InforLorV4, PascalFrancis, Corpus, bibRecord, 000C45

Case study : Additive linear logic and lattices

Identifieur interne : 000C45 ( PascalFrancis/Corpus ); précédent : 000C44; suivant : 000C46

Case study : Additive linear logic and lattices

Auteurs : J.-Y. Marion

Source :

Lecture notes in computer science [ 0302-9743 ] ; 1997.

RBID : Pascal:97-0403805

Descripteurs français

Pascal (Inist)
- Informatique théorique, Logique propositionnelle, Logique linéaire.

English descriptors

KwdEn :
- Computer theory, Propositional logic.

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.

Notice en format standard (ISO 2709)

Pour connaître la documentation sur le format Inist Standard.

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A05				`@2 1234`
A08	`01`	`1`	`ENG`	`@1 Case study : Additive linear logic and lattices`
A09	`01`	`1`	`ENG`	`@1 LFCS '97 : logical foundations of computer science : Yaroslavl, July 6-12, 1997`
A11	`01`	`1`		`@1 MARION (J.-Y.)`
A12	`01`	`1`		`@1 ADIAN (Sergei) @9 ed.`
A12	`02`	`1`		`@1 NERODE (Anil) @9 ed.`
A14	`01`			`@1 Université Nancy 2, CRIN - CNRS & INRIA Lorraine, Projet Calligramme, Campus Scientifique - B.P. 239 @2 54506 Vandoeuvre-lès-Nancy @3 FRA @Z 1 aut.`
A20				`@1 237-247`
A21				`@1 1997`
A23	`01`			`@0 ENG`
A43	`01`			`@1 INIST @2 16343 @5 354000061692060240`
A44				`@0 0000 @1 © 1997 INIST-CNRS. All rights reserved.`
A45				`@0 11 ref.`
A47	`01`	`1`		`@0 97-0403805`
A60				`@1 P @2 C`
A61				`@0 A`
A64	`01`	`1`		`@0 Lecture notes in computer science`
A66	`01`			`@0 DEU`
A66	`02`			`@0 USA`
C01	`01`		`ENG`	@0 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.
C02	`01`	`X`		`@0 001D02A05`
C03	`01`	`X`	`FRE`	`@0 Informatique théorique @5 01`
C03	`01`	`X`	`ENG`	`@0 Computer theory @5 01`
C03	`01`	`X`	`SPA`	`@0 Informática teórica @5 01`
C03	`02`	`X`	`FRE`	`@0 Logique propositionnelle @5 02`
C03	`02`	`X`	`ENG`	`@0 Propositional logic @5 02`
C03	`02`	`X`	`SPA`	`@0 Lógica proposicional @5 02`
C03	`03`	`X`	`FRE`	`@0 Logique linéaire @4 INC @5 72`
N21				`@1 244`

A30	`01`	`1`	`ENG`	`@1 Logical foundations of computer science. International symposium @2 4 @3 Yaroslavl RUS @4 1997-07-06`

Format Inist (serveur)

NO :	PASCAL 97-0403805 INIST
ET :	Case study : Additive linear logic and lattices
AU :	MARION (J.-Y.); ADIAN (Sergei); NERODE (Anil)
AF :	Université Nancy 2, CRIN - CNRS & INRIA Lorraine, Projet Calligramme, Campus Scientifique - B.P. 239/54506 Vandoeuvre-lès-Nancy/France (1 aut.)
DT :	Publication en série; Congrès; Niveau analytique
SO :	Lecture notes in computer science; ISSN 0302-9743; Allemagne; Da. 1997; Vol. 1234; Pp. 237-247; Bibl. 11 ref.
LA :	Anglais
EA :	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.
CC :	001D02A05
FD :	Informatique théorique; Logique propositionnelle; Logique linéaire
ED :	Computer theory; Propositional logic
SD :	Informática teórica; Lógica proposicional
LO :	INIST-16343.354000061692060240
ID :	97-0403805

Links to Exploration step

Pascal:97-0403805

Le document en format XML

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 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.</EA>
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Case study : Additive linear logic and lattices

Case study : Additive linear logic and lattices

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Abstract

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