AustralieFrV1, PascalFrancis, Corpus, bibRecord, 006304

Cut-free display calculi for nominal tense logics

Identifieur interne : 006304 ( PascalFrancis/Corpus ); précédent : 006303; suivant : 006305

Cut-free display calculi for nominal tense logics

Auteurs : S. Demri ; R. Gore

Source :

Lecture notes in computer science [ 0302-9743 ] ; 1999.

RBID : Pascal:99-0374328

Descripteurs français

Pascal (Inist)
- Démonstration automatique, Démonstration théorème, Logique propositionnelle, Logique modale, Analyse syntaxique, Analyse sémantique.

English descriptors

KwdEn :
- Automatic proving, Modal logic, Propositional logic, Semantic analysis, Syntactic analysis, Theorem proving.

Abstract

We define cut-free display calculi for nominal tense logics extending the minimal nominal tense logic (MNTL) by addition of primitive axioms. To do so, we use a translation of MNTL into the minimal tense logic of inequality (MTL_¬=) which is known to be properly displayable by application of Kracht's results. The rules of the display calculus δMNTL for MNTL mimic those of the display calculus δMTL_¬= for MTL_¬=. Since δMNTL does not satisfy Belnap's condition (C8), we extend Wansing's strong normalisation theorem to get a similar theorem for any extension of δMNTL by addition of structural rules satisfying Belnap's conditions (C2)-(C7). Finally, we show a weak Sahlqvist-style theorem for extensions of MNTL, and by Kracht's techniques, deduce that these Sahlqvist extensions of δMNTL also admit cut-free display calculi.

Notice en format standard (ISO 2709)

Pour connaître la documentation sur le format Inist Standard.

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A08	`01`	`1`	`ENG`	`@1 Cut-free display calculi for nominal tense logics`
A09	`01`	`1`	`ENG`	`@1 Automated reasoning with analytic tableaux and related methods : Saratoga Springs NY, 7-11 June 1999`
A11	`01`	`1`		`@1 DEMRI (S.)`
A11	`02`	`1`		`@1 GORE (R.)`
A12	`01`	`1`		`@1 MURRAY (Neil V.) @9 ed.`
A14	`01`			`@1 Laboratoire LEIBNIZ - C.N.R.S., 46 av. Felix Viallet @2 38000 Grenoble @3 FRA @Z 1 aut.`
A14	`02`			`@1 Automated Reasoning Project and Dept. of Computer Science, Australian National University @2 ACT 0200 Canberra @3 AUS @Z 2 aut.`
A20				`@1 155-170`
A21				`@1 1999`
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A43	`01`			`@1 INIST @2 16343 @5 354000084534670160`
A44				`@0 0000 @1 © 1999 INIST-CNRS. All rights reserved.`
A45				`@0 1 p.1/4`
A47	`01`	`1`		`@0 99-0374328`
A60				`@1 P @2 C`
A61				`@0 A`
A64	`01`	`1`		`@0 Lecture notes in computer science`
A66	`01`			`@0 DEU`
C01	`01`		`ENG`	@0 We define cut-free display calculi for nominal tense logics extending the minimal nominal tense logic (MNTL) by addition of primitive axioms. To do so, we use a translation of MNTL into the minimal tense logic of inequality (MTL_¬=) which is known to be properly displayable by application of Kracht's results. The rules of the display calculus δMNTL for MNTL mimic those of the display calculus δMTL_¬= for MTL_¬=. Since δMNTL does not satisfy Belnap's condition (C8), we extend Wansing's strong normalisation theorem to get a similar theorem for any extension of δMNTL by addition of structural rules satisfying Belnap's conditions (C2)-(C7). Finally, we show a weak Sahlqvist-style theorem for extensions of MNTL, and by Kracht's techniques, deduce that these Sahlqvist extensions of δMNTL also admit cut-free display calculi.
C02	`01`	`X`		`@0 001D02C01`
C03	`01`	`X`	`FRE`	`@0 Démonstration automatique @5 01`
C03	`01`	`X`	`ENG`	`@0 Automatic proving @5 01`
C03	`01`	`X`	`SPA`	`@0 Demostración automática @5 01`
C03	`02`	`X`	`FRE`	`@0 Démonstration théorème @5 02`
C03	`02`	`X`	`ENG`	`@0 Theorem proving @5 02`
C03	`02`	`X`	`SPA`	`@0 Demostración teorema @5 02`
C03	`03`	`X`	`FRE`	`@0 Logique propositionnelle @5 03`
C03	`03`	`X`	`ENG`	`@0 Propositional logic @5 03`
C03	`03`	`X`	`SPA`	`@0 Lógica proposicional @5 03`
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C03	`04`	`X`	`ENG`	`@0 Modal logic @5 04`
C03	`04`	`X`	`SPA`	`@0 Lógica modal @5 04`
C03	`05`	`X`	`FRE`	`@0 Analyse syntaxique @5 05`
C03	`05`	`X`	`ENG`	`@0 Syntactic analysis @5 05`
C03	`05`	`X`	`SPA`	`@0 Análisis sintáxico @5 05`
C03	`06`	`X`	`FRE`	`@0 Analyse sémantique @5 06`
C03	`06`	`X`	`ENG`	`@0 Semantic analysis @5 06`
C03	`06`	`X`	`SPA`	`@0 Análisis semántico @5 06`
N21				`@1 242`

