Standard completeness theorem for ΠMTL

Archive for Mathematical Logic 44 (4):413-424 (2005)


.ΠMTL is a schematic extension of the monoidal t-norm based logic 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 in the real unit interval [0,1] generates the variety of all ΠMTL-algebras.

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