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

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.
Gerla, Brunella
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1491999
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