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Standard completeness theorem for ΠMTL

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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.

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Correspondence to Rostislav Horĉík.

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The work was supported by the Grant Agency of the Czech Republic under projects GACR 201/02/1540, 401/03/H047, and by Net CEEPUS SK-042.

Set offprint requests to: Rostislav Horĉík

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Horĉík, R. Standard completeness theorem for ΠMTL. Arch. Math. Logic 44, 413–424 (2005). https://doi.org/10.1007/s00153-004-0254-y

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  • DOI: https://doi.org/10.1007/s00153-004-0254-y

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