALL_m with multiple antecedents and succedents. ALL_m is complete for non-distributive lattices and is equivalent to the additive fragment of linear logic. Weakenings and contractions are postulated for ALL_m and cut is redundant. We extend this construction in order to get a sequent calculus for propositional linear logic with both additive and multiplicative contexts. Then we show that a bottom-up decision procedure based on the cut-free sequent calculi runs in exponential time. We provide a decision algorithm that exploits analytic cuts and whose runtime is polynomial.
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" wicri:score="63">Case Study : Additive Linear Logic and Lattices</title></titleStmt><publicationStmt><idno type="RBID">CRIN:marion97a</idno><date when="1997" year="1997">1997</date><idno type="wicri:Area/Crin/Corpus">001F96</idno><idno type="wicri:Area/Crin/Curation">001F96</idno><idno type="wicri:explorRef" wicri:stream="Crin" wicri:step="Curation">001F96</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Case Study : Additive Linear Logic and Lattices</title><author><name sortKey="Marion, Jean Yves" sort="Marion, Jean Yves" uniqKey="Marion J" first="Jean-Yves" last="Marion">Jean-Yves Marion</name></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Decision procedures</term><term>Free lattices</term><term>Linear Logic</term><term>Sequent Calculus</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en" wicri:score="2459">We investigate sequent calculus where contexts, called additive contexts, are governed by the operations of a non-distributive lattice. We present a sequent calculus ALL_m with multiple antecedents and succedents. ALL_m is complete for non-distributive lattices and is equivalent to the additive fragment of linear logic. Weakenings and contractions are postulated for ALL_m and cut is redundant. We extend this construction in order to get a sequent calculus for propositional linear logic with both additive and multiplicative contexts. Then we show that a bottom-up decision procedure based on the cut-free sequent calculi runs in exponential time. We provide a decision algorithm that exploits analytic cuts and whose runtime is polynomial.</div></front></TEI><BibTex type="inproceedings"><ref>marion97a</ref><crinnumber>97-R-291</crinnumber><category>3</category><equipe>CALLIGRAMME</equipe><author><e>Marion, Jean-Yves</e></author><title>Case Study : Additive Linear Logic and Lattices</title><booktitle>{4th International Symposium Logical, Foundations of Computer Science - LFCS'97, Yaroslavl, Russia}</booktitle><year>1997</year><editor>S. Adian A. Nerode</editor><volume>1234</volume><series>Lecture notes in Computer Science</series><pages>237-247</pages><month>jul</month><publisher>Springer</publisher><keywords><e>Linear Logic</e><e>Free lattices</e><e>Sequent Calculus</e><e>Decision procedures</e></keywords><abstract>We investigate sequent calculus where contexts, called additive contexts, are governed by the operations of a non-distributive lattice. We present a sequent calculus ALL_m with multiple antecedents and succedents. ALL_m is complete for non-distributive lattices and is equivalent to the additive fragment of linear logic. Weakenings and contractions are postulated for ALL_m and cut is redundant. We extend this construction in order to get a sequent calculus for propositional linear logic with both additive and multiplicative contexts. Then we show that a bottom-up decision procedure based on the cut-free sequent calculi runs in exponential time. We provide a decision algorithm that exploits analytic cuts and whose runtime is polynomial.</abstract></BibTex></record>Pour manipuler ce document sous Unix (Dilib)
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