Fundamenta Informaticae - Volume 79, issue 3-4

Authors: Suraj,, Zbigniew | Fryc, Barbara

Article Type: Research Article

Abstract: Approximate Petri nets (AP-nets) can be used for the knowledge representation and approximate reasoning. The AP-net model is defined on the basis of the rough set approach, fuzzy Petri nets and coloured Petri nets. One of the main advantages of AP-net model is a possibility to present the reachability set of a given AP-net by means of an occurrence graph. Such graphs can serve, among others, for analyzing and evaluating an approximate reasoning realized by using …AP-net model. The main contribution of the paper is to present the algorithms for construction and analysis of occurrence graphs for the AP-nets, especially in the context of searching for the best decision and finding the shortest distance in order to compute such decision. This approach can be applied to the design and analysis of the formal models for expert systems, control systems, communication systems, etc. Show more

Keywords: approximate Petri nets, approximate reasoning, knowledge representation, occurrence graphs

Citation: Fundamenta Informaticae, vol. 79, no. 3-4, pp. 541-551, 2007

Authors: Suraj, Zbigniew | Pancerz, Krzysztof

Article Type: Research Article

Abstract: This paper provides new algorithms for computing consistent and partially consistent extensions of information systems. A maximal consistent extension of a given information system includes only objects corresponding to known attribute values which are consistent with all rules extracted from the original information system. A partially consistent extension of a given information system includes objects corresponding to known attribute values which are consistent to a certain degree with the knowledge represented by …rules extracted from the original information system. This degree can be between 0 and 1, 0 for the full inconsistency and 1 for the full consistency. The algorithms presented here do not involve computing any rules true in a given information system. This property differentiates them from methods presented in the earlier papers which concerned extensions of information systems. Show more

Keywords: rough sets, information systems, consistent extensions, partially consistent extensions

Citation: Fundamenta Informaticae, vol. 79, no. 3-4, pp. 553-566, 2007

Authors: Wolski, Marcin

Article Type: Research Article

Abstract: The present paper investigates approximation spaces in the context of mathematical structures which axiomatise the notion of nearness. Starting with the framework of information quanta which distinguishes two levels of information structures, namely property systems (the first level) and information quantum relational systems (the second level), we shall introduce the notion of Pawlak property system. These systems correspond bijectively to finite approximation spaces, i.e. their respective information quantum relational systems. Then we …characterise Pawlak property systems in terms of symmetric topological spaces. In the second part of the paper, these systems are defined by means of topological structures based on the concept of nearness. We prove that the category of Pawlak property systems is isomorphic to the category of finite topological nearness spaces and provide its additional topological characterisation. Show more

Citation: Fundamenta Informaticae, vol. 79, no. 3-4, pp. 567-577, 2007

Authors: Zbrzezny, Andrzej | Półrola, Agata

Article Type: Research Article

Abstract: Reachability analysis for timed automata using SAT-based methods was considered in many papers, occurring to be a very efficient model checking technique. In this paper we show how to apply this method of verification to timed automata with discrete data, i.e., to standard timed automata augmented with integer variables. The theoretical description is supported by some preliminary experimental results.

Citation: Fundamenta Informaticae, vol. 79, no. 3-4, pp. 579-593, 2007