A theory of time and temporal incidence based on instants and periods

Time is fundamental in representing and reasoning about changing domains. A proper temporal representation requires characterizing two notions: (1) time itself, and (2) temporal incidence, i.e. the domain-independent properties for the truth-value of fluents and events throughout time. There are some problematic issues, such as the expression of instantaneous events and instantaneous holding of fluents, the specification of the properties for the temporal holding of fluents, and the “dividing instant problem”. This paper presents a theory of time and temporal incidence which is more natural than its predecessors and satisfactorily addresses the issues above. Our theory of time, called ℐ𝒫 (Instants and Periods), is based on having instants and periods at equal levels. We define a theory of temporal incidence upon it, whose main original feature is the distinction between continuous and discrete fluents