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Finite Models of Some Substructural Logics
Author(s) -
Buszkowski Wojciech
Publication year - 2002
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200201)48:1<63::aid-malq63>3.0.co;2-e
Subject(s) - mathematics , noncommutative geometry , commutative property , property (philosophy) , pure mathematics , algebra over a field , discrete mathematics , calculus (dental) , medicine , philosophy , dentistry , epistemology
We give a proof of the finite model property (fmp) of some fragments of commutative and noncommutative linear logic: the Lambek calculus, BCI, BCK and their enrichments, MALL and Cyclic MALL. We essentially simplify the method used in [4] for proving fmp of BCI and the Lambek ca culus and in [5] for proving fmp of MALL. Our construction of finite models also differs from that used in Lafont [8] in his proof of fmp of MALL (we do not use cut elimination).