A time-indexed mereology for SUMO

Abstract

While the period of time during which a subprocess occurs is precisely the time during which the part-whole relation with its main process takes place, part-whole relations between objects do not obey such a rule. The parts of an object can exist before the object is conformed as such, and can survive its dismantlement. In fact, there are no means for knowing when, during the existence of the part and the whole, their parthood relation holds unless an explicit account of time is represented. A time-indexed mereology characterizes how objects gain and lose parts over time by associating a time index to their part-whole relations. Keeping an account of when objects lose or gain parts is necessary for the correct representation of their spatial location and their participation in processes. Upper-level ontologies characterize the properties of the most basic, domain-independent entities, such as time, space, objects and processes. Two upper-level ontologies broadly used are The Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE) and The Suggested Upper Merged Ontology (SUMO). However, while DOLCE provides a first-order time-indexed mereology for structuring its entities over time, SUMO provides a weaker axiomatization that does not represent the rules that determine how the mereological structure of objects evolve through time in the real world. This work proposes a first-order logic time-indexed mereology for SUMO based on its current representation of objects, time, and temporal location, thereby characterizing how objects gain and lose parts over time. The proposed theory sets the stage for the development of a time-indexed theory of spatial location, and for the representation of temporal restrictions on the participation of objects in processes. The time-indexed mereology of DOLCE and the proposed theory are formally compared, and their relative strength established by using ontology mapping. In order to achieve such a comparison, the representations of time, and temporal location of both upper-level ontologies are also formally compared.