Non-deterministic algebraization of logics by swap structures

Autor(es)

Coniglio, Marcelo E. ^{[1, 2]} ; Figallo-Orellano, Aldo ^{[2, 3]} ; Golzio, Ana Claudia ^[2]

Afiliação do(s) autor(es)

^[1] Univ Campinas Unicamp, Inst Philosophy & Humanities IFCH, Campinas, SP - Brazil

^[2] Univ Campinas Unicamp, Ctr Log Epistemol & Hist Sci CLE, Campinas, SP - Brazil

^[3] Natl Univ South UNS, Dept Math, Bahia Blanca, Buenos Aires - Argentina

• Tipo de documento: Artigo Científico
• Fonte: LOGIC JOURNAL OF THE IGPL; v. 28, n. 5, p. 1021-1059, OCT 2020.
• Citações Web of Science: 3

Resumo

Multialgebras (or hyperalgebras or non-deterministic algebras) have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency (or LFIs) that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff's representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics (as independently introduced by M. Fidel and D. Vakarelov). This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI (which is closely connected with Kalman's functor), suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (AU)

• Processo FAPESP: 16/21928-0 - Semânticas não-determinísticas para as lógicas da inconsistência formal
• Beneficiário: Aldo Figallo Orellano
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 13/04568-1 - Matrizes não-determinísticas: teoria e aplicações à semântica algébrica
• Beneficiário: Ana Cláudia de Jesus Golzio
• Modalidade de apoio: Bolsas no Brasil - Doutorado