Toward a comprehensive treatment of temporal constraints about periodic events

Abstract

In this article, we propose an Allen-like approach to deal with different types of temporal constraints about periodic events. We consider the different components of such constraints (thus, unlike Allen, we also take into account quantitative constraints) including frame times, user-defined periods, qualitative temporal constraints, and numeric quantifiers and the interactions between such components. We propose a specialized high-level formalism to represent temporal constraints about periodic events; temporal reasoning on the formalism is performed by a path-consistency algorithm repeatedly applying our operations of inversion, intersection, and composition and by a specialized reasoner about periods and numeric quantification. The high-level formalism has been designed in such a way that different types of temporal constraints about periodic events can be represented in a compact and (hopefully) user-friendly way and path-consistency-based temporal reasoning on the formalism can be performed in polynomial time. We also prove that our definitions of inversion, intersection, and composition and, thus, of our path-consistency algorithm, are correct. This article also sketches the general architecture of the temporal manager for periodic events (TeMP ϩ ), that has been designed on the basis of our approach. As a working example, we show an application of our approach to scheduling in a school.

Temporal reasoning about composite and/or periodic events

“…In our previous work, we defined a high-level language to deal with user-defined periodicity (Terenziani 2003a) and with period-dependent qualitative temporal constraints between repeated events (which are coped with as 'classes' of events) and constraint propagation algorithms operating on them (Terenziani 1997(Terenziani , 2003b. 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).…”

“…Thus, in the field of Artificial Intelligence (henceforth, AI) many formalisms and reasoning techniques have been defined to deal with time-related phenomena. Roughly speaking, one could identify two different mainstreams (see Terenziani (2003b)). The first mainstream is mainly devoted to the definition of formalisms general enough to represent a wide range of temporal phenomena.…”

A knowledge server for reasoning about temporal constraints between classes and instances of events

“…In Ref. 34, we extended such an approach to cope also with numeric quantifiers (e.g., "each Tuesday, a unit of Math precedes two units of History"). On the other hand, issue iii is still an open problem.…”

Recursive representation of periodicity and temporal reasoning

“…Such constraints are used in a "predictive" way: temporal reasoning is used for projecting the constraints on the durations in the future using the current domain information. 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 the context of temporal constraint reasoning, in literature much attention has been devoted to some of these aspects (e.g. see the surveys in [2,23]). In particular, since the beginning of the eighties, several domain-independent knowledge servers specifically designed to manage temporal information (i.e.…”