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IP An Instant-Period--based Theory of Time
IP: An Instant-Period{based Theory of TimeLlus VilaIIIA { CSICCam de Sta. Barbara, s/n, 17300 Blanes, Catalonia, Spainvila@ceab.esAbstractInstants have been criticised as temporal primitive for common-sense reasoning onontological {for being just abstract entities not concerned with common-sense{ andsemantical {the Divided Instant Problem (DIP){ arguments. Therefore, period-basedtheories have received special attention. In this paper we provide arguments for incor-porating instants to the time ontology. We present an axiomatization of time basedon instants and periods (IP), characterize all the models of the theory, and exploreits relations with other Period{ and Instant-Period{based theories appeared in theAI community. Finally, we discuss its suitability for supporting temporal knowledgerepresentation and the Divided Instant Problem is revisited.1 IntroductionSeveral theories of time have been porposed aiming at providing a formal basis for common-sense reasoning in Articial Intelligence. Historically, the contenders as ontological primitiveof time has been two: points of time {instants{ and intervals of time {periods. Recalling the\temporal pioneers in AI, McDermott [11] proposed a theory based on a left-linearly right-partially ordered unbounded and dense collection of instants. Allen [1, 2], on the other hand,claims that the period should be the only temporal primitive since it is the most adequateconcept for representing both states and events. A general criticism against instant-basedtheories is their articiality {as long as, according to Allen Hayes [4], they start with somemathematical structure which uses to be too \rich wrt. the common-sense intuitions oneis intended to capture. Allen [1] takes a basic set of 13 primitive binary period relationsthat correspond to every possible simple qualitative relationship that may exist betweentwo periods. Given these relationships, Allen formulates a set of axioms that dene theirbehaviour in terms of the fol
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