Abstract
Interval Temporal Logic (ITL) is a formalism for reasoning about time periods. To date no one has proved completeness of a relatively simple ITL deductive system supporting infinite time and permitting infinite sequential iteration comparable to ω-regular expressions. We have developed a complete axiomatization for such a version of quantified ITL over finite domains and can show completeness by representing finite-state automata in ITL and then translating ITL formulas into them. Here we limit ourselves to finite time. The full paper (and another conference paper [15]) extends the approach to infinite time.
Part of the research described here has been kindly supported by EPSRC research grant GR/K25922.
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References
H. Bowman and S. J. Thompson. A complete axiomatization of Interval Temporal Logic with projection. Technical Report 6-00, Computing Lab., Univ. of Kent, UK, Jan. 2000.
A. Cau and H. Zedan. Refining Interval Temporal Logic specifications. In M. Bertran and T. Rus, eds., Transformation-Based Reactive Systems Development, LNCS 1231, pp. 79–94. AMAST, Springer-Verlag, 1997.
B. Dutertre. Complete proof systems for first order interval temporal logic. In Proc. 10th LICS, pp. 36–43. IEEE Computer Soc. Press, June 1995.
M. J. Fischer and R. E. Ladner. Propositional dynamic logic of regular programs. J. Comput. Syst. Sci., 18(2):194–211, Apr. 1979.
R. W. S. Hale. Programming in Temporal Logic. PhD thesis, Computer Laboratory, Cambridge University, Cambridge, England, Oct. 1988.
J. Halpern, Z. Manna, and B. Moszkowski. A hardware semantics based on temporal intervals. In J. Diaz, ed., Proc. ICALP’ 83, LNCS 154, pp. 278–291. Springer-Verlag, 1983.
Y. Kesten and A. Pnueli. A complete proof system for QPTL. In Proc. 10th LICS, pp. 2–12. IEEE Computer Soc. Press, 1995.
B. Moszkowski. Reasoning about Digital Circuits. PhD thesis, Dept. Computer Science, Stanford Univ., 1983. Tech. rep. STAN-CS-83-970.
B. Moszkowski. A temporal logic for multi-level reasoning about hardware. In Proc. 6-th Int’l. Symp. on Computer Hardware Description Languages, pp. 79–90, Pittsburgh, Penn., May 1983. North-Holland Pub. Co.
B. Moszkowski. A temporal logic for multilevel reasoning about hardware. Computer, 18:10–19, 1985.
B. Moszkowski. Executing Temporal Logic Programs. Cambridge U. Press, 1986.
B. Moszkowski. Some very compositional temporal properties. In E.-R. Olderog, ed., Programming Concepts, Methods and Calculi, IFIP Transactions A-56, pp. 307–326. IFIP, Elsevier Science B.V (North-Holland), 1994.
B. Moszkowski. Compositional reasoning about projected and infinite time. In Proc. 1st IEEE Int’l Conf. on Engineering of Complex Computer Systems (ICECCS’95), pp. 238–245. IEEE Computer Soc. Press, 1995.
B. Moszkowski. Compositional reasoning using Interval Temporal Logic and Tempura. In W.-P. deRoever et al., eds., Compositionality: The Significant Difference, LNCS 1536, pp. 439–464. Springer-Verlag, 1998.
B. Moszkowski. A complete axiomatization of interval temporal logic with infinite time. In Proc. 15th Annual IEEE Symp. on Logic in Computer Science (LICS 2000). IEEE Computer Soc. Press, June 2000.
B. Paech. Gentzen-systems for propositional temporal logics. In E. Börger et al., eds., Proc. 2nd Workshop on Computer Science Logic, Duisburg (FRG), LNCS 385, pp. 240–253. Springer-Verlag, Oct. 1988.
V. R. Pratt. Semantical considerations on Floyd-Hoare logic. In 17-th Annual IEEE Symposium on Foundations of Computer Science, pp. 109–121, 1976.
R. Rosner and A. Pnueli. A choppy logic. In Proc. 1st LICS, pp. 306–313. IEEE Computer Soc. Press, June 1986.
D. Siefkes. Decidable Theories I: Büchi’s Monadic Second Order Successor Arithmetic, Lecture Notes in Mathematics 120. Springer-Verlag, Berlin, 1970.
Wang Hanpin and Xu Qiwen. Temporal logics over infinite intervals. Technical Report 158, UNU/IIST, Macau, 1999.
Zhou Chaochen, C. A. R. Hoare, and A. P. Ravn. A calculus of durations. Inf. Process. Lett., 40(5):269–276, 1991.
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Moszkowski, B.C. (2000). An Automata-Theoretic Completeness Proof for Interval Temporal Logic. In: Montanari, U., Rolim, J.D.P., Welzl, E. (eds) Automata, Languages and Programming. ICALP 2000. Lecture Notes in Computer Science, vol 1853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45022-X_19
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DOI: https://doi.org/10.1007/3-540-45022-X_19
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