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Loop-Check Specification for a Sequent Calculus of Temporal Logic


In our previous work we have introduced loop-type sequent calculi for propositional linear discrete tense logic and proved that these calculi are sound and complete. Decision procedures using the calculi have been constructed for the considered logic. In the present paper we restrict ourselves to the logic with the unary temporal operators “next” and “henceforth always”. Proof-theory of the sequent calculus of this logic is considered, focusing on loop specification in backward proof-search. We describe cyclic sequents and prove that any loop consists of only cyclic sequents. A class of sequents for which backward proof-search do not require loop-check is presented. It is shown how sequents can be coded by binary strings that are used in backward proof-search for the sake of more efficient loop-check.

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Correspondence to Romas Alonderis.

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Presented by Jacek Malinowski; Received January 20, 2022.

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Alonderis, R., Pliuškevičius, R., Pliuškevičienė, A. et al. Loop-Check Specification for a Sequent Calculus of Temporal Logic. Stud Logica 110, 1507–1536 (2022).

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  • Temporal logics
  • Sequent calculi
  • Derivation loops