Recursive representation of periodicity and temporal reasoning

Representing and reasoning with repeated and periodic events is important in many real-world domains, such as protocol and guideline management. In this set, it is important to give support to complex periodicities, that can involve non-symmetric repetitions, imprecision, variability, pauses between repetitions, and nested time intervals. Also, in these domains it can be useful to give support to composite events, as well as classes of events (i.e. types of actions) and instances of events (i.e. specific actions). In this paper, we propose a general-purpose domain-independent knowledge server dealing with all these issues. In particular, we describe a compact and (hopefully) user-friendly formalism for representing repetition/periodicity temporal constraints that supports arbitrarily nested repetitions as well as possibly imprecise and variable delays between repetitions. Moreover, we define two algorithms for performing consistency checking on knowledge bases of (possibly repeated/periodic) classes and instances of events retaining the efficiency of less expressive approaches.