# Uniform labelled calculi for preferential conditional logics based on neighbourhood semantics

1 PARTOUT - Automatisation et ReprésenTation: fOndation du calcUl et de la déducTion
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
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.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-02330319
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Submitted on : Thursday, February 3, 2022 - 9:45:22 AM
Last modification on : Tuesday, May 3, 2022 - 6:26:04 PM

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

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