On classical behavior of intuitionistic modalities

• Authors: Drobyshevich Sergey
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

intuitionistic logic; modal logics; intuitionistic modalities; compositions; possibility; necessity; un-necessity; impossibility

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2015
• Volume: 24
• Issue: 1
• Pages: 79–104

Dates

published

2015-03-01

online

2014-08-16

Contributors

author

Drobyshevich Sergey

• Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk, 630090, Russia

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Identifiers

DOI

10.12775/LLP.2014.019