Routley Star in Information-Based Semantics

0559694 - FLÚ 2023 RIV AU eng C - Conference Paper (international conference)
Punčochář, Vít - Sedlár, Igor
Routley Star in Information-Based Semantics.
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. 285-297. 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]
R&D Projects: GA ČR(CZ) GM21-23610M
Institutional support: RVO:67985955
Keywords : deductive systems * information states * non-classical logics * Routley star * negation
OECD category: Philosophy, History and Philosophy of science and technology
https://doi.org/10.4204/EPTCS.358.21

It is common in various non-classical logics, especially in relevant logics, to characterize negation semantically via the operation known as Routley star. This operation works well within relational semantic frameworks based on prime theories. We study this operation in the context of “information-based” semantics for which it is characteristic that sets of formulas supported by individual information states are theories that do not have to be prime. We will show that, somewhat surprisingly, the incorporation of Routley star into the information-based semantics does not lead to a collapse or a trivialization of the whole semantic system. On the contrary, it leads to a technically elegant though quite restricted semantic framework that determines a particular logic. We study some basic properties of this semantics. For example, we show that within this framework double negation law is valid only in involutive linear frames. We characterize axiomatically the logic of all linear frames and show that the logic of involutive linear frames coincides with a system that Mike Dunn coined Kalman logic. This logic is the {∧, ∨, ¬}-fragment of the “semi-relevant” logic known as R-mingle. Finally, we characterize by a deductive system the logic of all information frames equipped with Routley star.
Permanent Link: https://hdl.handle.net/11104/0334056