@article{Petrukhin_2021, title={S5-Style Non-Standard Modalities in a Hypersequent Framework}, volume={31}, url={https://apcz.umk.pl/LLP/article/view/33865}, DOI={10.12775/LLP.2021.020}, abstractNote={<p>The aim of the paper is to present some non-standard modalities (such as non-contingency, contingency, essence and accident) based on <strong>S5</strong>-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 <strong>S5</strong>. 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.</p>}, number={3}, journal={Logic and Logical Philosophy}, author={Petrukhin, Yaroslav}, year={2021}, month={Dec.}, pages={427–456} }