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International Conference on Temporal Logic

ICTL 1994: Temporal Logic pp 430–444Cite as

Annotation-based deduction in temporal logic

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 827))

Abstract

This paper presents a deductive system for predicate temporal logic with induction.

Representing temporal operators by first-order expressions enables temporal deduction to use the already developed techniques of first-order deduction. But when translating from temporal logic to first-order logic is done indiscriminately, the ensuing quantifications and comparisons of time expressions encumber formulas, hindering deduction. So in the deductive system presented here, translation occurs more carefully, via reification rules. These rules paraphrase selected temporal formulas as nontemporal first-order formulas with time annotations. This time reification process suppresses quantifications (the process is analogous to quantifier skolemization) and uses addition instead of complicated combinations of comparisons. Some ordering conditions on arithmetic expressions can arise, but such are handled automatically by a special-purpose unification algorithm plus a decision procedure for Presburger arithmetic.

This deductive system is relatively complete.

This research was supported in part by the National Science Foundation under grant CCR-92-23226, by the Advanced Research Projects Agency under contract NAG2-703 and grant NAG2-892, and by the United States Air Force Office of Scientific Research under contract F49620-93-1-0139.

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References

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Author information

Authors and Affiliations

  1. Computer Science Department, Stanford University, 94305, Stanford, California, USA

    Hugh McGuire & Zohar Manna

  2. Artificial Intelligence Center, SRI International, 94025, Menlo Park, California, USA

    Richard Waldinger

Authors
  1. Hugh McGuire
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  2. Zohar Manna
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  3. Richard Waldinger
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Editor information

Dov M. Gabbay Hans Jürgen Ohlbach

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© 1994 Springer-Verlag Berlin Heidelberg

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McGuire, H., Manna, Z., Waldinger, R. (1994). Annotation-based deduction in temporal logic. In: Gabbay, D.M., Ohlbach, H.J. (eds) Temporal Logic. ICTL 1994. Lecture Notes in Computer Science, vol 827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014003

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  • DOI: https://doi.org/10.1007/BFb0014003

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58241-0

  • Online ISBN: 978-3-540-48585-8

  • eBook Packages: Springer Book Archive

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