Defining Relations: A General Incremental Approach with Spatial Temporal Case Studies

Brandon Bennett, Heshan Du, Lucía Gómez Álvarez, Anthony G. Cohn

Abstract: This paper aims to lay a foundation for a systematic study of mechanisms for construction of definitions within a formal theory, by investigating operators for incremental construction of definitions of new relations from an existing set of primitives and previously defined relations. To illustrate our method, we apply it to two of the best known relation sets studied in KRR: Allen's Interval Algebra and Region Connection Calculus. We also show that systematic exploration of definitional possibilities can yield interesting insights into relation sets that were originally defined in a more ad hoc way, and opens the possibility for discovering new vocabulary for extending or refining existing calculi or for developing completely new calculi.