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 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.

Generalized Markov branching processes

A generalized Markov Brnching Process (GMBP) is a Markov branching model where the infinitesimal branching rates are modified with an interaction index. It is proved that there always exists only one GMBP. An associated differential-integral equation is derived. The extinction probalility and the mean and conditional mean extinction times are obtained. Ergodicity and stability of GMBP with resurrection are also considered. Easy checking criteria are established for ordinary and strong ergodicty. The equilibrium distribution is given in an elegant closed form. The probability meaning of our results is clear and thus explained.

Ergodicity and stability of generalised Markov branching processes with resurrection

This paper concentrates on investigating ergodicity and stability for generalised Markov branching processes with resurrection. Easy checking criteria including several clear-cut corollaries are established for ordinary and strong ergodicity of such processes. The equilibrium distribution is given in an elegant closed form for the ergodic case. The probabilistic interpretation of the results is clear and thus explained.

Birth-death processes with an instantaneous reflection barrier

A new structure with the special property that an instantaneous reflection barrier is imposed on the ordinary birth-death processes is considered. An easy-checking criterion for the existence of such Markov processes is first obtained. The uniqueness criterion is then established. In the nonunique case, all the honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. It is proved that honest processes are always ergodic without necessarily imposing any extra conditions. Equilibrium distributions for all these ergodic processes are established. Several examples are provided to illustrate our results.

Representing and recognizing scenario patterns

This paper presents a formal method for representing and recognizing scenario patterns with rich internal temporal aspects. A scenario is presented as a collection of time-independent fluents, together with the corresponding temporal knowledge that can be relative and/or with absolute values. A graphical representation for temporal scenarios is introduced which supports consistence checking as for the temporal constraints. In terms of such a graphical representation, graph-matching algorithms/methodologies can be directly adopted for recognizing scenario patterns.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Trust, leadership and economic necessity in post-compulsory education

Trust is a complex concept that has increasingly been debated in academic research (Kramer and Tyler, 1996). Research on 'trust and leadership' (Caldwell and Hayes, 2007) has suggested, unsurprisingly, that leadership behaviours influence 'follower' perceptions of leaders' trustworthiness. The development of 'ethical stewardship' amongst leaders may foster high trust situations (Caldwell, Hayes, Karri and Bernal, 2008), yet studies on the erosion of teacher professionalism in UK post-compulsory education have highlighted the distrust that arguably accompanies 'new managerialism', performativity and surveillance within a climate of economic rationalisation established by recent deterministic skills-focused government agendas for education (Avis, 2003; Codd, 1999, Deem, 2004, DFES, 2006). Given the shift from community to commercialism identified by Collinson and Collinson (2005) in a global economic environment characterised by uncertainty and rapid change, trust is, simultaneously, increasingly important and progressively both more fragile and limited in a post compulsory education sector dominated by skills-based targets and inspection demands. Building on such prior studies, this conference paper reports on the analysis of findings from a 2007-8 funded research study on 'trust and leadership' carried out in post-compulsory education. The research project collected and analysed case study interview and survey data from the lifelong learning sector, including selected tertiary, further and higher education (FE and HE) institutions. We interviewed 18 UK respondents from HE and FE, including principals, middle managers, first line managers, lecturers and researchers, supplementing and cross-checking this with a small number of survey responses (11) on 'trust and leadership' and a larger number (241) of survey responses on more generalised leadership issues in post-compulsory education. A range of facilitators and enablers of trust and their relationship to leadership were identified and investigated. The research analysed the ways in which interviewees defined the concept of 'trust' and the extent to which they identified that trust was a mediating factor affecting leadership and organisational performance. Prior literature indicates that trust involves a psychological state in which, despite dependency, risk and vulnerability, trustors have some degree of confident expectation that trustees will behave in benevolent rather than detrimental ways. The project confirmed the views of prior researchers (Mayer, Davis and Schoorman, 1995) that, since trust inevitably involves potential betrayal, estimations of leadership 'trustworthiness' are based on followers' cognitive and affective perceptions of the reliability, competence, benevolence and reputation of leaders. During the course of the interviews it also became clear that some interviewees were being managed in more or less transaction-focused, performative, audit-dominated cultures in which trust was not regarded as particularly important: while 'cautious trust' existed, collegiality flourished only marginally in small teams. Economic necessity and survival were key factors influencing leadership and employee behaviours, while an increasing distance was reported between senior managers and their staff. The paper reflects on the nature of the public sector leadership and management environment in post-compulsory education reported by interviewees and survey respondents. Leadership behaviours to build trust are recommended, including effective communication, honesty, integrity, authenticity, reliability and openness. It was generally felt that building trust was difficult in an educational environment largely determined by economic necessity and performativity. Yet, despite this, the researchers did identify a number of examples of high trust leadership situations that are worthy of emulation.