Nonassociative Substructural Logics and Their Semilinear Extensions: Axiomatization and Completeness Properties

Kód výsledku v IS VaVaI

RIV/67985556:_____/13:00395361 - isvavai.cz

Nalezeny alternativní kódy

RIV/67985807:_____/13:00395361

Výsledek na webu

http://dx.doi.org/10.1017/S1755020313000099

DOI - Digital Object Identifier

10.1017/S1755020313000099

Jazyk výsledku

angličtina

Název v původním jazyce

Nonassociative Substructural Logics and Their Semilinear Extensions: Axiomatization and Completeness Properties

Popis výsledku v původním jazyce

Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on the study of their algebraic counterparts: residuated lattices. Recently, a nonassociative generalization of FL (which we call SL) has been studied by Galatos and Ono as the logic of lattice-ordered residuated unital groupoids. This paper is based on an alternative Hilbert-style presentation for SL which is almost MP-based. This presentation is then used to obtain, in a uniform way applicable to most (both associative and nonassociative) substructural logics, a form of local deduction theorem, description of filter generation, and proper forms of generalized disjunctions. A special stress is put on semilinear substructural logics (i.e., logics complete with respect to linearly ordered algebras). Axiomatizations of the weakest semilinear logic over SL and other prominent substructural logics are provided and their completeness with respect to chains defined o

Název v anglickém jazyce

Nonassociative Substructural Logics and Their Semilinear Extensions: Axiomatization and Completeness Properties

Popis výsledku anglicky

Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on the study of their algebraic counterparts: residuated lattices. Recently, a nonassociative generalization of FL (which we call SL) has been studied by Galatos and Ono as the logic of lattice-ordered residuated unital groupoids. This paper is based on an alternative Hilbert-style presentation for SL which is almost MP-based. This presentation is then used to obtain, in a uniform way applicable to most (both associative and nonassociative) substructural logics, a form of local deduction theorem, description of filter generation, and proper forms of generalized disjunctions. A special stress is put on semilinear substructural logics (i.e., logics complete with respect to linearly ordered algebras). Axiomatizations of the weakest semilinear logic over SL and other prominent substructural logics are provided and their completeness with respect to chains defined o

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Review of Symbolic Logic

ISSN

1755-0203

e-ISSN

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Svazek periodika

6

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

30

Strana od-do

394-423

Kód UT WoS článku

000323167200002

EID výsledku v databázi Scopus

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