MTL 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.
Poset representation for Godel and Nilpotent Minimum logics / S. Aguzzoli, B. Gerla, C. Manara - In: Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 8th European Conference, ECSQARU 2005 : Barcelona, Spain, July 6-8, 2005 : Proceedings / Lluis Godo. - Berlin : Springer, 2005. - ISBN 3540273263. - pp. 662-674 (( Intervento presentato al 8th. convegno European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty tenutosi a Barcellona, Spagna nel 2005.
Poset representation for Godel and Nilpotent Minimum logics
S. AguzzoliPrimo
;
2005
Abstract
MTL 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.
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