On an ω-Decidable Deductive Procedure for Non-Horn Sequents of a Restricted FTL
A new deduction-based procedure is presented for non-Horn, so-called DR-sequents with repetitions of a restricted first-order linear temporal logic with temporal operators “next” and “always”. The main part of the proposed deductive procedure is automatic generation of the inductive hypothesis. The proposed deductive procedure consists of three separate decidable deductive procedures replacing the infinitary omega-type rule for the operator “always”. These three decidable parts cannot be joined. Therefore the proposed deductive procedure (by analogy with ω-completeness) is only ω-decidable. The specific shape of DR-sequents allows us in all the three parts of the proposed deductive procedure to construct: (1) a deduction tree in some linear form, i.e., with one ”temporal” branch; (2) length-preserving derivations, i.e., the lengths of generated sequents are the same.
KeywordsSimilarity Index Temporal Logic Function Symbol Atomic Formula Linear Temporal Logic
Unable to display preview. Download preview PDF.
- 2.Fisher M.: A normal form for temporal logics and its applications in theorem proving and execution. Journal of Logic and Computation 7(4) (1997).Google Scholar
- 4.Hodkinson I., Wolter F., Zakharyaschev M.: Decidable fragments of first-order temporal logics. (To appear in: Annals of Pure and Applied Logic).Google Scholar
- 6.Pliuškevičius R.: The saturated tableaux for a linear miniscoped Horn-like temporal logic. Journal of Automated Reasoning 13 (1994) 51–67.Google Scholar
- 9.Pliuškevičius R.: An effective deductive procedure for a restricted first-order linear temporal logic. (Submitted to Annals of Pure and Applied Logic).Google Scholar