**Dept. of Computer and Information science, Linköping University**

## IDA Technical Reports: abstract

*Generated: Wed, 18 Jan 2017 00:30:38 *

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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