The logic of conditional beliefs: neighbourhood semantics and sequent calculus

Marianna Girlando (1, 2) , Sara Negri (3) , Nicola Olivetti (1, 2) , Vincent Risch (1)

1 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
2 LIRICA - Logique, Interaction, Raisonnement et Inférence, Complexité, Algèbre
3 Helsingin yliopisto = Helsingfors universitet = University of Helsinki

The logic of Conditional Beliefs has been introduced by Board, Baltag and Smets to reason about knowledge and revisable beliefs in a multi-agent setting. It is shown that the semantics of this logic, defined in terms of plausibility models, can be equivalently formulated in terms of neighbourhood models, a multi-agent generalisation of Lewis' spheres models. On the base of this new semantics, a labelled sequent calculus for this logic is developed. The calculus has strong proof-theoretic properties, in particular cut and contraction are admissible and that the calculus provides a direct decision procedure for this logic. Further, its semantic completeness is used to obtain a constructive proof of the finite model property of the logic.

Mots clés: Epistemic logic; conditional logic; neighbourhood semantics; sequent calculus; decision procedure

Domaines: Informatique [cs]

Marianna Girlando, Sara Negri, Nicola Olivetti, Vincent Risch. The logic of conditional beliefs: neighbourhood semantics and sequent calculus. Advances in Modal Logics 2016, L. Beklemishev, S. Demri and A. Màté, Aug 2016, Budapest, Hungary. pp.322-341. ⟨hal-01794369⟩