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Communication Dans Un Congrès Année : 2018

Constructive Decision via Redundancy-Free Proof-Search

Procédure de décision constructive par recherche de preuves non-redondantes

Résumé

We give a constructive account of Kripke-Curry’s method which was used to establish the decidability of Implicational Relevance Logic (R→). To sustain our approach, we mechanize this method in axiom-free Coq, abstracting away from the specific features of R→ to keep only the essential ingredients of the technique. In particular we show how to replace Kripke/Dickson’s lemma by a constructive form of Ramsey’s theorem based on the notion of almost full relation. We also explain how to replace König’s lemma with an inductive form of Brouwer’s Fan theorem. We instantiate our abstract proof to get a constructive decision procedure for R→ and discuss potential applications to other logical decidability problems.
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Dates et versions

hal-02333361 , version 1 (09-11-2020)

Identifiants

Citer

Dominique Larchey-Wendling. Constructive Decision via Redundancy-Free Proof-Search. 9th International Joint Conference on Automated Reasoning, IJCAR 2018, Jul 2018, Oxford, United Kingdom. pp.422-438, ⟨10.1007/978-3-319-94205-6_28⟩. ⟨hal-02333361⟩
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