An Algebraic Formulation of Temporal Knowledge for Reasoning about Recurring Events

We formulate an algebra of binary tem poral relations between events the number of occurrences of which is unknown but which are known to recur in time Onto logically we view the temporal domain of recurring events as a set of convex in tervals of unknown cardinality Thus an explicit declarative representation of time adequate to solve reasoning problems in volving recurring events indicates a form of higher order reasoning about relations be tween collections or sequences of intervals The relations de ned here are each formed out of convex interval relations by apply ing an operator like always or some times An operator of this kind imposes a mapping between subintervals of one set of intervals and subintervals of another Al though in general higher order reasoning problems are undecidable a restricted sys tem for reasoning about binary relations between collections of intervals is demon strably tractable The means to achieving this desirable result is to impose restric tions on the kinds of mappings imposed by the temporal operators Despite this restriction in expressive power non trivial reasoning problems can be solved utilizing this class of relations