Abstract
We describe how we used the interactive theorem prover Isabelle to formalise and check the laws of the Timed Interval Calculus (TIC). We also describe some important corrections to, clarifications of, and flaws in these laws, found as a result of our work.
Supported by an Australian Research Council Large Grant
Supported by an Australian Research Council QEII Fellowship
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J F Allen. Towards a theory of action and time. Artif. Intel. 23:123–154, 1984.
A Cerone. Axiomatisation of an Interval Calculus for Theorem Proving. In C J Fidge (Ed), CATS’00: Elect. Notes in Theor. Comp. Sci. 42, Elsevier 2001.
A Church. A formulation of the simple theory of types. JSL, 5:56–68, 1940.
C J Fidge, I J Hayes, A P Martin, A K Wabenhorst, A Set-Theoretic Model for Real-Time Specification and Reasoning. In J Jeuring (Ed), Proc. MPC’98, LNCS 1422:188–206, Springer, 1998.
R I Goldblatt, Logics of Time and Computation, CSLI Lecture Notes Number 7, Center for the Study of Language and Information, Stanford, 1987.
S T Heilmann, Proof Support for Duration Calculus, PhD thesis, Dept. of Inf. Tech., Tech. Univ. of Denmark, Jan. 1999. See http://www.sth.dk/sth/.
M J C Gordon and T F Melham. Introduction to HOL: a Theorem Proving Environment for Higher Order Logic. Cambridge University Press, 1993.
L C Paulson. The Isabelle Reference Manual. Comp. Lab., Univ. of Cambridge, 1999. See http://www.cl.cam.ac.uk/Research/HVG/Isabelle/docs.html
L C Paulson. Isabelle’s Logics. Computer Lab. Univ. of Cambridge, 1999. See http://www.cl.cam.ac.uk/Research/HVG/Isabelle/docs.html
B P Mahony and C Millerchip and I J Hayes. A boiler control system: A case study in timed refinement. International Invitational Workshop-Design and Review of Software Controlled Safety-Related Systems, Ottawa, June, 1993.
J Skakkebæk, A verification assistant for a real-time logic, PhD thesis, TR 150, Dept. of Computer Science, Technical University of Denmark, 1994.
A Wabenhorst. Induction in the Timed Interval Calculus. Technical Report 99-36, SVRC, University of Queensland, 1999.
M R Hansen and Z Chaochen. Duration calculus, logical foundations. Formal Aspects of Computing, 9 (1997), 283–303.
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© 2002 Springer-Verlag Berlin Heidelberg
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Dawson, J.E., Goré, R. (2002). Machine-Checking the Timed Interval Calculus. In: McKay, B., Slaney, J. (eds) AI 2002: Advances in Artificial Intelligence. AI 2002. Lecture Notes in Computer Science(), vol 2557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36187-1_9
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DOI: https://doi.org/10.1007/3-540-36187-1_9
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