Constructing Probabilistic ATMS Using Extended Incidence Calculus

This paper discusses the relations between extended incidence calculus and assumption-based truth maintenance systems (ATMSs). We first prove that managing labels for statements (nodes) in an ATMS is equivalent to producing incidence sets of these statements in extended incidence calculus. We then demonstrate that the justification set for a node is functionally equivalent to the implication relation set for the same node in extended incidence calculus. As a consequence, extended incidence calculus can provide justifications for an ATMS, because implication relation sets are discovered by the system automatically. We also show that extended incidence calculus provides a theoretical basis for constructing a probabilistic ATMS by associating proper probability distributions on assumptions. In this way, we can not only produce labels for all nodes in the system, but also calculate the probability of any of such nodes in it. The nogood environments can also be obtained automatically. Therefore, extended incidence calculus and the ATMS are equivalent in carrying out inferences at both the symbolic level and the numerical level. This extends a result due to Laskey and Lehner

Extended incidence calculus and its comparison with related theories

This thesis presents a comprehensive study o f incidence calculus, a probabilistic logic for reasoning under uncertainty which extends two-value propositional logic to a multiple-value logic. There are three main contributions in this thesis.First of all, the original incidence calculus is extended considerably in three aspects: (a) the original incidence calculus is generalized; (b) an efficient algorithm for incidence assignment based on generalized incidence calculus is developed; (c) a combination rule is proposed for the combination of both independent and some dependent pieces of evidence. Extended incidence calculus has the advantages of representing information flexibly and combining multiple sources o f evidence.Secondly, a comprehensive comparison between extended incidence calculus and the Dempster-Shafer (DS) theory of evidence is provided. It is proved that extended incidence calculus is equivalent to DS theory in representing evidence and combining independent evidence but superior to DS theory in combining de­pendent evidence.Thirdly, the relations between extended incidence calculus and the assumption- based truth maintenance systems are discussed. It is proved that extended inci­dence calculus is equivalent to the ATM S in calculating labels for nodes. Extended incidence calculus can also be used as a basis for constructing probabilistic ATMSs.The study in this thesis reveals that extended incidence calculus can be re­garded as a bridge between numerical and symbolic reasoning mechanisms

A blackboard-based system for learning to identify images from feature data

A blackboard-based system which learns recognition rules for objects from a set of training examples, and then identifies and locates these objects in test images, is presented. The system is designed to use data from a feature matcher developed at R.S.R.E. Malvern which finds the best matches for a set of feature patterns in an image. The feature patterns are selected to correspond to typical object parts which occur with relatively consistent spatial relationships and are sufficient to distinguish the objects to be identified from one another. The learning element of the system develops two separate sets of rules, one to identify possible object instances and the other to attach probabilities to them. The search for possible object instances is exhaustive; its scale is not great enough for pruning to be necessary. Separate probabilities are established empirically for all combinations of features which could represent object instances. As accurate probabilities cannot be obtained from a set of preselected training examples, they are updated by feedback from the recognition process. The incorporation of rule induction and feedback into the blackboard system is achieved by treating the induced rules as data to be held on a secondary blackboard. The single recognition knowledge source effectively contains empty rules which this data can be slotted into, allowing it to be used to recognise any number of objects - there is no need to develop a separate knowledge source for each object. Additional object-specific background information to aid identification can be added by the user in the form of background checks to be carried out on candidate objects. The system has been tested using synthetic data, and successfully identified combinations of geometric shapes (squares, triangles etc.). Limited tests on photographs of vehicles travelling along a main road were also performed successfully

Math Anxiety: Relationship with Sex, College Major, Mathematics Background, Mathematics Achievement, Mathematics Performance, Mathematics Avoidance, Self-Rating of Mathematics Ability, and Self-Rating of Mathematics Anxiety as Measured by the Revised Mathematics Anxiety Rating Scale (RMARS)

Mathematics educators and psychologists blame math anxiety for affecting mathematics learning, performance, and enrollment, and, subsequently, choice of college major and career. Researchers have yet to agree on prevalence, stability, and effects of math anxiety. This study (1) investigated the prevalence and intensity of math anxiety in college students (as a whole, by major, and by sex), (2) determined the stability of math anxiety over time, and (3) investigated those background and experimental factors related to its occurrence in college students, using data gathered on 173 college students in mathematics, education, and English classrooms. The data concerned college students\u27 math anxiety as measured by the Revised Mathematics Anxiety Rating Scale (RMARS) and selected cognitive correlates of math anxiety, and were analyzed by analyses of variance, t-tests, and correlational analyses. Based upon the statistical analyses, these results were achieved: (1) math anxiety is related to choice of college major, (2) males and females do not differ in math anxiety levels, (3) math anxiety levels change little over a short time interval, (4) math anxiety shows relatively little relationship to mathematics performance, (5) math anxiety shows a moderate relationship to mathematics background, achievement, and avoidance, and (6) the higher one\u27s level of math anxiety (as measured by the RMARS), the lower one\u27s self-rating of mathematics ability and the higher one\u27s self-rating of mathematics anxiety. Based upon the results, these conclusions were drawn: (1) improving mathematics performance will require programs that do more than reduce math anxiety, (2) re-entry students would appear to benefit most from treatment of math anxiety, (3) math anxiety appears to be related to inherent mathematical abilities of students, (4) the RMARS seems to adequately measure one\u27s level of math anxiety as perceived by oneself for all groups except for the Technical Majors enrolled in Precalculus Mathematics, (5) sex-related differences in math anxiety may exist, but are probably much smaller than suggested previously, and (6) the reduction of math anxiety in the Technical Majors Groups could be attributed primarily to the unique elements of these groups: course content, prerequisites, and position in the sequence

A source modelling system and its use for uncertainty management

Human agents have to deal with a considerable amount of information from their environment and are also continuously faced with the need to take actions. As that information is largely of an uncertain nature, human agents have to decide whether, or how much, to believe individual pieces of information. To enable a reasoning system to deal in general with the demands of a real environment, and with information from human sources in particular, requires tools for uncertainty management and belief formation. This thesis presents a model for the management of uncertain information from human sources. Dealing, more specifically, with information which has been pre-processed by a natural language processor and transformed into an event-based representation, the model assesses information, forms beliefs and resolves conflicts between them in order to maintain a consistent world model. The approach is built on the fundamental principle that the uncertainty of information from people can, in the majority of situations, successfully be assessed through source models which record factors concerning the source's abilities and trustworthiness. These models are adjusted to reflect changes in the behaviour of the source. A mechanism is presented together with the underlying principles to reproduce such a behaviour. A high-level design is also given to make the proposed model reconstructible, and the successful operation of the model is demonstrated on two detailed examples

Dying to Get out of Debt: Consumer Insolvency Law and Suicide in Japan

This Article explores the complex relation between consumer insolvency law and suicide in Japan, where bankruptcies and suicides have increased dramatically in recent years. The statistical and interview evidence, some of which relates to the creation of a relatively efficient and socially acceptable insolvency mechanism in 2001, suggests that law is at least indirectly relevant to decisions to take one’s own life. Law can bring about debt control and stigma mitigation, each of which can lead to lower levels of stress and depression, each of which can lead to lower suicide rates. Still, responses to the law, even in relatively homogeneous Japan, are varied and ambiguous, and seldom if ever is insolvency law the sole cause of suicide. The causal mechanism behind the law’s apparent force appears to be a complex calculus of economic and social factors