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Standard completeness theorem for ΠMTL

Standard completeness theorem for ΠMTL

Authors :
Rostislav Horĉík
Source :
Archive for Mathematical Logic. 44:413-424
Publication Year :
2004
Publisher :
Springer Science and Business Media LLC, 2004.

Abstract

ΠMTL is a schematic extension of the monoidal t-norm based logic (MTL) by the characteristic axioms of product logic. In this paper we prove that ΠMTL satisfies the standard completeness theorem. From the algebraic point of view, we show that the class of ΠMTL-algebras (bounded commutative cancellative residuated l-monoids) in the real unit interval [0,1] generates the variety of all ΠMTL-algebras.

Details

ISSN :
14320665 and 09335846
Volume :
44
Database :
OpenAIRE
Journal :
Archive for Mathematical Logic
Accession number :
edsair.doi...........478ace9661acbbd66817970c0cf5ff51
Full Text :
https://doi.org/10.1007/s00153-004-0254-y