Multioperation is any operation that return for even argument a set of values instead of a single value and an algebraic structure equipped with at least one multioperation is called multialgebra. In the realm of Logic, multialgebras were considered by Avron and his collaborators under the name of non-deterministic matrices and used as semantics tool for characterizing some logics which cannot be characterized by a single finite matrix. Later Carnielli and Coniglio [1] introduced the semantics of swap structures for LFIs (Logics of Formal Inconsistency), which are non-deterministic matrices defined over triples in a Boolean algebra, generalizing Avron’s semantics. In this talk, we will present recent developments about the algebraization of some systems not algebraizable by standard methods as Blok and Pigozzi general theory.

Reference

[1] W.A. Carnielli; M.E. Coniglio. Paraconsistent Logic: Consistency, Contradiction and Negation. Volume 40 in the Logic, Epistemology, and the Unity of Science Series, Springer, 2016.