Reasoning about time often involves incomplete information about periods and their relationships. Varieties of incompleteness include uncertainty about the number of objects involved, the distribution of a set of temporal relations among these objects, and what can be called the participation of a set of objects in a temporal relation. A solution to the problem of representing and reasoning about incomplete temporal information of these kinds is forthcoming if a restricted class of non-convex intervals (called n-tntervals) is added to the temporal domain of discourse. An n-interval corresponds to the common sense notion of a recurring period of time with a (possibly) unspecified number of occurrences. In this paper, we formalize a representation for temporal reasoning problems using n-intervals. The language of the framework is restricted in such a way that tractable techniques from constraint satisfaction can be applied. Specifically, it is demonstrated how the problem of determining path-consistency in a network of binary n-interval relations can be solved.
[1]
Peter B. Ladkin,et al.
Time Representation: A Taxonomy of Internal Relations
,
1986,
AAAI.
[2]
P. V. Beek.
Exact and approximate reasoning about qualitative temporal relations
,
1992
.
[3]
Henry A. Kautz,et al.
Integrating Metric and Qualitative Temporal Reasoning
,
1991,
AAAI.
[4]
Johannes A. G. M. Koomen.
Localizing Temporal Constraint Propagation
,
1989,
KR.
[5]
Eugene C. Freuder.
Synthesizing constraint expressions
,
1978,
CACM.
[6]
Gérard Ligozat,et al.
Weak Representations of Interval Algebras
,
1990,
AAAI.
[7]
Johannes A. G. M. Koomen.
Localizing temporal constraint propagation: defaults and exceptions
,
1989,
KR 1989.
[8]
James F. Allen.
Maintaining knowledge about temporal intervals
,
1983,
CACM.
[9]
Lina Khatib,et al.
An interval-based temporal relational calculus for events with gaps
,
1991,
J. Exp. Theor. Artif. Intell..