Integrated Temporal Reasoning with Periodic Events

Abstract

In many areas of Computer Science, including planning, workflows, guidelines, and protocol management, one has to deal with abstract plans, procedures, or schedules involving temporal constraints between classes of actions that have to be repeated at periodic times and may be instantiated in Ž . different ways for different executions of the plans procedures, schedules . In this paper we propose an integrated framework to deal with both qualitative temporal constraints on classes of actions and temporal constraints between instances of actions, in which temporal reasoning is used to amalgamate both types of constraints and to check their consistency. In particular, we consider an expressive Ž formalism to deal with temporal constraints between classes of actions with special attention to . periodic actions which takes into account different components such as frame times, numeric quantifi-Ž . cation, periods, and qualitative relations. We define the notions of contextual concretization of qualitative temporal constraints between classes and use this notion to formally define the consistency of a knowledge base of temporal constraints between classes and a set of temporal constraints on instances, and to define the algorithm for checking such a consistency. An application for scheduling lessons in a school is shown in an example.

Temporal reasoning about composite and/or periodic events

“…We also proposed an initial algorithm to check the consistency of a knowledge base of such constraints with a set of instances of events exactly located in time (Terenziani 2000). Afterwards, we started to approach the problem of integrating both qualitative and quantitative constraints between classes and instances of events in a more general perspective, but not supporting periodic and composite events (Terenziani 2002, Terenziani andAnselma 2004), and proposed an initial approach to cope with qualitative and quantitative and periodic repetition constraints between classes of events in clinical guidelines (Terenziani et al 2002a, b, Terenziani and.…”

Recursive representation of periodicity and temporal reasoning

“…In [19] Terenziani proposed a high-level language to deal with periodicity and in [13,23] a highlevel language to deal with period-dependent qualitative temporal constraints between repeated events, which are used as "classes". In [14] he also defined an initial algorithm for temporal reasoning with such constraints and a set of instances of events exactly located in time. In [16] he approached the problem of checking the [20] Terenziani and the author of this paper defined an approach dealing with periodic, qualitative, and quantitative constraints between both classes and instances of events.…”

Symbolic user-defined periodicity in temporal relational databases

“…For instance, within the artificial intelligence community, most attention has been devoted to the treatment of qualitative temporal constraints (e.g., "before") between events which repeat in time (see, e.g., [25], [26], [28], [33], [40], [43]). On the other hand, approaches in classical temporal logic (see, e.g., [1], [30]) deal with truth and validity of logical formulae, specifying how predicates change value over time.…”