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Communication Dans Un Congrès Année : 2019

A Dialectica-Like Interpretation of a Linear MSO on Infinite Words

Résumé

We devise a variant of Dialectica interpretation of intuition-istic linear logic for LMSO, a linear logic-based version MSO over infinite words. LMSO was known to be correct and complete w.r.t. Church's synthesis , thanks to an automata-based realizability model. Invoking Büchi-Landweber Theorem and building on a complete axiomatization of MSO on infinite words, our interpretation provides us with a syntactic approach , without any further construction of automata on infinite words. Via Dialectica, as linear negation directly corresponds to switching players in games, we furthermore obtain a complete logic: either a closed formula or its linear negation is provable. This completely axiomatizes the theory the realizability model of LMSO. Besides, this shows that in principle, one can solve Church's synthesis for a given ∀∃-formula by only looking for proofs of either that formula or its linear negation.
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Dates et versions

hal-01925701 , version 1 (17-11-2018)

Identifiants

  • HAL Id : hal-01925701 , version 1

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Cécilia Pradic, Colin Riba. A Dialectica-Like Interpretation of a Linear MSO on Infinite Words. FOSSACS'19, Apr 2019, Prague, Czech Republic. ⟨hal-01925701⟩
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