Formulating the Temporal Causal Relationships Between Events and Their Results

We introduce in this paper a formalism for representing flexible temporal causal relationships between events and their effects. A formal characterization of the so-called (most) General Temporal Constraint (GTC) is formulated, which guarantees the common-sense assertion that “the beginning of the effect cannot precede the beginning of its causal event”. It is shown that there are actually in total 8 possible temporal causal relationships which satisfy the GTC. These include cases where, (1) the effect becomes true immediately after the end of the event and remains true for some time after the event; (2) the effect holds only over the same time over which the event is in progress; (3) the beginning of the effect coincides with the beginning of the event, and the effect ends before the event completes; (4) the beginning of the effect coincides with the beginning of the event, and the effect remains true for some time after the event; (5) the effect only holds over some time during the progress of the event; (6) the effect becomes true during the progress of the event and remains true until the event completes; (7) the effect becomes true during the progress of the event and remains true for some time after the event; and (8) where there is a time delay between the event and its effect. We shall demonstrate that the introduced formulation is versatile enough to subsume those existing representative formalisms in the literature.