Comparative plausibility in neighbourhood models: axiom systems and sequent calculi

TL;DR

This paper develops a unified proof theoretical framework for comparative plausibility logics over neighbourhood models, introducing axiom systems and analytic proof systems, and establishing soundness, completeness, and cut admissibility.

Contribution

It introduces a family of comparative plausibility logics with axiom systems and proof calculi, advancing the understanding of their semantics and proof theory.

Findings

Axiom systems for the family of logics are sound and complete.

Two types of analytic proof systems are developed: a sequent calculus and a hypersequent calculus.

Cut admissibility is proved for the sequent calculus.

Abstract

We introduce a family of comparative plausibility logics over neighbourhood models, generalising Lewis' comparative plausibility operator over sphere models. We provide axiom systems for the logics, and prove their soundness and completeness with respect to the semantics. Then, we introduce two kinds of analytic proof systems for several logics in the family: a multi-premisses sequent calculus in the style of Lellmann and Pattinson, for which we prove cut admissibility, and a hypersequent calculus based on structured calculi for conditional logics by Girlando et al., tailored for countermodel construction over failed proof search. Our results constitute the first steps in the definition of a unified proof theoretical framework for logics equipped with a comparative plausibility operator.