169,859 research outputs found
Poset representation for Godel and Nilpotent Minimum logics
No full textMTL is the logic of all left-continuous t-norms and their residua. Its algebraic semantics is constituted by the variety V(MTL) of MTL-algebras. Among schematic extensions of MTL there are infinite-valued logics L such that the finitely generated free algebras in the corresponding subvariety V(L) of V(MTL) are finite. In this paper we focus on Godel and Nilpotent Minimum logics. We give concrete representations of their associated free algebras in terms of finite algebras of sections over finite posets
On fuzzy truth-values and quasi-standard completeness
No full textPropositional many-valued logics constitute formalisation of fuzzy logics, as the intended set of truth-values is the real unit interval [0, 1], or meaningful subsets of it. In this paper we propose to frame some intuitive notion about fuzzy truth-values in formal logic and algebraic definitions, inducing some reflections about the usual notion of standard completeness
Algebras of Fuzzy Sets in Logics Based on Continuous Triangular Norms.
No full textAssociated with any [0,1]-valued propositional logic with a complete algebraic semantics, one can consider algebras of families of fuzzy sets over a classical universe, endowed with the appropriate operations. For the three most important schematic extensions of Hájek’s Basic (Fuzzy) Logic, we investigate the existence and the structure of such algebras of fuzzy sets in the corresponding algebraic varieties. In the general case of Basic Logic itself, and in sharp contrast to the three aforementioned extensions, we show that there actually exist different, incomparable notions of algebras of fuzzy sets
Algebraic and Proof-theoretic Aspects of Non-classical Logics
No full textLecture Notes in Computer Science, Vol. 446
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