Abstract

AbstractMTL is the logic of all left-continuous t-norms and their residua. Its algebraic semantics is constituted by the variety \(\mathbb{V}\)(MTL) of MTL-algebras. Among schematic extensions of MTL there are infinite-valued logics \(\mathcal{L}\) such that the finitely generated free algebras in the corresponding subvariety \(\mathbb{V}\)(\(\mathcal{L}\)) of \(\mathbb{V}\)(MTL) are finite. In this paper we focus on Gödel and Nilpotent Minimum logics. We give concrete representations of their associated free algebras in terms of finite algebras of sections over finite posets.KeywordsFree AlgebraHasse DiagramAlgebraic SemanticSchematic ExtensionAxiomatic ExtensionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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