Logica Universalis 12 (1-2):207-219 (2018)

Marek Nasieniewski
Nicolaus Copernicus University
In Béziau a logic \ was defined with the help of the modal logic \. In it, the negation operator is understood as meaning ‘it is not necessary that’. The strong soundness–completeness result for \ with respect to a version of Kripke semantics was also given there. Following the formulation of \ we can talk about \-like logics or Beziau-style logics if we consider other modal logics instead of \—such a possibility has been mentioned in [1]. The correspondence result between modal logics and respective Beziau-style logics has been generalised for the case of normal logics naturally leading to soundness–completeness results [see Marcos :279–300, 2005) and Mruczek-Nasieniewska and Nasieniewski :229–248, 2005)]. In Mruczek-Nasieniewska and Nasieniewski :185–196, 2008), :189–203, 2009) some partial results for non-normal cases are given. In the present paper we try to give similar but more general correspondence results for the non-normal-worlds case. To achieve this aim we have to enrich original Beziau’s language with an additional negation operator understood as ‘it is necessary that not’.
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DOI 10.1007/s11787-018-0184-9
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References found in this work BETA

New Foundations for Lewis Modal Systems.E. J. Lemmon - 1957 - Journal of Symbolic Logic 22 (2):176-186.

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Citations of this work BETA

Universal Logic: Evolution of a Project.Jean-Yves Beziau - 2018 - Logica Universalis 12 (1-2):1-8.

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