A metric time-point and duration-based temporal model

Abstract

Constraint-based formalisms are a useful and common way to deal with temporal reasoning tasks. Assertions represent temporal constraints between temporal objects, time-points or intervals: Metric temporal constraints between time points permit us to express a minimum and maximum temporal distance between two time points and to define a valid temporal interval for each one. However, existing approaches have limited expressiveness for representing non-disjunctive qualitative constraints of point algebra and the empirical results do not seem very adequate for managing a great number of time points or when the time for management is limited.In this paper, an efficient and expressive time point and duration-based temporal representation model with metric constraints is presented. The main features of the model refer to the formal properties of the internal time model and the specific representation of temporal constraints, which integrates constraints on time-points and on durations and is more adequate for their computational management. Sound and complete management processes are specified on the basis of model properties. From this specification, two choices for management are proposed: (i) with neither propagation nor preprocessing techniques, complete management algorithms have an O(e*n) complexity, but a linear empirical cost is obtained; (ii) with complete propagation an O(n 2 ) complexity is achieved.