Temporal management using relative time in knowledge-based process control

In this paper, a knowledge-based approach is proposed for the management of temporal information in process control. A common-sense theory of temporal constraints over processes/events, allowing relative temporal knowledge, is employed here as the temporal basis for the system. This theory supports duration reasoning and consistency checking, and accepts relative temporal knowledge which is in a form normally used by human operators. An architecture for process control is proposed which centres on an historical database consisting of events and processes, together with the qualitative temporal relationships between their occurrences. The dynamics of the system is expressed by means of three types of rule: database updating rules, process control rules, and data deletion rules. An example is provided in the form of a life scheduler, to illustrate the database and the rule sets. The example demonstrates the transitions of the database over time, and identifies the procedure in terms of a state transition model for the application. The dividing instant problem for logical inference is discussed with reference to this process control example, and it is shown how the temporal theory employed can be used to deal with the problem.

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".

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.

A versatile characterization of causal relationships

This paper introduces a framework for representing versatile temporal relationships between events and their effects. The framework is based on a simple time model which characterizes each time element as a subset of the set of real numbers and allows expression of both absolute time values and relative temporal relations. The formalism presented here formally specifies 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”. 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. The causal relationships characterized in this paper are versatile enough to subsume those representatives in the literature.

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.

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.