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.

Guest Editorial. Special Issue: Temporal logic in engineering

Logic-based models are thriving within artificial intelligence. A great number of new logics have been defined, and their theory investigated. Epistemic logics introduce modal operators for knowledge or belief; deontic logics are about norms, and introduce operators of deontic necessity and possibility (i.e., obligation or prohibition). And then we have a much investigated class—temporal logics—to whose application to engineering this special issue is devoted. This kind of formalism deserves increased widespread recognition and application in engineering, a domain where other kinds of temporal models (e.g., Petri nets) are by now a fairly standard part of the modelling toolbox.

A sound and complete reified temporal logic

There are mainly two known approaches to the representation of temporal information in Computer Science: modal logic approaches (including tense logics and hybrid temporal logics) and predicate logic approaches (including temporal argument methods and reified temporal logics). On one hand, while tense logics, hybrid temporal logics and temporal argument methods enjoy formal theoretical foundations, their expressiveness has been criticised as not power enough for representing general temporal knowledge; on the other hand, although current reified temporal logics provide greater expressive power, most of them lack of complete and sound axiomatic theories. In this paper, we propose a new reified temporal logic with a clear syntax and semantics in terms of a sound and complete axiomatic formalism which retains all the expressive power of the approach of temporal reification.

Temporal structure and enablement representation for mutual wills: A Petri net approach

Those temporal formalisms that are sporadically found nowadays in the literature of AI & Law are based on temporal logic. We claim a revived role for another major class of temporal representation: Petri nets. This formalism, popular in computing from the 1970s, had its potential recognized on occasion in the literature of legal computing as well, but apparently the discipline has lost sight of it, and its practitioners on average need be tutored into this kind of representation. Asynchronous, concurrent processes—for which the approach is well‐suited—are found in the legal domain, in disparate contexts. We develop an example for Mutual Wills.

The completeness and soundness of temporal theories

Generally speaking, the term temporal logic refers to any system of rules and symbolism for representing and reasoning about propositions qualified in terms of time. In computer science, particularly in the domain of Artificial Intelligence, there are mainly two known approaches to the representation of temporal information: modal logic approaches including tense logic and hybrid temporal logic, and predicate logic approaches including temporal arguement method and reified temporal logic. On one hand, while tense logic, hybrid temporal logic and temporal argument method enjoy formal theoretical foundations, their expressiveness has been criticised as not power enough for representing general temporal knowledge; on the other hand, although reified temporal logic provides greater expressive power, most of the current systems following the temporal reification lack of complete and sound axiomatic theories. With there observations in mind, a new reified temporal logic with clear syntax and semantics in terms of a sound and complete axiomatic formalism is introduced in this paper, which retains all the expressive power of temporal reification.

Reified temporal logics: an overview

There are three main approaches to the representation of temporal information in AI literature: the so-called method of temporal arguments that simply extends functions and predicates of first-order language to include time as the additional argument; modal temporal logics which are extensions ofthe propositional or predicate calculus with modal temporal operators; and reified temporal logics which reify standard propositions of some initial language (e.g., the classical first-order or modal logic) as objects denoting propositional terms. The objective of this paper is to provide an overview onthe temporal reified approach by looking closely atsome representative existing systems featuring reified propositions, including those of Allen, McDermott, Shoham, Reichgelt, Galton, and Ma and Knight. We shall demonstrate that, although reified logics might be more complicated in expressing assertions about some given objects with respect to different times, they accord a special status to time and therefore have several distinct advantages in talking about some important issues which would be difficult (if not impossible) to express in other approaches.

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.

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.

Temporal modelling of short-term rainfall using Cox processes

We study two marked point process models based on the Cox process. These models are used to describe the probabilistic structure of the rainfall intensity process. Mathematical formulation of the models is described and some second-moment characteristics of the rainfall depth, and aggregated processes are considered. The derived second-order properties of the accumulated rainfall amounts at different levels of aggregation are used in order to examine the model fit. A brief data analysis is presented. Copyright © 1998 John Wiley & Sons, Ltd.

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.

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".

Building temporal constraints into knowledge bases for process control: an examination [Reply to author's reply]

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Deforestation and the spatio-temporal distribution of savannah and forest members of the Simulium damnosum complex in southern Ghana and south-western Togo

Spatio-temporal data on cytotaxonomic identifications of larvae of different members of the Simulium damnosum complex collected from rivers in southern Ghana and south-western Togo from 1975 until 1997 were analysed. When the data were combined, the percentages of savannah blackflies (S. damnosum sensu stricto and S. sirbanum) in the samples were shown to have been progressively increasing since 1975. The increases were statistically significant (P < 0·001), but the rates of increase were not linear. Further analyses were conducted according to the collection seasons and locations of the samples, to account for possible biases such as savannah flies occurring further south in the dry season or a preponderance of later samples from northern rivers having more savannah flies. These analyses showed that the increasing trend was statistically significant (P< 0·0001) only during the periods April to June and October to December. The presence of adult savannah flies carrying infective larvae (L3) indistinguishable from those of Onchocerca volvulus in the study zone was confirmed by examinations of captured flies. The percentages of savannah flies amongst the human-biting populations and the percentages with L3s in the head were higher during dry seasons than wet seasons and the savannah species were found furthest south (5 °25′N) in the dry season. Comparisons of satellite images taken in 1973 and 1990 over a study area in south-western Ghana encompassing stretches of the Tano and Bia rivers demonstrated that there have been substantial increases in urban and savannah areas, at the expense of forest. This was so not only for the whole images but also for subsamples of the images taken at 1, 2, 4, 8 and 16 km distant from sites alongside the River Tano. At every distance from the river, the percentages of pixels classified as urban or savannah have increased in 1990 compared with 1973, while those classified as degraded or dense forest have decreased. The possibility that the proportionate increases in savannah forms of the vectors of onchocerciasis, and hence in the likelihood of the transmission of savannah strains of the disease in formerly forested areas, were related to the decreases in forest cover is discussed.

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.