0600572 - MÚ 2026 RIV NL eng J - Journal Article
Akbar Tabatabai, Seyed Amirhossein - Jalali Keshavarz, Raheleh
Universal proof theory: Feasible admissibility in intuitionistic modal logics.
Annals of Pure and Applied Logic. Roč. 176, č. 2 (2025), č. článku 103526. ISSN 0168-0072. E-ISSN 1873-2461
R&D Projects: GA ČR(CZ) GA23-04825S; GA ČR(CZ) GA22-01137S
Institutional support: RVO:67985840
Keywords : admissible rules * feasible disjunction property * intuitionistic modal logics
OECD category: Pure mathematics; Pure mathematics (UIVT-O)
Impact factor: 0.6, year: 2023 ; AIS: 0.578, rok: 2023
Method of publishing: Limited access
Result website:
https://doi.org/10.1016/j.apal.2024.103526DOI: https://doi.org/10.1016/j.apal.2024.103526

We introduce a general and syntactically defined family of sequent-style calculi over the propositional language with the modalities {□,◇} and its fragments as a formalization for constructively acceptable systems. Calling these calculi constructive, we show that any strong enough constructive sequent calculus, satisfying a mild technical condition, feasibly admits all Visser's rules. This means that there exists a polynomial-time algorithm that, given a proof of the premise of a Visser's rule, provides a proof for its conclusion. As a positive application, we establish the feasible admissibility of Visser's rules in sequent calculi for several intuitionistic modal logics, including CK, IK, their extensions by the modal axioms T, B, 4, 5, and the axioms for bounded width and depth and their fragments CK□, propositional lax logic and IPC. On the negative side, we show that if a strong enough intuitionistic modal logic (satisfying a mild technical condition) does not admit at least one of Visser's rules, it cannot have a constructive sequent calculus. Consequently, no intermediate logic other than IPC has a constructive sequent calculus.
Permanent Link: https://hdl.handle.net/11104/0357882