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

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F13%3A00395361" target="_blank" >RIV/67985556:_____/13:00395361 - isvavai.cz</a>

Alternative codes found

RIV/67985807:_____/13:00395361

Result on the web

<a href="http://dx.doi.org/10.1017/S1755020313000099" target="_blank" >http://dx.doi.org/10.1017/S1755020313000099</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/S1755020313000099" target="_blank" >10.1017/S1755020313000099</a>

Result language

angličtina

Original language name

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

Original language description

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

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2013

Confidentiality

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

Name of the periodical

Review of Symbolic Logic

ISSN

1755-0203

e-ISSN

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Volume of the periodical

6

Issue of the periodical within the volume

3

Country of publishing house

GB - UNITED KINGDOM

Number of pages

30

Pages from-to

394-423

UT code for WoS article

000323167200002

EID of the result in the Scopus database

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