Reasoning about change over time: Actions, events and their effects

This paper presents a new formalism for reasoning about change over time. The formalism derives a clean separation between the notion of states and situations. It allows more flexible temporal causal relationships than do other formalisms for reasoning about causal change, such as the situation calculus and the event calculus. It includes effects that start during, immediately after, or some time after their causes, and which end before, simultaneously with, or after their causes. A formal distinction between actions, action-types and events is proposed, which allows the expression of common-sense causal laws at high level. It is shown how these laws can be used to deduce state change over time at low level, when events occur under certain preconditions hold. Two problems that beset most interval-based temporal systems, i.e., the so-called dividing instant problem and intermingling problem, are absent from the formalism.

Representing temporal relationships between events and their effects

Temporal relationships between events and their effects are complex. As the effects of a given event, a proposition may change its truth value immediately after the occurrence of the event and remain true until some other events occur, while another proposition may only become true/false from some time after the causal event has occurred. Expressing delayed effects of events has been a problematic question in most existing theories of action and change. This paper presents a new formalism for representing general temporal causal relationships between events and their effects. It allows expressions of both immediate and delayed effects of events, and supports common-sense assertions such as "effects cannot precede their causes".