Open AccessS5-Style Non-Standard Modalities in a Hypersequent Framework
Author(s) -
Yaroslav Petrukhin
Publication year - 2021
Publication title -
logic and logical philosophy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.416
H-Index - 10
eISSN - 2300-9802
pISSN - 1425-3305
DOI - 10.12775/llp.2021.020
Subject(s) - soundness , modalities , negation , constructive , contingency , calculus (dental) , argument (complex analysis) , computer science , style (visual arts) , mathematics , epistemology , philosophy , programming language , medicine , social science , dentistry , process (computing) , archaeology , sociology , history
The aim of the paper is to present some non-standard modalities (such as non-contingency, contingency, essence and accident) based on S5-models in a framework of cut-free hypersequent calculi. We also study negated modalities, i.e. negated necessity and negated possibility, which produce paraconsistent and paracomplete negations respectively. As a basis for our calculi, we use Restall's cut-free hypersequent calculus for S5. We modify its rules for the above-mentioned modalities and prove strong soundness and completeness theorems by a Hintikka-style argument. As a consequence, we obtain a cut admissibility theorem. Finally, we present a constructive syntactic proof of cut elimination theorem.