A versatile characterization of causal relationships

This paper introduces a framework for representing versatile temporal relationships between events and their effects. The framework is based on a simple time model which characterizes each time element as a subset of the set of real numbers and allows expression of both absolute time values and relative temporal relations. The formalism presented here formally specifies the so-called most general temporal constraint (GTC), which guarantees the common-sense assertion that “the beginning of the effect cannot precede the beginning of the cause”. It is shown that there are in fact 8 possible causal relationships which satisfy GTC, including cases where, on the one hand, effects start simultaneously with, during, immediately after, or some time after their causes, and on the other hand, events end before, simultaneously with, or after their causes. The causal relationships characterized in this paper are versatile enough to subsume those representatives in the literature.