Towards a temporal reasoning approach dealing with instance-of, part-of and periodicity

Recursive representation of periodicity and temporal reasoning

“…This goal is motivated by our ongoing work in the domain of guidelines automation ( [15,18,21,22], see also subsection 5.2). A first step in this direction has been made in [20], but with limitations that in some real-world cases it is necessary to overcome: in fact, while that approach can handle Ex. 1, it cannot handle more complex periodicities such as the one sketched in Ex.…”

“…This case presents not only multiple nested time intervals (four years, 88 weeks, a week, a day), but also temporal constraints between repetitions -the two days must be consecutive -, and uncertainness -it is not specified when the two consecutive days must occur in the week. In the present work, we make a step further wrt [20]; specifically, we extend the formalism for the specification of repetitions/periodicity to a considerably more powerful one, and we accordingly define new algorithms for temporal reasoning to deal with all the aspects mentioned above. Moreover, we show that, even with the richer representation language, the complexity of the temporal reasoning algorithms does not increase wrt the complexity of the algorithms in [20].…”

“…In the present work, we make a step further wrt [20]; specifically, we extend the formalism for the specification of repetitions/periodicity to a considerably more powerful one, and we accordingly define new algorithms for temporal reasoning to deal with all the aspects mentioned above. Moreover, we show that, even with the richer representation language, the complexity of the temporal reasoning algorithms does not increase wrt the complexity of the algorithms in [20]. The paper is organized as follows: in section 2, we introduce the problems that our temporal manager has to address; in section 3, we describe the language for representing classes and instances of events, the language for representing constraints on periodicity, and the one employed for internal representation; in section 4, we deal with consistency checking on classes only and with consistency checking on classes+instances by means of constraint inheritance (both with the assumption of complete observability and with the assumption of no observability in the future); moreover, we discuss the complexity of the reasoning mechanisms and present some preliminary experimental results; finally, in section 5, we draw some conclusions, discuss the related works in literature, and present applications and future work.…”

“…To do so, we extend the tractable temporal manager proposed in [20] in the direction of: -enhancing the expressive power of the representation language, especially the formalism regarding the periodicity/repetition constraints; -developing new algorithms for temporal reasoning without increasing the complexity of the algorithms in [20].…”

“…The high-level constraint language about instances retains the language described in [20]. It provides primitives in order to represent (possibly imprecise) dates, delays between endpoints of events, durations, and qualitative constraints between endpoints of events.…”