A30	`01`	`1`	`ENG`	`@1 TABLEAUX '99. International conference @3 Saratoga Springs NY USA @4 1999-06-07`

Format Inist (serveur)

NO :	PASCAL 99-0374328 INIST
ET :	Cut-free display calculi for nominal tense logics
AU :	DEMRI (S.); GORE (R.); MURRAY (Neil V.)
AF :	Laboratoire LEIBNIZ - C.N.R.S., 46 av. Felix Viallet/38000 Grenoble/France (1 aut.); Automated Reasoning Project and Dept. of Computer Science, Australian National University/ACT 0200 Canberra/Australie (2 aut.)
DT :	Publication en série; Congrès; Niveau analytique
SO :	Lecture notes in computer science; ISSN 0302-9743; Allemagne; Da. 1999; Vol. 1617; Pp. 155-170; Bibl. 1 p.1/4
LA :	Anglais
EA :	We define cut-free display calculi for nominal tense logics extending the minimal nominal tense logic (MNTL) by addition of primitive axioms. To do so, we use a translation of MNTL into the minimal tense logic of inequality (MTL_¬=) which is known to be properly displayable by application of Kracht's results. The rules of the display calculus δMNTL for MNTL mimic those of the display calculus δMTL_¬= for MTL_¬=. Since δMNTL does not satisfy Belnap's condition (C8), we extend Wansing's strong normalisation theorem to get a similar theorem for any extension of δMNTL by addition of structural rules satisfying Belnap's conditions (C2)-(C7). Finally, we show a weak Sahlqvist-style theorem for extensions of MNTL, and by Kracht's techniques, deduce that these Sahlqvist extensions of δMNTL also admit cut-free display calculi.
CC :	001D02C01
FD :	Démonstration automatique; Démonstration théorème; Logique propositionnelle; Logique modale; Analyse syntaxique; Analyse sémantique
ED :	Automatic proving; Theorem proving; Propositional logic; Modal logic; Syntactic analysis; Semantic analysis
SD :	Demostración automática; Demostración teorema; Lógica proposicional; Lógica modal; Análisis sintáxico; Análisis semántico
LO :	INIST-16343.354000084534670160
ID :	99-0374328

Links to Exploration step

Pascal:99-0374328

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<ET>Cut-free display calculi for nominal tense logics</ET>
<AU>DEMRI (S.); GORE (R.); MURRAY (Neil V.)</AU>
<AF>Laboratoire LEIBNIZ - C.N.R.S., 46 av. Felix Viallet/38000 Grenoble/France (1 aut.); Automated Reasoning Project and Dept. of Computer Science, Australian National University/ACT 0200 Canberra/Australie (2 aut.)</AF>
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<LA>Anglais</LA>
<EA>We define cut-free display calculi for nominal tense logics extending the minimal nominal tense logic (MNTL) by addition of primitive axioms. To do so, we use a translation of MNTL into the minimal tense logic of inequality (MTL<sub>¬=</sub>
) which is known to be properly displayable by application of Kracht's results. The rules of the display calculus δMNTL for MNTL mimic those of the display calculus δMTL<sub>¬=</sub>
 for MTL<sub>¬=</sub>
. Since δMNTL does not satisfy Belnap's condition (C8), we extend Wansing's strong normalisation theorem to get a similar theorem for any extension of δMNTL by addition of structural rules satisfying Belnap's conditions (C2)-(C7). Finally, we show a weak Sahlqvist-style theorem for extensions of MNTL, and by Kracht's techniques, deduce that these Sahlqvist extensions of δMNTL also admit cut-free display calculi.</EA>
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Cut-free display calculi for nominal tense logics

Cut-free display calculi for nominal tense logics

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Abstract

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