The notion of time plays a vital and ubiquitous role of a common universal reference. In knowledge-based systems, temporal information is usually represented in terms of a collection of statements, together with the corresponding temporal reference. This paper introduces a visualized consistency checker for temporal reference. It allows expression of both absolute and relative temporal knowledge, and provides visual representation of temporal references in terms of directed and partially weighted graphs. Based on the temporal reference of a given scenario, the visualized checker can deliver a verdict to the user as to whether the scenario is temporally consistent or not, and provide the corresponding analysis/diagnosis.

The so-called dividing instant (DI) problem is an ancient historical puzzle encountered when attempting to represent what happens at the boundary instant which divides two successive states. The specification of such a problem requires a thorough exploration of the primitives of the temporal ontology and the corresponding time structure, as well as the conditions that the resulting temporal models must satisfy. The problem is closely related to the question of how to characterize the relationship between time periods with positive duration and time instants with no duration. It involves the characterization of the ‘closed’ and ‘open’ nature of time intervals, i.e. whether time intervals include their ending points or not. In the domain of artificial intelligence, the DI problem may be treated as an issue of how to represent different assumptions (or hypotheses) about the DI in a consistent way. In this paper, we shall examine various temporal models including those based solely on points, those based solely on intervals and those based on both points and intervals, and point out the corresponding DI problem with regard to each of these temporal models. We shall propose a classification of assumptions about the DI and provide a solution to the corresponding problem.

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.

This paper presents a temporal database model which allows the expression of relative temporal knowledge of data transaction and data validity times. The system is founded on an extension to Allen's axiomitization of time, given previously by the authors, which takes both intervals and points as primitive time elements. A general retrieval mechanism is presented for a database with a purely relative temporal knowledge which allows queries with temporal constraints in terms of any logical combination of Allen's temporal predicates. When absolute temporal duration knowledge is added, the consistency checking algorithm upon which the inference mechanism is based reduces to a linear programming problem. A class of databases, termed time-limited databases, is introduced as a practical solution to the problem of computational complexity of retrieval. This class allows absolute and relative time knowledge in a form which is suitable for many practical applications, where relative temporal information is only occasionally needed. The architecture of such a system is given, and it is shown that the efficient retrieval mechanisms for absolute-time-stamped databases may be adapted to time-limited databases.

In this paper, a first-order theory of time is proposed as an underlying framework for most of the representative temporal models in artificial intelligence. The theory treats both points and intervals as primitive on an equal footing, and is shown to be powerful enough to subsume the interval based theories of Allen and Hayes, the point based theories of Bruce, of McDermott, and the interval and point based theories of Vilain and Knight and Ma. The approach is different from that of Ladkin, of Van Beek, of Dechter, Meiri and Pearl, and of Maiocchi, which is either to construct intervals out of points, or to treat points and intervals separately. Formal definitions are presented to characterize the open and closed nature of primitive intervals. The axiomatization allows non-linear time structures such as branching time and parallel time. Additional axioms specifying the linearity and density of time are separately presented.

This paper examines J.F. Allen's interval-based theory of action and time and the corresponding revisions suggested by A.P. Galton which have been proposed to accommodate the representation of facts concerning continuous change. Agreeing with Galton's argument that Allen's system needs revisions by means of diversifying the temporal ontology to include points, we show that Galton's determination to define time points in terms of the ‘meeting places’ of time intervals does not, as it stands, axiomatize points on the same footing as intervals, and hence that some problems still remain in these revisions. It is shown that it is necessary to revise the fundamental axioms about time itself so as to extend the abstract concept of time elements to include both intervals and points, and to extend the temporal relations between intervals to address points as well. We provide there a further revised theory which overcomes the problems in Allen's and Galton's systems. The revised system utilizes a new axiomatization of time, given previously by the authors, as the underlying temporal basis. A diversification of the range of properties/occurrences over intervals and points is also proposed which may replace both Allen's and Galton's results.

The problem of memory overflow and the efficient storage and retrieval of temporal knowledge is discussed in this paper. For temporal systems, dealing with continuous streams of time-ordered data, the problem of freeing memory is an important one. For humans the problem is one of selective forgetting and reorganisation of memory. There are several approaches to temporal representations which model human mechanisms, e.g. Allen's interval calculus [1], where the mechanisms for information loss are implicit in the relativistic nature of the representation itself or are treated as secondary to the representation. In this article we take the view that the mechanism for information loss is of prime importance and that it can define the representation. The objective is to make the mechanism explicit, by means of a production system architecture. A rule base defines an intelligent forgetting scheme, which manages a database of temporal facts. Two examples of rule bases are given. In the first, it is assumed that restructuring is directed at a particular application, so that ‘irrelevant’ data may be discarded. This assumption is shown to lead to a state-based temporal representation appropriate to the example. In the second, general information loss is modelled, where the resulting data stores are universally applicable, even if incomplete. The starting point for the discussion is a model of temporal data as a matrix of values, temporal order being represented as row order. This background model is used as a universe in which to examine derivable representations. Representations involving data compression without loss of information are examined first. Then principles governing controlled information loss are examined. Information loss is characterised by means of invariance groups of transformations on the data matrix and a model of information loss as a taxonomy of production rules for data deletion is proposed.