Uniform labelled calculi for preferential conditional logics based on neighbourhood semantics - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Logic and Computation Year : 2021

Uniform labelled calculi for preferential conditional logics based on neighbourhood semantics

Abstract

The preferential conditional logic $\mathbb{PCL}$, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalise Lewis' sphere models for counterfactual logics, is proposed. Soundness and completeness of $\mathbb{PCL}$ and its extensions with respect to this class of models are proved directly. Labelled sequent calculi for all logics of the family are then introduced. The cal-culi are modular and have standard proof-theoretical properties, the most important of which is admissibility of cut, that entails a syntactic proof of completeness of the calculi. By adopting a general strategy, root-first proof search terminates, thereby providing a decision procedure for $\mathbb{PCL}$ and its extensions. Finally, the semantic completeness of the calculi is established: from a finite branch in a failed proof attempt it is possible to extract a finite countermodel of the root sequent. The latter result gives a constructive proof of the finite model property of all the logics considered.
Fichier principal
Vignette du fichier
girlando_negri_olivetti_JLC2021.pdf (608.85 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-02330319 , version 1 (23-10-2019)
hal-02330319 , version 2 (06-04-2021)
hal-02330319 , version 3 (03-02-2022)

Identifiers

Cite

Marianna Girlando, Sara Negri, Nicola Olivetti. Uniform labelled calculi for preferential conditional logics based on neighbourhood semantics. Journal of Logic and Computation, 2021, 31 (3), pp.947-997. ⟨10.1093/logcom/exab019⟩. ⟨hal-02330319v3⟩
251 View
162 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More