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— This paper deals with the relationship between the termination of programs and the validity of certain modal formulas. We give a complete proof procedure for these formulas, which will allow to bring the correetness of these programs back to aproblem ofautomatic theorem-proving in modal logic. Résumé. — Cet article concerne la relation entre la terminaison de programmes et la validité de certaines formules modales. Une procédure complète de démonstration pour ces formules est présentée, ce qui nous permettra de ramener la correction de ces programmes à un problème de démonstration automatique en logique modale.

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