On Displaying Negative Modalities

Sergey Drobyshevich

doi:10.12775/LLP.2017.023

Autor

Sergey Drobyshevich Sobolev Institute of Mathematics and Novosibirsk State University

DOI:

https://doi.org/10.12775/LLP.2017.023

Słowa kluczowe

display calculus, bi-intuitionistic logic, negative modalities, unnecessity, impossibility, decidability, distributive logic

Abstrakt

We extend Takuro Onishi’s result on displaying substructural negations by formulating display calculi for non-normal versions of impossibility and unnecessity operators, called regular and co-regular negations, respectively, by Dimiter Vakarelov. We make a number of connections between Onishi’s work and Vakarelov’s study of negation. We also prove a decidability result for our display calculus, which can be naturally extended to obtain decidability results for a large number of display calculi for logics with negative modal operators.

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