Axiomatic theories of the ontology of time in GFO

Time is a pervasive notion of high impact in information systems and computer science altogether. Respective understandings of the domain of time are fundamental for numerous areas, frequently in combination with closely related entities such as events, changes, and processes. The conception and representation of time entities and reasoning about temporal data and knowledge are thus significant research areas. Each representation of temporal knowledge bears ontological commitments concerning time. Thus it is important to base temporal representations on a foundational ontology that covers general categories of time entities. In this article we introduce and discuss two consecutive ontologies of time that have been developed for the top-level ontology General Formal Ontology (GFO). The first covers intervals, named chronoids, and time boundaries of chronoids as a kind of time points. One important specialty of time boundaries is their ability to coincide with other time boundaries. The second theory extends the first one by additionally addressing time regions, i.e., mereological sums of chronoids. Both ontologies are partially inspired by ideas of Franz Brentano, especially from his writings about the continuum. In particular, we view continuous time intervals as a genuine phenomenon which should not be identified with intervals (sets) of real numbers. On these grounds the resulting ontologies allow for proposing novel contributions to several problematic issues in temporal representation and reasoning, among others, the Dividing Instant Problem and the problem of persistence and change. Following our general approach to ontology development, both ontologies are axiomatized as formal theories in first-order logic and are analyzed metalogically. We prove the consistency of both ontologies, and completeness and decidability for one. Moreover, standard time theories with points and intervals are covered by both theories.