The Relationship between Fuzzy Reasoning and Its Temporal Characteristics for Knowledge Management

The knowledge management systems based on artificial reasoning (KMAR) tries to provide computers the capabilities of performing various intelligent tasks for which their human users resort to their knowledge and collective intelligence. There is a need for incorporating aspects of time and imprecision into knowledge management systems, considering appropriate semantic foundations. The aim of this paper is to present the FRTES, a real-time fuzzy expert system, embedded in a knowledge management system. Our expert system is a special possibilistic expert system, developed in order to focus on fuzzy knowledge.Knowledge Management, Artificial Reasoning, predictability

Conditionals and modularity in general logics

In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics

Interpolative and extrapolative reasoning in propositional theories using qualitative knowledge about conceptual spaces

International audienceMany logical theories are incomplete, in the sense that non-trivial conclusions about particular situations cannot be derived from them using classical deduction. In this paper, we show how the ideas of interpolation and extrapolation, which are of crucial importance in many numerical domains, can be applied in symbolic settings to alleviate this issue in the case of propositional categorization rules. Our method is based on (mainly) qualitative descriptions of how different properties are conceptually related, where we identify conceptual relations between properties with spatial relations between regions in Gärdenfors conceptual spaces. The approach is centred around the view that categorization rules can often be seen as approximations of linear (or at least monotonic) mappings between conceptual spaces. We use this assumption to justify that whenever the antecedents of a number of rules stand in a relationship that is invariant under linear (or monotonic) transformations, their consequents should also stand in that relationship. A form of interpolative and extrapolative reasoning can then be obtained by applying this idea to the relations of betweenness and parallelism respectively. After discussing these ideas at the semantic level, we introduce a number of inference rules to characterize interpolative and extrapolative reasoning at the syntactic level, and show their soundness and completeness w.r.t. the proposed semantics. Finally, we show that the considered inference problems are PSPACE-hard in general, while implementations in polynomial time are possible under some relatively mild assumptions

Practical Model-Based Diagnosis with Qualitative Possibilistic Uncertainty

An approach to fault isolation that exploits vastly incomplete models is presented. It relies on separate descriptions of each component behavior, together with the links between them, which enables focusing of the reasoning to the relevant part of the system. As normal observations do not need explanation, the behavior of the components is limited to anomaly propagation. Diagnostic solutions are disorders (fault modes or abnormal signatures) that are consistent with the observations, as well as abductive explanations. An ordinal representation of uncertainty based on possibility theory provides a simple exception-tolerant description of the component behaviors. We can for instance distinguish between effects that are more or less certainly present (or absent) and effects that are more or less certainly present (or absent) when a given anomaly is present. A realistic example illustrates the benefits of this approach.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

Rule model simplification

Centre for Intelligent Systems and their ApplicationsDue to its high performance and comprehensibility, fuzzy modelling is becoming more and more popular in dealing with nonlinear, uncertain and complex systems for tasks such as signal processing, medical diagnosis and financial investment. However, there are no principal routine methods to obtain the optimum fuzzy rule base which is not only compact but also retains high prediction (or classification) performance. In order to achieve this, two major problems need to be addressed. First, as the number of input variables increases, the number of possible rules grows exponentially (termed curse of dimensionality). It inevitably deteriorates the transparency of the rule model and can lead to over-fitting, with the model obtaining high performance on the training data but failing to predict the unknown data successfully. Second, gaps may occur in the rule base if the problem is too compact (termed sparse rule base). As a result, it cannot be handled by conventional fuzzy inference such as Mamdani. This Ph.D. work proposes a rule base simplification method and a family of fuzzy interpolation methods to solve the aforementioned two problems. The proposed simplification method reduces the rule base complexity via Retrieving Data from Rules (RDFR). It first retrieves a collection of new data from an original rule base. Then the new data is used for re-training to build a more compact rule model. This method has four advantages: 1) It can simplify rule bases without using the original training data, but is capable of dealing with combinations of rules and data. 2) It can integrate with any rule induction or reduction schemes. 3) It implements the similarity merging and inconsistency removal approaches. 4) It can make use of rule weights. Illustrative examples have been given to demonstrate the potential of this work. The second part of the work concerns the development of a family of transformation based fuzzy interpolation methods (termed HS methods). These methods first introduce the general concept of representative values (RVs), and then use this to interpolate fuzzy rules involving arbitrary polygonal fuzzy sets, by means of scale and move transformations. This family consists of two sub-categories: namely, the original HS methods and the enhanced HS methods. The HS methods not only inherit the common advantages of fuzzy interpolative reasoning -- helping reduce rule base complexity and allowing inferences to be performed within simple and sparse rule bases -- but also have two other advantages compared to the existing fuzzy interpolation methods. Firstly, they provide a degree of freedom to choose various RV definitions to meet different application requirements. Secondly, they can handle the interpolation of multiple rules, with each rule having multiple antecedent variables associated with arbitrary polygonal fuzzy membership functions. This makes the interpolation inference a practical solution for real world applications. The enhanced HS methods are the first proposed interpolation methods which preserve piece-wise linearity, which may provide a solution to solve the interpolation problem in a very high Cartesian space in the mathematics literature. The RDFR-based simplification method has been applied to a variety of applications including nursery prediction, the Saturday morning problem and credit application. HS methods have been utilized in truck backer-upper control and computer hardware prediction. The former demonstrates the simplification potential of the HS methods, while the latter shows their capability in dealing with sparse rule bases. The RDFR-based simplification method and HS methods are further integrated into a novel model simplification framework, which has been applied to a scaled-up application (computer activity prediction). In the experimental studies, the proposed simplification framework leads to very good fuzzy rule base reductions whilst retaining, or improving, performance

Reasoning-Supported Quality Assurance for Knowledge Bases

The increasing application of ontology reuse and automated knowledge acquisition tools in ontology engineering brings about a shift of development efforts from knowledge modeling towards quality assurance. Despite the high practical importance, there has been a substantial lack of support for ensuring semantic accuracy and conciseness. In this thesis, we make a significant step forward in ontology engineering by developing a support for two such essential quality assurance activities

Adaptive fuzzy interpolation

Fuzzy interpolative reasoning strengthens the power of fuzzy inference by the enhancement of the robustness of fuzzy systems and the reduction of the systems' complexity. However, after a series of interpolations, it is possible that multiple object values for a common variable are inferred, leading to inconsistency in interpolated results. Such inconsistencies may result from defective interpolated rules or incorrect interpolative transformations. This paper presents a novel approach for identification and correction of defective rules in interpolative transformations, thereby removing the inconsistencies. In particular, an assumption-based truth-maintenance system (ATMS) is used to record dependences between interpolations, and the underlying technique that the classical general diagnostic engine (GDE) employs for fault localization is adapted to isolate possible faulty interpolated rules and their associated interpolative transformations. From this, an algorithm is introduced to allow for the modification of the original linear interpolation to become first-order piecewise linear. The approach is applied to a realistic problem, which predicates the diarrheal disease rates in remote villages, to demonstrate the potential of this study