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Vol. 14(1), 2014

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Vol. 16(4), 2016
Towards an hyperalgebraic theory of non-algebraizable logics
(1) Marcelo Esteban Coniglio(1), Aldo Figallo-Orellano(2) and Ana Claudia Golzio(3)

(1)Institute of Philosophy and Human Sciences - IFCH, and Centre for Logic, Epistemology and the History of Science - CLE University of Campinas, Brazil
(2) Departament of Matematics - National University of the South, and Centre for Logic, Epistemology and the History of Science - CLE University of Campinas, Brazil
(3) Ph.D. Program in Philosophy Institute of Philosophy and Human Sciences - IFCH, and Centre for Logic, Epistemology and the History of Science - CLE University of Campinas, Brazil


Date Posted: October 14, 2016

  vol.16,n.4,2016

   
Abstract:

Multialgebras (or hyperalgebras) have been very much studied in the literature. In the realm of Logic, they were considered by Avron and his collaborators under the name of non-deterministic matrices (or Nmatrices) as a useful semantics tool for characterizing some logics (in particular, several logics of formal inconsistency or LFIs) which cannot be characterized by a single finite matrix. In particular, these LFIs are not algebraizable by any method, including Blok and Pigozzi general theory. Carnielli and Coniglio introduced a semantics of swap structures for LFIs, which are Nmatrices defined over triples in a Boolean algebra, generalizing Avron's semantics. In this paper we develop the first steps towards the possibility of defining an algebraic theory of swap structures for LFIs, by adapting concepts of universal algebra to multialgebras in a suitable way.



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