Formalization and Specification of Geometric Knowledge Objects

This paper presents our work on the identification, formalization, structuring, and specification of geometric knowledge objects for the purpose of semantic representation and knowledge management. We classify geometric knowledge according to how it has been accumulated and represented in the geometric literature, formalize geometric knowledge statements by adapting the language of first-order logic, specify knowledge objects with embedded knowledge in a retrievable and extensible data structure, and organize them by modeling the hierarchic structure of relations among them. Some examples of formal specification for geometric knowledge objects are given to illustrate our approach. The underlying idea of the approach has been used successfully for automated geometric reasoning, knowledge base creation, and electronic document generation.     

A matrix-based VaR model for risk identification in power supply networks

This paper presents a value-at-risk (VaR) model based on the singular value decomposition (SVD) of a sparsity matrix for voltage risk identification in power supply networks. The matrix-based model provides a more computationally efficient risk assessment method than conventional models such as probability analysis and sensitivity analysis, for example, and provides decision makers in the power supply industry with sufficient information to minimize the risk of network collapse or blackouts. The VaR model is incorporated into a risk identification system (RIS) programmed in the MATLAB environment. The feasibility of the proposed approach is confirmed by performing a series of risk assessment simulations using the standard American Electric Power (AEP) test models (i.e. 14-, 30- and 57-node networks) and a real-world power network (Taiwan power network), respectively. In general, the simulated results confirm the ability of the matrix-based model VaR model to efficient identify risk of power supply networks.     

Hybrid possibilistic networks

Possibilistic networks and possibilistic logic are two standard frameworks of interest for representing uncertain pieces of knowledge. Possibilistic networks exhibit relationships between variables while possibilistic logic ranks logical formulas according to their level of certainty. For multiply connected networks, it is well-known that the inference process is a hard problem. This paper studies a new representation of possibilistic networks called hybrid possibilistic networks. It results from combining the two semantically equivalent types of standard representation. We first present a propagation algorithm through hybrid possibilistic networks. This inference algorithm on hybrid networks is strictly more efficient (and confirmed by experimental studies) than the one of standard propagation algorithm.     

An epistemic model of an agent who does not reflect on reasoning processes

This paper introduces an epistemic model of a boundedly rational agent under the two assumptions that (i) the agent’s reasoning process is in accordance with the model but (ii) the agent does not reflect on these reasoning processes. For such a concept of bounded rationality a semantic interpretation by the possible world semantics of the Kripke (1963) type is no longer available because the definition of knowledge in these possible world semantics implies that the agent knows all valid statements of the model. The key to my alternative semantic approach is the extension of the method of truth tables, first introduced for the propositional logic by Wittgenstein (1922), to an epistemic logic so that I can determine the truth value of epistemic statements for all relevant truth conditions. In my syntactic approach I define an epistemic logic–consisting of the classical calculus of propositional logic plus two knowledge axioms–that does not include the inference rule of necessitation, which claims that an agent knows all theorems of the logic. As my main formal result I derive a determination theorem linking my semantic with my syntactic approach. The difference between my approach and existing knowledge models is illustrated in a game-theoretic application concerning the epistemic justification of iterative solution concepts.     

A hybrid macroscopic-based model for traffic flow in road networks

Recently, the unquestionable growth of interest to increase the operational efficiency and capability of transportation systems led to the development of a large number of traffic modeling theories. One of the major operational issues when developing a transportation system management model lies in the selection of the appropriate methodological approach with respect to several decisions, such as the selection of the type of input and output data as well as the qualitative representation and the computational power of the model. Despite the considerable effort in the area, there is still not an approach which per se models effectively the various dynamically evolving features of traffic in road networks. The present paper addresses this issue by introducing a new hybrid approach which combines the complementary features and capabilities of both continuum mathematical models e.g. 1, 6, 23 and 26 and knowledge-based models e.g. 7, 22 and 28 in order to describe effectively traffic flow in road networks.     

Model checking MASL specification of distributed real-time systems

We present model checking algorithms for MASL specification of distributed real-time systems. The proposed algorithms use symbolic model checking approach by analogy with model checking algorithms for branching-time temporal logic CTL and alternating-time temporal logic ATL. For the fixed environment case, the algorithm is polynomial-time in the specification length and sizes of the sets of system states and actions. For the dynamic environment case, the algorithm is polynomial-time in the model size, but it is exponential-time in the structure of environment specification.     

An epistemic model of an agent who does not reflect on reasoning processes

This paper introduces an epistemic model of a boundedly rational agent under the two assumptions that (i) the agent’s reasoning process is in accordance with the model but (ii) the agent does not reflect on these reasoning processes. For such a concept of bounded rationality a semantic interpretation by the possible world semantics of the Kripke (1963) type is no longer available because the definition of knowledge in these possible world semantics implies that the agent knows all valid statements of the model. The key to my alternative semantic approach is the extension of the method of truth tables, first introduced for the propositional logic by Wittgenstein (1922), to an epistemic logic so that I can determine the truth value of epistemic statements for all relevant truth conditions. In my syntactic approach I define an epistemic logic–consisting of the classical calculus of propositional logic plus two knowledge axioms–that does not include the inference rule of necessitation, which claims that an agent knows all theorems of the logic. As my main formal result I derive a determination theorem linking my semantic with my syntactic approach. The difference between my approach and existing knowledge models is illustrated in a game-theoretic application concerning the epistemic justification of iterative solution concepts.     

