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On bivalent semantics and natural deduction for some infectious logicsстатья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Автор: Belikov Alex
- Журнал: Logic Journal of the IGPL
- Том: 3
- Номер: 1
- Год издания: 2022
- Издательство: Oxford University Press
- Местоположение издательства: United Kingdom
- Первая страница: 186
- Последняя страница: 210
- DOI: 10.1093/jigpal/jzaa071
- Аннотация: In this work, we propose a variant of so-called informational semantics, a technique elaborated by Voishvillo, for two infectious logics, Deutsch’s Sfde and Szmuc’s dSfde. We show how the machinery of informational semantics can be effectively used to analyse truth and falsity conditions of disjunction and conjunction. Using this technique, it is possible to claim that disjunction and conjunction can be rightfully regarded as such, a claim which was disputed in the recent literature. Both Sfde and dSfde are formalized in terms of natural deduction. This allows us to solve several problems: to develop a natural deduction calculus for Sfde containing the standard form of disjunction elimination (in contrast to the calculus by Petrukhin), to introduce the first natural deduction calculus for dSfde and to reflect the fundamental symmetry between Sfde and dSfde on proof-theoretical level forming a convenient basis for obtaining their well-known extensions Kw3 and PWK.
- Добавил в систему: Беликов Александр Александрович