A formalization of structured temporal objects and repetition

We propose an approach to formally representing structured temporal objects. These new temporal objects are recursively made up of convex intervals and Allen's convex relations. The major emphasis in our approach is on temporal repetition. To that effect we define the time loop. Time loops allow us to abstract common elements in repetitive temporal patterns. A loop is parameterized by a cycle which is a structured temporal element possibly including subloops, a relation between instances of the cycle and a repetition factor or dimension. Atemporal assertions are true during these temporal objects, and thus this formalism allows one to concisely represent and reason with assertions which have an inherent temporal structure. Hence, this formalism allows one to concisely represent, for example, the scheduling of regular meetings in a university, where meeting may in turn be composed of structured repetitive processes such as those occurring in an assembly line.