Universal proof theory: Feasible admissibility in intuitionistic modal logics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00600572" target="_blank" >RIV/67985840:_____/25:00600572 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985807:_____/25:00600572

Výsledek na webu

<a href="https://doi.org/10.1016/j.apal.2024.103526" target="_blank" >https://doi.org/10.1016/j.apal.2024.103526</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.apal.2024.103526" target="_blank" >10.1016/j.apal.2024.103526</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Universal proof theory: Feasible admissibility in intuitionistic modal logics

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Universal proof theory: Feasible admissibility in intuitionistic modal logics

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annals of Pure and Applied Logic

ISSN

0168-0072

e-ISSN

1873-2461

Svazek periodika

176

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

40

Strana od-do

103526

Kód UT WoS článku

001349603400001

EID výsledku v databázi Scopus

2-s2.0-85207773176