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Swap structures semantics for Ivlev-like modal logics
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DOI：10.1007/s00500-018-03707-4.png)
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Abstract
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In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally a non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Farinas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum-Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum-Tarski algebras.
Keywords:
Swap structures
Modal logics
Non-deterministic matrices
Lindenbaum-Tarski algebra
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