Addressing time intervals

One of the fundamental questions regarding the temporal ontology is what is time composed of. While the traditional time structure is based on a set of points, a notion that has been prevalently adopted in classical physics and mathematics, it has also been noticed that intervals have been widely adopted for expre~sion of common sense temporal knowledge, especially in the domain of artificial intelligence. However, there has been a longstanding debate on how intervals should be addressed, leading to two different approaches to the treatment of intervals. In the first, intervals are addressed as derived objects constructed from points, e.g., as sets of points, or as pairs of points. In the second, intervals are taken as primitive themselves. This article provides a critical examination of these two approaches. By means of proposing a definition of intervals in terms of points and types, we shall demonstrate that, while the two different approaches have been viewed as rivals in the literature, they are actually reducible to logically equivalent expressions under some requisite interpretations, and therefore they can also be viewed as allies.

Some models for discretized series of events

A discretized series of events is a binary time series that indicates whether or not events of a point process in the line occur in successive intervals. Such data are common in environmental applications. We describe a class of models for them, based on an unobserved continuous-time discrete-state Markov process, which determines the rate of a doubly stochastic Poisson process, from which the binary time series is constructed by discretization. We discuss likelihood inference for these processes and their second-order properties and extend them to multiple series. An application involves modeling the times of exposures to air pollution at a number of receptors in Western Europe.

A qualitative temporal information system for process control

A general system is presented in this paper which supports the expression of relative temporal knowledge in process control and management. This system allows knowledge of Allen's temporal relations over time elements, which may be both intervals and points. The objectives and characteristics of two major temporal attributes, i.e. ‘transaction time’ and ‘valid time’, are described. A graphical representation for the temporal network is presented, and inference over the network may be made by means of a consistency checker in terms of the graphical representation. An illustrative example of the system as applied to process control and management is provided.

Representing temporal knowledge in legal discourse

This paper presents a formalism for representing temporal knowledge in legal discourse that allows an explicit expression of time and event occurrences. The fundamental time structure is characterized as a well‐ordered discrete set of primitive times, i.e. non‐decomposable intervals with positive duration or points with zero duration), from which decomposable intervals can be constructed. The formalism supports a full representation of both absolute and relative temporal knowledge, and a formal mechanism for checking the temporal consistency of a given set of legal statements is provided. The general consistency checking algorithm which addresses both absolute and relative temporal knowledge turns out to be a linear programming problem, while in the special case where only relative temporal relations are involved, it becomes a simple question of searching for cycles in the graphical representation of the corresponding legal text.

Representing the dividing instant

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.

A framework for historical case-based reasoning

This paper presents a framework for Historical Case-Based Reasoning (HCBR) which allows the expression of both relative and absolute temporal knowledge, representing case histories in the real world. The formalism is founded on a general temporal theory that accommodates both points and intervals as primitive time elements. A case history is formally defined as a collection of (time-independent) elemental cases, together with its corresponding temporal reference. Case history matching is two-fold, i.e., there are two similarity values need to be computed: the non-temporal similarity degree and the temporal similarity degree. On the one hand, based on elemental case matching, the non-temporal similarity degree between case histories is defined by means of computing the unions and intersections of the involved elemental cases. On the other hand, by means of the graphical presentation of temporal references, the temporal similarity degree in case history matching is transformed into conventional graph similarity measurement.

Non-preemptive two-machine open shop scheduling with non-availability constraints

We study a two-machine open shop scheduling problem, in which the machines are not continuously available for processing. No preemption is allowed in the processing of any operation. The objective is to minimize the makespan. We consider approximability issues of the problem with more than one non-availability intervals and present an approximation algorithm with a worst-case ratio of 4/3 for the problem with a single non-availability interval.

Ontological considerations of time, meta-predicates and temporal propositions

A natural approach to representing and reasoning about temporal propositions (i.e., statements with time-dependent truth-values) is to associate them with time elements. In the literature, there are three choices regarding the primitive for the ontology of time: (1) instantaneous points, (2) durative intervals and (3) both points and intervals. Problems may arise when one conflates different views of temporal structure and questions whether some certain types of temporal propositions can be validly and meaningfully associated with different time elements. In this paper, we shall summarize an ontological glossary with respect to time elements, and diversify a wider range of meta-predicates for ascribing temporal propositions to time elements. Based on these, we shall also devise a versatile categorization of temporal propositions, which can subsume those representative categories proposed in the literature, including that of Vendler, of McDermott, of Allen, of Shoham, of Galton and of Terenziani and Torasso. It is demonstrated that the new categorization of propositions, together with the proposed range of meta-predicates, provides the expressive power for modeling some typical temporal terms/phenomena, such as starting-instant, stopping-instant, dividing-instant, instigation, termination and intermingling etc.

Characterizing the most general temporal constraint

This paper introduces a characterization of the so-called most general temporal constraint (GTC), which guarantees the common-sense assertion that "the beginning of the effect cannot precede the beginning of the cause". The formalism is based on general time theory which takes both points and intervals as primitive. It is shown that there are in fact 8 possible causal relationships which satisfy GTC, including cases where, on the one hand, effects start simultaneously with, during, immediately after, or some time after their causes, and on the other hand, events end before, simultaneously with, or after their causes. These causal relationships are versatile enough to subsume those representatives in the literature.

