Abstract
A method for the investigation of undecidable and noncompact temporal logic is presented. It begins with a construction of a Gentzen-like calculus containing some infinitary rules reflecting semantics of the temporal logic. Some semantic (e.g., completeness) and proof theoretical (e.g., cut elimination) properties for this infinitary calculus are proved. The main part of the method consists of reducing an arbitrary derivation in the infinitary restricted calculus into the cut-free derivation in the finitary calculus (in short reduction of the infinitary calculus to the finitary one). As the infinitary rules are similar to the ω-induction rule the method is called the ω-reduction. The method allows: 1) to construct a finitary calculus with efficient proof-theoretical properties and 2) to prove the completeness theorem for the considered restricted first order temporal logic.
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© 1991 Springer-Verlag Berlin Heidelberg
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Pliuškevičius, R. (1991). Investigation of finitary calculus for a discrete linear time logic by means of infinitary calculus. In: Bārzdinš, J., Bjørner, D. (eds) Baltic Computer Science. BCS 1991. Lecture Notes in Computer Science, vol 502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0019366
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DOI: https://doi.org/10.1007/BFb0019366
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