A unifying semantics for time and events

We give a formal semantics for a highly expressive language for representing temporal relationships and events. This language, which we call Versatile Event Logic (VEL), provides a general temporal ontology and semantics encompassing many other representations. The system incorporates a number of features that have not been widely employed in AI formalisms. It has the ability to describe alternative histories using a modal operator. It provides a semantics for individuals that explicitly models their identity through time and across alternative possible histories; and enables one to distinguish between necessary and extensional identity of individuals. In virtue of its treatment of individuals and count nouns, the formalism offers a solution to certain puzzles of identity, which arise when individuals are described in different ways. We propose that VEL can be used as a foundational interlingua for comparing and interfacing different AI languages and illustrate this by considering how Situation Calculus and Event Calculus can be represented within VEL.