Implementation of cognitive mapping, spatial representation and wayfinding behaviours of people within evacuation modelling tools

Within the building evacuation context, wayfinding describes the process in which an individual located within an arbitrarily complex enclosure attempts to find a path which leads them to relative safety, usually the exterior of the enclosure. Within most evacuation modelling tools, wayfinding is completely ignored; agents are either assigned the shortest distance path or use a potential field to find the shortest path to the exits. In this paper a novel wayfinding technique that attempts to represent the manner in which people wayfind within structures is introduced and demonstrated through two examples. The first step is to encode the spatial information of the enclosure in terms of a graph. The second step is to apply search algorithms to the graph to find possible routes to the destination and assign a cost to the routes based on their personal route preferences such as "least time" or "least distance" or a combination of criteria. The third step is the route execution and refinement. In this step, the agent moves along the chosen route and reassesses the route at regular intervals and may decide to take an alternative path if the agent determines that an alternate route is more favourable e.g. initial path is highly congested or is blocked due to fire.

Approximation results for flow shop scheduling problems with machine availability constraints

This paper considers two-machine flow shop scheduling problems with machine availability constraints. When the processing of a job is interrupted by an unavailability period of a machine, we consider both the resumable scenario in which the processing can be resumed when the machine next becomes available, and the semi-resumable scenario in which some portion of the processing is repeated but the job is otherwise resumable. For the problem with several non-availability intervals on the first machine under the resumable scenario, we present a fast (3/2)-approximation algorithm. For the problem with one non-availability interval under the semi-resumable scenario, a polynomial-time approximation scheme is developed.

A framework for state-based time-series analysis and prediction

Time-series analysis and prediction play an important role in state-based systems that involve dealing with varying situations in terms of states of the world evolving with time. Generally speaking, the world in the discourse persists in a given state until something occurs to it into another state. This paper introduces a framework for prediction and analysis based on time-series of states. It takes a time theory that addresses both points and intervals as primitive time elements as the temporal basis. A state of the world under consideration is defined as a set of time-varying propositions with Boolean truth-values that are dependent on time, including properties, facts, actions, events and processes, etc. A time-series of states is then formalized as a list of states that are temporally ordered one after another. The framework supports explicit expression of both absolute and relative temporal knowledge. A formal schema for expressing general time-series of states to be incomplete in various ways, while the concept of complete time-series of states is also formally defined. As applications of the formalism in time-series analysis and prediction, we present two illustrating examples.

A robust approach to subsequence matching

In terms of a general time theory which addresses time-elements as typed point-based intervals, a formal characterization of time-series and state-sequences is introduced. Based on this framework, the subsequence matching problem is specially tackled by means of being transferred into bipartite graph matching problem. Then a hybrid similarity model with high tolerance of inversion, crossover and noise is proposed for matching the corresponding bipartite graphs involving both temporal and non-temporal measurements. Experimental results on reconstructed time-series data from UCI KDD Archive demonstrate that such an approach is more effective comparing with the traditional similarity model based algorithms, promising robust techniques for lager time-series databases and real-life applications such as Content-based Video Retrieval (CBVR), etc.

The influence of alkali metal chlorides on the loss of water from glass-ionomer dental cements

The water loss behaviour of a clinical glass-ionomer dental cement has been studied with and without the addition of alkali metal chlorides. Dehydrating conditions were provided by placing specimens in a desiccator over concentrated sulphuric acid. Cements were prepared using either pure water or an aqueous solution of metal chloride (LiCl, NaCl, KCl) at 1.0 mol/dm(3). In addition, NaCl at 0.5 mol/dm(3) was also used to fabricate cements. Disc-shaped specimens of size 6 mm diameter x 2 mm thickness were made, six performulation, and cured at 37 degrees C for 1 hour They were then exposed to desiccating conditions, and the mass measured at regular intervals. All formulations were found to lose water in a diffusion process that equilibrated after approximately 3 weeks. Diffusion coefficients ranged from 2.27 (0.13) x 10(9) with no additive to 1.85 (0.07) x 10(9) m(2)/s with 1.0 mol/dm(3) KCl. For the salts, diffusion coefficients decreased in the order LiCl > NaCl > KCl. There was no statistically significant difference between the diffusion coefficients for 1.0 and 0.5 mol/dm(3) NaCl. For all salts at 1.0 mol/dm(3) and also additive-free cements, equilibrium losses were, with statistical limits, the same, ranging from 6.23 to 6.34%. On the other hand, 0.5 mol/dm(3) NaCl lost significantly more water 7.05%.

8-OH-DPAT inhibits both prandial and waterspray-induced grooming

The effects of 8-OH-DPAT treatment on rat grooming behaviour, elicited either prandially or in response to spraying with water were investigated. Dose (0.1 mg/kg s.c.) response studies employed momentary time sampling over 30 or 60 min with behaviour being scored in one of 6 or 7 (depending on food availability) mutually exclusive categories (feeding, active, scratching, face-grooming, body grooming, genital-grooming and resting) at 15 s intervals. In non-deprived rats, tested with wet mash available, feeding and activity frequencies were increased, but resting and total grooming were inhibited by 8-OH-DPAT. Face-, body- and genital-grooming occurred at higher levels than scratching, but all categories were reduced with reductions in scratching occurring at a lower dose (0.01 mg/kg). Misting rats with a fine water spray selectively increased body grooming and decreased activity without altering feeding, while 8-OH-DPAT increased feeding and reduced face-, body- and genital-grooming, without affecting already low levels of scratching. In misted rats, tested without food, 8-OH-DPAT reduced face-, body- and genital-grooming and increased resting. These results confirm i) that the water spray technique is a useful method for increasing grooming and ii) that 8-OH-DPAT has a suppressant effect on grooming independent of response competition from enhanced feeding.