Models of circular causality

Causality is often interpreted as establishing dependencies between events. The standard view is that an event b causally depends on an event a if, whenever b occurs, then a has already occurred. If the occurrences of a and b mutually depend on each other, i.e. a depends on b and vice versa, then (under the standard notion of causality) neither of them can ever occur. This does not faithfully capture systems where, for instance, an agent promises to do event a provided that b will be eventually done, and vice versa. In this case, the circularity between the causal dependencies should allow both a and b to occur, in any order. In this paper we review three models for circular causality, one based on logic (declarative), one based on event structures (semantical), and one based on Petri nets (operational). We will cast them in a coherent picture pointing out their relationships.