Here and There modal logic with dual implication

Philippe Balbiani (1, 2) , Martin Dieguez (3, 4)

1 IRIT-LILaC - Logique, Interaction, Langue et Calcul
2 CNRS - Centre National de la Recherche Scientifique
3 Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
4 CERV - Centre Européen de Réalité Virtuelle

We define and study an extension of the logic of Here and There with dual implication and modal operators of necessity and possibility. We provide a complete axiomatisation. We prove as well other results such as the interdefinability of modal operators and the Hennessy-Milner property. We give an upper bound to the complexity of the satisfiability problem.

Mots clés: modal logic; dual implication; axiomatization and completeness; Hennessy-Milner propert

Domaines: Intelligence artificielle [cs.AI]; Logique [math.LO]

Philippe Balbiani, Martin Dieguez. Here and There modal logic with dual implication. 12th Advances in Modal Logic conference (AiML 2018), Aug 2018, Bern, Switzerland. pp.63-82. ⟨hal-01891169⟩