A sequent calculus for a first order linear temporal logic with equality

  • Jurate Sakalauskaite
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 620)


We consider a first order temporal logic of linear discrete time with temporal modalities ○ (“next”), D (“always in the future”) which includes equality, time-dependant predicate as well as time-dependant function symbols. It is known that this logic is not finitary axiomatizable. We present an infinite cut-free Gentzen-style calculus for the logic. The inference rules for equality which have no counterparts in sequent calculi for first order predicate logic with equality are introduced. Soundness and completeness are proved for the calculus.


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  1. 1.
    M.Abadi, The power of temporal proofs, Theoret. Comput. Sci. 65 (1989), 35–83.CrossRefGoogle Scholar
  2. 2.
    H.Andreka, I.Nemeti, I.Sain, On the strength of temporal proofs, Proc. Conf. MFCS'89, LNCS 379, Springer Verlag, Berlin (1989), 135–144.Google Scholar
  3. 3.
    J.H.Gallier, Logic for computer science, Harper & Row Publishers, New York, (1986).Google Scholar
  4. 4.
    J.W.Garson, Quantification in modal logic in: D. Gabbay and F.Guenthner (eds.), Handbook of Philosophical Logics II, D.Reidel Publishing Company, (1984), 249–309.Google Scholar
  5. 5.
    S.Kanger, A simplified proof method for elementary logic, Computer Programming and Formal Systems, North-Holland, Amsterdam (1963), 87–94.Google Scholar
  6. 6.
    H.Kawai, Sequential calculus for a first order infinitary temporal logic, Zeitschr. f. math. Logic und Grundlagen d.Math. 33 (1987), 423–432.Google Scholar
  7. 7.
    F.Kröger, LAR: a logic for algorithmic reasoning about programs, Acta Informatica 8 (1977), 242–260.CrossRefGoogle Scholar
  8. 8.
    V.A.Lifshitz, Specialization of the form of deduction in the predicate calculus with equality and function symbols, Proc. Steklov Inst. Math. 98 (1968), 1–24.Google Scholar
  9. 9.
    Z.Manna, A.Pnueli, How to cook a temporal proof system for your pet language, in: Proc. Tenth ACM Symp. on Principles of Programming Languages (1983), 141–154.Google Scholar
  10. 10.
    G.Mirkowska, A. Salwicki, Algorithmic logic, D. Reidel Publishing Company (1987), 56–64.Google Scholar
  11. 11.
    R.Pliuškevičius, Investigation of finitary calculus for a discrete linear time logic by means of finitary calculus, LNCS 502, Springer Verlag, Berlin (1991) 504–528.Google Scholar
  12. 12.
    A.Szalas, A complete axiomatic characterization of first-order temporal logic of linear time, Theoretical Comp. Sci. 54 (1987), 199–214.CrossRefGoogle Scholar
  13. 13.
    M.E.Szabo, A sequent calculus for Kröger's logic, LNCS 148, Springer Verlag, Berlin (1983) 295–303.Google Scholar
  14. 14.
    G.Takeuti, Proof theory, North-Holland (1975).Google Scholar
  15. 15.
    S.C.Kleene, Mathematical logic, John Wiley & Sons, Inc., New York (1967).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Jurate Sakalauskaite
    • 1
  1. 1.Institute of Mathematics and InformaticsVilniusLithuania

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