Undecidable problems for modal definability

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

1 IRIT-LILaC - Logique, Interaction, Langue et Calcul
2 CNRS - Centre National de la Recherche Scientifique
3 Софийски университет = Sofia University

The core of our article is the computability of the problem of deciding the modal definability of first-order sentences with respect to classes of frames. It gives a new proof of Chagrova's Theorem telling that, with respect to the class of all frames, the problem of deciding the modal definability of first-order sentences is undecidable. It also gives the proofs of new variants of Chagrova's Theorem

Mots clés: First-order logic; Modal logic; Modal definability; Chagrova's Theorem; Computability

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

Philippe Balbiani, Tinko Tinchev. Undecidable problems for modal definability. Journal of Logic and Computation, 2017, 27 (3), pp.901-920. ⟨10.1093/logcom/exv094⟩. ⟨hal-01740019⟩