De la théorie de la démonstration pour logiques conditionnelles
Marianna Girlando · Työväentutkimus Vuosikirja · 2019
This thesis can be ideally placed at the intersection of three research topics: conditional logics, proof theory and neighbourhood semantics. The family of logics under scope stems from the works of Stalnaker and Lewis, and extends classical propositional logic by means of a two-place modal operator, which expresses a fine-grained notion of conditionality. The semantics of these logics is modularly defined in terms of neighbourhoodmodels. The research aim is to investigate the proof theory of conditional logics, by defining sequent calculi for them. The proof systems introduced are extensions of Gentzen’s sequent calculus; they are either labelled, defined by enriching the language, or internal, which add structural connectives to the sequents. Moreover, the calculi are standard: they are composed of a finite number of rules, each displaying a fixed number of premisses.The thesis is organized in six chapters. Chapters 1 contains an axiomatic and semantic overview of conditional logics, while Chapter 2 is a short introduction to proof theory. The original contributions to the subject are presented in chapters 3 – 6. Chapter 3 introduces labelled calculi based on neighbourhood models for preferential conditional logics, and Chapter 4 presents different internal proof systems covering counterfactual logics, a subfamily of preferential logics. Chapter 5 analyses the relationship between proof systems by presenting a mapping between a labelled and an internal calculus. Finally, the proof-theoretic methods developed for conditional logics are applied in chapter 6 to a multi-agent epistemic logic.