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Article Dans Une Revue Journal of Automated Reasoning Année : 2020

Constructive Decision via Redundancy-Free Proof-Search

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-02944196 , version 1 (21-09-2020)

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Dominique Larchey-Wendling. Constructive Decision via Redundancy-Free Proof-Search. Journal of Automated Reasoning, 2020, Special issue: Selected Extended Papers from IJCAR 2018, ⟨10.1007/s10817-020-09555-y⟩. ⟨hal-02944196⟩
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