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The SOL time theory: a formalization of structured temporal objects and repetition

We propose to formally represent time with structured temporal objects. Structured temporal objects denote related time intervals (and recursively, related temporal objects) which are conceived as structured objects, rather than relations among such intervals. The major emphasis in this approach is on temporal repetition. To that effect, a new temporal object, the time loop, is defined. The intent of a time loop is to capture a structured notion of repetition. We propose a first order theory formalizing these objects. The building blocks of this formalism are time intervals and Allen's qualitative interval relations. We prove a number of key desirable results including the consistency of the theory, and extensively compare expressions in this theory with previous related work. We argue that this theory presents temporality and temporal repetition in a simple, commonsense manner. Furthermore, we argue that it presents an alternative, succinct and more general view than previous proposals to represent temporal repetition.