Qualitative and quantitative temporal constraints about numerically quantified periodic events

The paper describes an integrated temporal formalism which deals with (i) quantitative information about the frame of time and the user-defined calendar-dates (periods) in which periodic events are located, (ii) (possibly multiple) numeric quantifiers indicating the number of repetitions of events and (iii) qualitative relations between periodic events. The paper defines the operations of intersection and composition of temporal specifications in the given formalism, which are used in order to perform temporal reasoning. An algorithm supporting specialised forms of reasoning about the number of repetitions of events is also described. Moreover, the paper introduces an expressive query language for extracting different types of temporal constraints from a knowledge base of temporal specifications in the formalism, sketching the reasoning algorithms needed to answer the queries.