A discrete formalism for reasoning about action and change

This paper presents a discrete formalism for temporal reasoning about actions and change, which enjoys an explicit representation of time and action/event occurrences. The formalism allows the expression of truth values for given fluents over various times including nondecomposable points/moments and decomposable intervals. Two major problems which beset most existing interval-based theories of action and change, i.e., the so-called dividing instant problem and the intermingling problem, are absent from this new formalism. The dividing instant problem is overcome by excluding the concepts of ending points of intervals, and the intermingling problem is bypassed by means of characterising the fundamental time structure as a well-ordered discrete set of non-decomposable times (points and moments), from which decomposable intervals are constructed. A comprehensive characterisation about the relationship between the negation of fluents and the negation of involved sentences is formally provided. The formalism provides a flexible expression of temporal relationships between effects and their causal events, including delayed effects of events which remains a problematic question in most existing theories about action and change.

A reified temporal logic

This paper presents a reified temporal logic for representing and reasoning about temporal and non-temporal relationships between non-temporal assertions. A clear syntax and semantics for the logic is formally provided. Three types of predicates, temporal predicates, non-temporal predicates and meta-predicates, are introduced. Terms of the proposed language are partitioned into three types, temporal terms, non-temporal terms and propositional terms. Reified propositions consist of formulae with each predicate being either a temporal predicate or a meta-predicate. Meta-predicates may take both temporal terms and propositional terms together as arguments or take propositional terms alone. A standard formula of the classical first-order language with each predicate being a non-temporal predicate taking only non-temporal terms as arguments is reified as just a propositional term. A general time ontology has been provided which can be specialized to a variety of existing temporal systems. The new logic allows one to predicate and quantify over propositional terms while according a special status of time; for example, assertions such as ‘effects cannot precede their causes’ is ensured in the logic, and some problematic temporal aspects including the delay time between events and their effects can be conveniently expressed. Applications of the logic are presented including the characterization of the negation of properties and their contextual sentences, and the expression of temporal relations between actions and effects.

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.