Knowledge Representation, Reasoning and Integration Using Temporal Logic with Clocks

Representation, reasoning about and integrating knowledge based on multiple time granularities in knowledge-based systems is important, especially when talking about events that take place in the real world. Formal approaches based on temporal logics have been successfully applied in many application domains of knowledge-based systems where the evolution of a system and its environment through time is central. This paper presents a methodology based on temporal logic to deal with knowledge based on multiple time granularities in knowledge-based systems. The temporal logic we consider is especially suitable for modelling events with different rates and/or scales of progress. The methodology includes an approach to the representation of timing systems, a method used for representing facts and rules in a knowledge-based system that involve multiple time granularities using temporal logic, and several deductive reasoning techniques. The work presented in this article has been supported in part by The Australian Research Council and Macquarie University. Note that this paper is an extended and revised version of Orgun, Liu and Nayak [37].     

Funnel control for fully actuated systems under a fragment of signal temporal logic specifications

Temporal logics have lately proven to be a valuable tool for various control applications by providing a rich specification language. Existing temporal logic-based control strategies discretize the underlying dynamical system in space and/or time. We will not use such an abstraction and consider continuous-time systems under a fragment of signal temporal logic specifications by using the associated robust semantics. In particular, this paper provides computationally-efficient funnel-based feedback control laws for a class of systems that are, in a sense, feedback equivalent to single integrator systems, but where the dynamics are partially unknown for the control design so that some degree of robustness is obtained. We first leverage the transient properties of a funnel-based feedback control strategy to maximize the robust semantics of some atomic temporal logic formulas. We then guarantee the satisfaction for specifications consisting of conjunctions of such atomic temporal logic formulas with overlapping time intervals by a suitable switched control system. The result is a framework that satisfies temporal logic specifications with a user-defined robustness when the specification is satisfiable. When the specification is not satisfiable, a least violating solution can be found. The theoretical findings are demonstrated in simulations of the nonlinear Lotka–Volterra equations for predator–prey models.     

Discovering the dynamic behavior of unknown systems using fuzzy logic

To know the dynamic behavior of a system it is convenient to have a good dynamic model of it. However, in many cases it is not possible either because of its complexity or because of the lack of knowledge of the laws involved in its operation. In these cases, obtaining models from input–output data is shown as a highly effective technique. Specifically, intelligent modeling techniques have become important in recent years in this field. Among these techniques, fuzzy logic is especially interesting because it allows to incorporate to the model the knowledge that is possessed of the system, besides offering a more interpretable model than other techniques. A fuzzy model is, formally speaking, a mathematical model. Therefore, this model can be used to analyze the original system using known systems analysis techniques. In this paper a methodology for extract information from unknown systems using fuzzy logic is presented. More precisely, it is presented the exact linearization of a Takagi–Sugeno fuzzy model with no restrictions in use or distribution of its membership functions, as well as obtaining its equilibrium states, the study of its local behavior and the search for periodic orbits by the application of Poincaré.     

IDES: influence diagram based expert system

Influence diagrams have been used effectively in applied decision analysis to model complex systems, identify probabilistic dependence and characterize the flow of information. Their graphical representation and intuitive framework are particularly effective in representing knowledge from experts with diverse backgrounds and varying degrees of technical proficiency. They allow both a symbolic representation of the system interrelationships and a quantitative measure that can be of discrete or continuous functional form. By exploiting this abstraction hierarchy, successive degrees of specification can be made by several individuals, each encoding his or her expert knowledge of the problem and bounds on critical parameters. It is proposed that an interactive computer program that automates this influence diagram technology would provide an excellent tool for building expert systems. This paper describes such a modeling tool: the IDES (Influence Diagram Based Expert System) developed at the University of California at Berkeley as a modeling tool for building expert systems requiring reasoning with uncertain or incomplete information. The Diagnostician's Problem is presented as a tutorial for describing the IDES solution procedure.     

Past–future separation and normal forms in temporal predicate logic specifications

Temporal specifications are often used when phenomena are modelled where dynamics play a main role. If simulation is one of the aims of modelling, usually a restricted, executable modelling language format is used, based on some form of past to future implications. In this paper a detailed transformation procedure is described that takes any temporal predicate logic specification and generates a specification in a past-implies-future normal format. The procedure works for temporal specifications in which the atoms either express time ordering relations or are state-related, i.e., include only one time variable.     

A self-organizing adaptive fuzzy controller

There are two main parts in this paper. The first part presents a knowledge representation and reasoning scheme, called tree-searched neural networks (TNN). The TNN is based on a well-known intuitive knowledge representation (IKR) and can reduce the number of the processing nodes in the neural networks. The second part proposes a self-organizing adaptive fuzzy controller (SOAFC) based on the TNN model. It can help acquire control knowledge and thus can reduce the dependence on experts. Furthermore, designers do not need to predefine all membership functions to cover whole input space domain. For improving its performance further, we design a D-controller which is included within the SOAFC. Whether the fuzzy controller is incorporated with the D-controller or not, it is also guaranteed to be globally stable. Simulation results show that this approach has faster convergence speed, results in better transient response, and in addition requires less total control energy.     

Optimal Hierarchies for Quadrilateral Surfaces

Multiresolution representation of quadrilateral surface approximation (MRQSA) is a useful representation for progressive graphics transmission in networks. Based on two requirements: (1) minimum mean square error and (2) fixed reduction ratio between levels, this paper first transforms the MRQSA problem into the problem of solving a sequence of near-Toeplitz tridiagonal linear systems. Employing the matrix perturbation technique, the MRQSA problem can be solved using about 24mn floating-point operations, i.e. linear time, if we are given a polygonal surface with (2m–1)×(2n–1) points. A numerical stability analysis is also given. To the best of our knowledge, this is the first time that such a linear algebra approach has been used for solving the MRQSA problem. Some experimental results are carried out to demonstrate the applicability of the proposed method.