Deriving Inverse Operators for Modal Logic

Michell Guzman (1, 2) , Salim Perchy (1, 2) , Camilo Rueda (2, 3) , Frank Valencia (1, 3, 2)

1 COMETE - Concurrency, Mobility and Transactions
2 AVISPA Resarch Group - Ambientes VISuales de Progamación Aplicativa
3 Pontificia universidad Javeriana, Cali

Spatial constraint systems are algebraic structures from concurrent constraint programming to specify spatial and epistemic behavior in multi-agent systems. We shall use spatial constraint systems to give an abstract characterization of the notion of normality in modal logic and to derive right inverse/reverse operators for modal languages. In particular, we shall identify the weakest condition for the existence of right inverses and show that the abstract notion of normality corresponds to the preservation of finite suprema. We shall apply our results to existing modal languages such as the weakest normal modal logic, Hennessy-Milner logic, and linear-time temporal logic. We shall discuss our results in the context of modal concepts such as bisimilarity and inconsistency invariance.

Mots clés: kripke structures; inverse operators; order theory; constraint systems; modal algebra; bisimulation; modal logic

Domaines: Logique en informatique [cs.LO]; Mathématique discrète [cs.DM]; Logique [math.LO]; Système multi-agents [cs.MA]

Michell Guzman, Salim Perchy, Camilo Rueda, Frank Valencia. Deriving Inverse Operators for Modal Logic. Theoretical Aspects of Computing – ICTAC 2016, Oct 2016, Taipei, Taiwan. pp.214-232, ⟨10.1007/978-3-319-46750-4_13⟩. ⟨hal-01328188v2⟩