We propose the notion of automata over Lukasiewicz many-valued logic, extending fuzzy automata ([9])Indeed, MV-algebras, i.e., algebraic structures related with many-valued Lukasiewicz logic, are made of two semiring reducts obtained considering the supremum operation together with the Lukasiewicz conjunction and the infimum operation together with Lukasiewicz disjunction. Vice-versa, given two semirings over the same domain, and given an isomorphism between these two algberas we can set some conditions in order to have an MV-algebra.Following the tradition of semirings, in this paper we shall study "many-valued automata" and "many-valued formal languages" interpreted in Lukasiewicz logic.
Automata over MV-algebras
GERLA, BRUNELLA
2004-01-01
Abstract
We propose the notion of automata over Lukasiewicz many-valued logic, extending fuzzy automata ([9])Indeed, MV-algebras, i.e., algebraic structures related with many-valued Lukasiewicz logic, are made of two semiring reducts obtained considering the supremum operation together with the Lukasiewicz conjunction and the infimum operation together with Lukasiewicz disjunction. Vice-versa, given two semirings over the same domain, and given an isomorphism between these two algberas we can set some conditions in order to have an MV-algebra.Following the tradition of semirings, in this paper we shall study "many-valued automata" and "many-valued formal languages" interpreted in Lukasiewicz logic.
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