Semantic Labelled Tableaux for propositional BI (without bottom)
Identifieur interne : 003946 ( Crin/Corpus ); précédent : 003945; suivant : 003947Semantic Labelled Tableaux for propositional BI (without bottom)
Auteurs : Didier Galmiche ; Daniel MerySource :
- Journal of Logic and Computation ; 2003.
English descriptors
- KwdEn :
Abstract
In this paper, we study semantic labelled tableaux for the propositional Bunched Implications logic (BI) that freely combines intuitionistic logic (IL) and multiplicative intuitionistic linear logic (MILL). BI is a resource-aware logic that captures interferences between resources and it is well suited, because of its resource-based sharing interpretation, for reasoning about mutable data structures. We propose a labelled tableau calculus for BI without bottom, that is the unit of the additive disjunction, based on particular labels and constraints. We prove the soundness and completeness of this calculus wrt the Kripke resource semantics with an emphasis on countermodel construction. In addition, we prove the finite model property and as a consequence the decidability. Moreover, we analyze some algorithmic aspects of the tableau construction by providing a free variable variant of the calculus. We also develop the restrictions to IL and MILL that provide new tableau methods for both logics with generation of countermodels.
Links to Exploration step
CRIN:galmiche03cLe document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" wicri:score="412">Semantic Labelled Tableaux for propositional BI (without bottom)</title></titleStmt><publicationStmt><idno type="RBID">CRIN:galmiche03c</idno><date when="2003" year="2003">2003</date><idno type="wicri:Area/Crin/Corpus">003946</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Semantic Labelled Tableaux for propositional BI (without bottom)</title><author><name sortKey="Galmiche, Didier" sort="Galmiche, Didier" uniqKey="Galmiche D" first="Didier" last="Galmiche">Didier Galmiche</name></author><author><name sortKey="Mery, Daniel" sort="Mery, Daniel" uniqKey="Mery D" first="Daniel" last="Mery">Daniel Mery</name></author></analytic><series><title level="j">Journal of Logic and Computation</title><imprint><date when="2003" type="published">2003</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>bunched implications logic</term><term>decidability.</term><term>labels</term><term>semantics</term><term>tableaux</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en" wicri:score="2715">In this paper, we study semantic labelled tableaux for the propositional Bunched Implications logic (BI) that freely combines intuitionistic logic (IL) and multiplicative intuitionistic linear logic (MILL). BI is a resource-aware logic that captures interferences between resources and it is well suited, because of its resource-based sharing interpretation, for reasoning about mutable data structures. We propose a labelled tableau calculus for BI without bottom, that is the unit of the additive disjunction, based on particular labels and constraints. We prove the soundness and completeness of this calculus wrt the Kripke resource semantics with an emphasis on countermodel construction. In addition, we prove the finite model property and as a consequence the decidability. Moreover, we analyze some algorithmic aspects of the tableau construction by providing a free variable variant of the calculus. We also develop the restrictions to IL and MILL that provide new tableau methods for both logics with generation of countermodels.</div></front></TEI><BibTex type="article"><ref>galmiche03c</ref><crinnumber>A03-R-212</crinnumber><category>1</category><equipe>TYPES</equipe><author><e>Galmiche, Didier</e><e>Mery, Daniel</e></author><title>Semantic Labelled Tableaux for propositional BI (without bottom)</title><journal>Journal of Logic and Computation</journal><year>2003</year><volume>13</volume><number>5</number><pages>707-753</pages><month>Oct</month><keywords><e>semantics</e><e>tableaux</e><e>labels</e><e>bunched implications logic</e><e>decidability.</e></keywords><abstract>In this paper, we study semantic labelled tableaux for the propositional Bunched Implications logic (BI) that freely combines intuitionistic logic (IL) and multiplicative intuitionistic linear logic (MILL). BI is a resource-aware logic that captures interferences between resources and it is well suited, because of its resource-based sharing interpretation, for reasoning about mutable data structures. We propose a labelled tableau calculus for BI without bottom, that is the unit of the additive disjunction, based on particular labels and constraints. We prove the soundness and completeness of this calculus wrt the Kripke resource semantics with an emphasis on countermodel construction. In addition, we prove the finite model property and as a consequence the decidability. Moreover, we analyze some algorithmic aspects of the tableau construction by providing a free variable variant of the calculus. We also develop the restrictions to IL and MILL that provide new tableau methods for both logics with generation of countermodels.</abstract></BibTex></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Crin/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 003946 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Crin/Corpus/biblio.hfd -nk 003946 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Crin
|étape= Corpus
|type= RBID
|clé= CRIN:galmiche03c
|texte= Semantic Labelled Tableaux for propositional BI (without bottom)
}}
| This area was generated with Dilib version V0.6.33. |  |