Analytic proof theory for Åqvist's system F - Aix-Marseille Université
Communication Dans Un Congrès Année : 2023

Analytic proof theory for Åqvist's system F

Résumé

The key strength of preference-based logics for conditional obligation is their ability to handle contrary-to-duty paradoxes and account for exceptions. Here we investigate Åqvist's system F, a well-known logic in this family. F has the notable feature that every satisfiable formula has a "best" element. Thus far, the only proof system for F was a Hilbert calculus, impeding applications and deeper investigations. We fill this gap, constructing the first analytic calculus for F. The calculus possesses good proof-theoretical properties-in particular, cut-elimination, which greatly facilitates proof search. Our calculus is used to provide explanations of logical consequences, as a decision-making tool, and to obtain a preliminary complexity upper bound for F (giving a theoretical limit on its automated behavior).
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Dates et versions

hal-04457336 , version 1 (14-02-2024)

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  • HAL Id : hal-04457336 , version 1

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Agata Ciabattoni, Nicola Olivetti, Xavier Parent, Revantha Ramanayake, Dmitry Rozplokhas. Analytic proof theory for Åqvist's system F. Deontic Logic and Normative Systems - 16th International Conference, DEON 2023, Jul 2023, Trois Rivieres, Canada, Canada. ⟨hal-04457336⟩
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