Temporal optimisations and temporal cardinality on the tOWL language

The tOWL language is a temporal web ontology language based on OWL-DL without nominals. The language enables the representation of time and time-related aspects, such as state transitions. The design choices of the language pose new challenges from a temporal perspective. One such challenge is the representation of temporal cardinality. Another challenge consists of optimising the temporal representations in order to reduce the number of axioms. One such optimisation is temporal coalescing, which merges concepts that are associated with time intervals that either meet or share at least one instant with each other. In this paper we formally introduce these concepts into the tOWL language and illustrate how they can be applied.