论文信息 - Standard completeness theorem for ΠMTL

Standard completeness theorem for ΠMTL

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.

Rostislav Horcík

[1] U. Höhle. Commutative, residuated 1—monoids , 1995 .

[2] Franco Montagna,et al. A Proof of Standard Completeness for Esteva and Godo's Logic MTL , 2002, Stud Logica.

[3] Petr Hájek,et al. Observations on the monoidal t-norm logic , 2002, Fuzzy Sets Syst..

[4] Petr Hájek,et al. Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[5] Lluis Godo,et al. Monoidal t-norm based logic: towards a logic for left-continuous t-norms , 2001, Fuzzy Sets Syst..

[6] Franco Montagna,et al. On the Standard and Rational Completeness of some Axiomatic Extensions of the Monoidal T-norm Logic , 2002, Stud Logica.