On the da Costa, Dubikajtis and Kotas’ system of the discursive logic, D*2

Janusz Ciuciura

doi:10.12775/LLP.2005.015

Autor

Janusz Ciuciura Department of Logic, Nicolaus Copernicus University

DOI:

https://doi.org/10.12775/LLP.2005.015

Słowa kluczowe

discursive (discussive) logic, D2, paraconsistent logic, labelled tableaux

Abstrakt

In the late forties, Stanisław Jaśkowski published two papers on the discursive (or discussive) sentential calculus, D₂. He provided a definition of it by an interpretation in the language of S5 of Lewis. The known axiomatization of D₂ with discursive connectives as primitives was introduced by da Costa, Dubikajtis and Kotas in 1977. It turns out, however, that one of the axioms they used is not a thesis of the real Jaśkowski’s calculus. In fact, they built a new system, D*₂ for short, that differs from D₂ in many respects. The aim of this paper is to introduce a direct Kripke-type semantics for the system, axiomatize it in a new way and prove soundness and completeness theorems. Additionally, we present labelled tableaux for D*₂.

Biogram autora

Janusz Ciuciura - Department of Logic, Nicolaus Copernicus University

Department of Logic

Bibliografia

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