Connection methods in linear logic and proof nets construction
Identifieur interne : 00A337 ( Main/Merge ); précédent : 00A336; suivant : 00A338Connection methods in linear logic and proof nets construction
Auteurs : D. Galmiche [France]Source :
- Theoretical Computer Science [ 0304-3975 ] ; 2000.
English descriptors
- Teeft :
- Additive, Additive connectives, Additive sequent, Algorithm, Analyse, Analytic tableaux, Atomic formula, Atomic formulae, Atomic path, Atomic paths, Axiom, Calculus, Canonical, Canonical proof, Cient, Classical logic, Complementary connection, Comput, Computer science, Conjunctive, Conjunctive subformula, Connection characterization, Connection method, Connection methods, Connection structure, Decision procedure, Decomposition tree, Direct logic, Erent, Formula tree, Fragment, Free leaf, Galmiche, Girard, Inductive, Inductive construction, Inference rules, Initial sequent, Intuitionistic, Intuitionistic logic, Intuitionistic logics, Inverse method, July, Lecture notes, Linear logic, Linear sequent calculus, Logic, Logical foundations, Main result, Mall fragment, Matrix, Minimal path, Multiplicative, Permutability results, Proof, Proof construction, Proof nets, Proof nets construction, Proof search, Proof structure, Proof structures, Provability, Provable, Resp, Same element, Search space, Second premise, Sequent, Sequent calculus, Sequent proof, Sequent reconstruction, Sequents, Special rules, Special type, Springer, Subformula, Subformulae, Subnets, Subset, Tableau.
Abstract
Abstract: Linear logic (LL) is the logical foundation of some type-theoretic languages and also of environments for specification and theorem proving. In this paper, we analyse the relationships between the proof net notion of LL and the connection notion used for efficient proof search in different logics. Aiming at using proof nets as a tool for automated deduction in linear logic, we define a connection-based characterization of provability in Multiplicative Linear Logic (MLL). We show that an algorithm for proof net construction can be seen as a proof-search connection method. This central result is illustrated with a specific algorithm that is able to construct, for a provable MLL sequent, a set of connections, a proof net and a sequent proof. From these results we expect to extend to other LL fragments, we analyse what happens with the additive connectives of LL by tackling the additive fragment in a similar way.
Url:
DOI: 10.1016/S0304-3975(99)00176-0
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Galmiche</name><affiliation wicri:level="4"><country xml:lang="fr">France</country><wicri:regionArea>LORIA – Université Henri Poincaré, Campus Scientifique – B.P. 239, 54506 Vandœuvre-lès-Nancy Cedex</wicri:regionArea><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Vandœuvre-lès-Nancy</settlement></placeName><orgName type="university">Université Henri Poincaré</orgName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Theoretical Computer Science</title><title level="j" type="abbrev">TCS</title><idno type="ISSN">0304-3975</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="2000">2000</date><biblScope unit="volume">232</biblScope><biblScope unit="issue">1–2</biblScope><biblScope unit="page" from="231">231</biblScope><biblScope unit="page" to="272">272</biblScope></imprint><idno type="ISSN">0304-3975</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0304-3975</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="Teeft" xml:lang="en"><term>Additive</term><term>Additive connectives</term><term>Additive sequent</term><term>Algorithm</term><term>Analyse</term><term>Analytic tableaux</term><term>Atomic formula</term><term>Atomic formulae</term><term>Atomic path</term><term>Atomic paths</term><term>Axiom</term><term>Calculus</term><term>Canonical</term><term>Canonical proof</term><term>Cient</term><term>Classical logic</term><term>Complementary connection</term><term>Comput</term><term>Computer science</term><term>Conjunctive</term><term>Conjunctive subformula</term><term>Connection characterization</term><term>Connection method</term><term>Connection methods</term><term>Connection structure</term><term>Decision procedure</term><term>Decomposition tree</term><term>Direct logic</term><term>Erent</term><term>Formula tree</term><term>Fragment</term><term>Free leaf</term><term>Galmiche</term><term>Girard</term><term>Inductive</term><term>Inductive construction</term><term>Inference rules</term><term>Initial sequent</term><term>Intuitionistic</term><term>Intuitionistic logic</term><term>Intuitionistic logics</term><term>Inverse method</term><term>July</term><term>Lecture notes</term><term>Linear logic</term><term>Linear sequent calculus</term><term>Logic</term><term>Logical foundations</term><term>Main result</term><term>Mall fragment</term><term>Matrix</term><term>Minimal path</term><term>Multiplicative</term><term>Permutability results</term><term>Proof</term><term>Proof construction</term><term>Proof nets</term><term>Proof nets construction</term><term>Proof search</term><term>Proof structure</term><term>Proof structures</term><term>Provability</term><term>Provable</term><term>Resp</term><term>Same element</term><term>Search space</term><term>Second premise</term><term>Sequent</term><term>Sequent calculus</term><term>Sequent proof</term><term>Sequent reconstruction</term><term>Sequents</term><term>Special rules</term><term>Special type</term><term>Springer</term><term>Subformula</term><term>Subformulae</term><term>Subnets</term><term>Subset</term><term>Tableau</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Linear logic (LL) is the logical foundation of some type-theoretic languages and also of environments for specification and theorem proving. In this paper, we analyse the relationships between the proof net notion of LL and the connection notion used for efficient proof search in different logics. Aiming at using proof nets as a tool for automated deduction in linear logic, we define a connection-based characterization of provability in Multiplicative Linear Logic (MLL). We show that an algorithm for proof net construction can be seen as a proof-search connection method. This central result is illustrated with a specific algorithm that is able to construct, for a provable MLL sequent, a set of connections, a proof net and a sequent proof. From these results we expect to extend to other LL fragments, we analyse what happens with the additive connectives of LL by tackling the additive fragment in a similar way.</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
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