Natural Deduction for Assertibility and Deniability

0559695 - FLÚ 2023 RIV AU eng C - Konferenční příspěvek (zahraniční konf.)
Punčochář, Vít - Grimau, Berta
Natural Deduction for Assertibility and Deniability.
Proceedings of the 10th International Conference on Non-Classical Logics. Theory and Applications, NCL 2022, Łódź, Poland, 14-18 March 2022. online: Open Publishing Association, 2022 - (Indrzejczak, A.; Zawidzki, M.), s. 41-54. Electronic Proceedings in Theoretical Computer Science (EPTCS), 358. E-ISSN 2075-2180.
[Non-Classical Logics. Theory and Applications (NCL) /10./. Łódź (PL), 14.03.2022-18.03.2022]
Grant CEP: GA ČR(CZ) GM21-23610M
Institucionální podpora: RVO:67985955
Klíčová slova: semantics * natural deduction * assertibility * deniability * possible worlds
Obor OECD: Philosophy, History and Philosophy of science and technology
https://doi.org/10.4204/EPTCS.358.4

In this paper we split every basic propositional connective into two versions, one is called extensional and the other one intensional. The extensional connectives are semantically characterized by standard truth conditions that are relative to possible worlds. Assertibility and deniability of sentences built out of atomic sentences by extensional connectives are defined in terms of the notion of truth. The intensional connectives are characterized directly by assertibility and deniability conditions without the notion of truth. We pay special attention to the deniability condition for intensional implication. We characterize the logic of this mixed language by a system of natural deduction that sheds some light on the inferential behaviour of these two kinds of connectives and on the way they can interact.
Trvalý link: https://hdl.handle.net/11104/0334055