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Qualitative Constraint Calculi: Heterogeneous Verification of Composition Tables

Stefan Wölfl; Till Mossakowski; Lutz Schröder
In: David Wilson; Geoff Sutcliffe (Hrsg.). 20th International FLAIRS Conference. International FLAIRS Conference (FLAIRS-20), May 7-9, Key West, Florida, USA, Pages 665-670, AAAI Press, 2007.


In the domain of qualitative constraint reasoning, a subfield of AI which has evolved in the past 25 years, a large number of calculi for efficient reasoning about spatial and temporal entities have been developed. Reasoning techniques developed for these constraint calculi typically rely on the respective composition table of the calculus at hand, but often these composition tables are developed in a quite informal manner only and hence are prone to errors. In view of possible safety critical applications of qualitative calculi it is desirable to formally verify these composition tables. In general, however, the verification of composition tables is a tedious task, in particular, in those cases where the semantics of the calculus depends on higher-order constructs such as sets. In this paper we address this problem by presenting a heterogeneous proof method that allows for combining a higher-order proof assistance system (such as Isabelle) with an automatic (first order) reasoner (such as SPASS). The benefit of this method is that the number of proof obligations that is to be proven by hand with a semi-automatic reasoner can be minimized to an acceptable level.

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