@techreport{R-89-38,
TITLE = {Combining Logic and Differential Equations for Describing Real-World Systems},
AUTHOR = {Erik Sandewall},
YEAR = {1989},
NUMBER = {R-89-38},
INSTITUTION = ida,
ADDRESS = idaaddr,
ABSTRACTURL = {/publications/cgi-bin/tr-fetch.pl?r-89-38+abstr},
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.},
IDANR = {LiTH-IDA-R-89-38},
NOTE = {Also in Proc. of the Conf. on Representation and Reasoning about Knowledge, Toronto, Canada, 1989}