On A Semi-Automatic Method for Generating Composition Tables

Originating from Allen's Interval Algebra, composition-based reason- ing has been widely acknowledged as the most popular reasoning technique in qualitative spatial and temporal reasoning. Given a qualitative calculus (i.e. a re- lation model), the first thing we should do is to establish its composition table (CT). In the past three decades, such work is usually done manually. This is un- desirable and error-prone, given that the calculus may contain tens or hundreds of basic relations. Computing the correct CT has been identified by Tony Cohn as a challenge for computer scientists in 1995. This paper addresses this problem and introduces a semi-automatic method to compute the CT by randomly gen- erating triples of elements. For several important qualitative calculi, our method can establish the correct CT in a reasonable short time. This is illustrated by ap- plications to the Interval Algebra, the Region Connection Calculus RCC-8, the INDU calculus, and the Oriented Point Relation Algebras. Our method can also be used to generate CTs for customised qualitative calculi defined on restricted domains. Relations in each particular qualitative calculus are used to represent temporal or spatial information at a certain granularity. For example, The Netherlands is west of Germany, The Alps partially overlaps Italy, I have today an appointment with my doctor followed by a check-up. Given a set of qualitative knowledge, new knowledge can be derived by using con- straint propagation. Consider an example in RCC-5. Given that The Alps partially over- laps Italy and Switzerland, and Italy is a proper part of the European Union (EU), and Switzerland is discrete from the EU, we may infer that The Alps partially overlaps the EU. The above inference can be obtained by using composition-based reasoning. The composition-based reasoning technique has been extensively used in qualitative

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