A. Di Nola, B. Gerla
Algebras of Lukasiewicz's Logic and their Semiring Reducts
Preprint series: ESI preprints

MSC:

06D30 De Morgan algebras, Lukasiewicz algebras, See also {03G20}

16Y60 Semirings, See also {12K10}

Abstract: In this paper we shall establish some links between the
algebras of {\L}ukasiewicz logic (MV-algebras) and the semirings.
The relationship of these algebraic structures gives a hint
on how to construct linear algebra starting from MV-algebras.
Indeed here the role of sum and product is played respectively
by a lattice operation and by an arithmetical operation.
In this way, following the tradition of semirings,
it makes full sense to consider "many-valued automata"
and "many-valued formal languages" interpreted in Lukasiewicz logic.