Sandewall, E. (1989). Combining Logic and Differential Equations for Describing Real-World Systems. Technical Report LiTH-IDA-R-89-38, Department of Computer and Information Science, Linköping University, Sweden. Also in Proc. of the Conf. on Representation and Reasoning about Knowledge, Toronto, Canada, 1989. (bibtex),
Abstract: The paper shows how to combine non-monotonic temporal logic with differential calculus. A temporal logic is defined where time is real-valued and not discrete, and where real-valued, continuous parameters are used with their derivatives. Differential equations can therefore be used directly as axioms, and need not be transformed into confluences. This logic is used for characterizing common-sense physical systems where some parameters, or some of their derivatives, are occasionally discontinuous. Differential calculus then serves for characterizing the parameters during time-segments where they are continuous, and logic is used for characterizing the parameters around the discontinuity points. Models and preferential entailment is defined for this logic. For a simple scenario example (ball falling into shaft) it is shown what geometrical and physical axioms are needed, and how the axioms preferentially entail the desired common-sense conclusion.
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