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On Displaying Negative Modalities

100%

Drobyshevich S.

Logic and Logical Philosophy

2018

vol. 27

issue 2

161-192

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.

On classical behavior of intuitionistic modalities

84%

Drobyshevich S.

Logic and Logical Philosophy

2015

vol. 24

issue 1

79–104

We study connections between four types of modal operators – necessity, possibility, un-necessity and impossibility – over intuitionitstic logic in terms of compositions of these modal operators with intuitionistic negation. We investigate which basic compositions, i.e. compositions of the form ¬δ, δ¬ or ¬δ¬, yield modal operators of the same type over intuitionistic logic as over classical logic. We say that such compositions behave classically. We study which modal properties correspond to each basic compositions behaving classically over intuitionistic logic and also prove that KC constitutes the smallest superintuitionistic logic over which all basic compositions behave classically.

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2 Logic and Logical Philosophy

2 Drobyshevich S.

1 2018

1 2015

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On Displaying Negative Modalities

On classical behavior of intuitionistic modalities