The notion of causality is very important in many applications areas. Because of this importance, there are several formalizations of this notion in physics and in AI. Most of these definitions describe causality as a crisp ("yes"-"no") relation between two events or two processes -- cause and effect. However, such descriptions do not fully capture the intuitive idea of causality: first, often, several conditions are needed to be present for an effect to occur, and, second, the effect is often a matter of degree. In this paper, we show how to modify the current description of causality so as to take both these phenomena into account -- in particular, by extending the notion of directed acyclic graph to hypergraphs. As a somewhat unexpected side effect of our analysis, we get a natural explanation of why, in contrast to space-time of Special Relativity -- in which division into space and time depends on the observer, in cosmological solutions there is a clear absolute separation between space and time.
Technical Report: UTEP-CS-23-05a
To appear in Proceedings of the 2023 Annual Conference of the North American Fuzzy Information Processing Society NAFIPS'2023, Cincinnati, Ohio, May 31 - June 2, 2023.