Rules with parameters in modal logic I

0444112 - MÚ 2016 RIV NL eng J - Článek v odborném periodiku
Jeřábek, Emil
Rules with parameters in modal logic I.
Annals of Pure and Applied Logic. Roč. 166, č. 9 (2015), s. 881-933. ISSN 0168-0072. E-ISSN 1873-2461
Grant CEP: GA AV ČR IAA100190902; GA ČR GBP202/12/G061
Institucionální podpora: RVO:67985840
Klíčová slova: modal logic * admissible rule * equational unification
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.582, rok: 2015
http://www.sciencedirect.com/science/article/pii/S0168007215000366

We study admissibility of inference rules and unification with parameters in transitive modal logics: we generalize various results on parameter-free admissibility and unification to the setting with parameters. We give a characterization of projective formulas generalizing Ghilardi's characterization in the parameter-free case, leading to new proofs of Rybakov's results that admissibility with parameters is decidable and unification is finitary for logics satisfying suitable frame extension properties (called cluster-extensible logics in this paper). We construct explicit bases of admissible rules with parameters for cluster-extensible logics, and give their semantic description. We show that in the case of finitely many parameters, these logics have independent bases of admissible rules, and determine which logics have finite bases. We also show that cluster-extensible logics have nice properties: they are finitely axiomatizable, and have an exponential-size model property. ...
Trvalý link: http://hdl.handle.net/11104/0246692