Frame-validity games and absolute minimality of modal axioms

Philippe Balbiani (1, 2) , David Fernández-Duque (3) , Andreas Herzig (1, 2) , Petar Iliev (1)

1 IRIT-LILaC - Logique, Interaction, Langue et Calcul
2 CNRS - Centre National de la Recherche Scientifique
3 UGENT - Universiteit Gent = Ghent University

We introduce frame-equivalence games tailored for reasoning about the size, modal depth, number of occurrences of symbols and number of different propositional variables of modal formulae defining a given property. Using these games we prove that the Löb axiom and the (m, n)-transfer axioms are optimal among those defining their respective class of frames.

Mots clés: modal logic; correspondence theory; formula-size games; lower bounds on formula-size

Domaines: Logique en informatique [cs.LO]

Philippe Balbiani, David Fernández-Duque, Andreas Herzig, Petar Iliev. Frame-validity games and absolute minimality of modal axioms. 12th International Conference on Advances in Modal Logic (AiML 2018), Aug 2018, Berne, Switzerland. pp.83-102. ⟨hal-03046246⟩