Definability and canonicity for Boolean logic with a binary relation

Philippe Balbiani (1, 2) , Tinko Tinchev (3)

1 IRIT-LILaC - Logique, Interaction, Langue et Calcul
2 CNRS - Centre National de la Recherche Scientifique
3 Department of Mathematical Logic and Applications (Sofia, Bulgaria)

This paper studies the concepts of definability and canonicity in Boolean logic with a binary relation. Firstly, it provides formulas defining first-order or second-order conditions on frames. Secondly, it proves that all formulas corresponding to compatible first-order conditions on frames are canonical.

Mots clés: Boolean Algebra; Modal Logic; Definability; Canonicity

Domaines: Intelligence artificielle [cs.AI]; Apprentissage [cs.LG]; Logique en informatique [cs.LO]; Informatique et langage [cs.CL]

Philippe Balbiani, Tinko Tinchev. Definability and canonicity for Boolean logic with a binary relation. Fundamenta Informaticae, 2014, vol. 129 (n° 4), pp. 301-327. ⟨10.3233/FI-2014-973⟩. ⟨hal-01120594⟩