Temporal representation of state transitions

This paper describes a knowledge-based temporal representation of state transitions for industrial real-time systems. To allow expression of uncertainty, we shall define fluents as disjuncts of positive/negative time-varying properties. A state of the world is represented as a collection of fluents, which is usually incomplete in the sense that neither the positive form nor the negative form of some properties can be implied from it. The world under consideration is assumed to persist in a given state until an action(s) takes place to effect a transition of it into another state, where actions may either be instantaneous or durative. High-level causal laws are characterized in terms of relationships between actions and the involved world states. An effect completion axiom is imposed on each causal law to guarantee that all the fluents that can be affected by the performance of the corresponding action are governed. This completion requirement is practical for most industrial real-time applications and in fact provides a simple and effective treatment to the so-called frame problem.

Using set operations to deal with the frame problem

This paper presents a simple approach to the so-called frame problem based on some ordinary set operations, which does not require non-monotonic reasoning. Following the notion of the situation calculus, we shall represent a state of the world as a set of fluents, where a fluent is simply a Boolean-valued property whose truth-value is dependent on the time. High-level causal laws are characterised in terms of relationships between actions and the involved world states. An effect completion axiom is imposed on each causal law, which guarantees that all the fluents that can be affected by the performance of the corresponding action are always totally governed. It is shown that, compared with other techniques, such a set operation based approach provides a simpler and more effective treatment to the frame problem.