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MODELING OF FUZZY REASONING IN PREDICATE LOGIC BASED ON PETRI NETS
Abstract
Methods of deductive inference that are various modifications of the principle of resolutions are quite effective in logic. The results and justifications for the fuzzy conclusion of the resolution type are widespread in the predicate calculus. The existing models of the resolution inference are effective, and also quite simple and convenient, for conventional reasoning under incomplete information and for automatic processing of uncertain knowledge in interactive systems. However, in such models the set of generated resolvents does not have a structure, therefore the process of logical reasoning is neither visual nor reflecting the influence of fuzzy degrees of truth of some predicates on fuzzy degrees of truth of others. As a model of knowledge representation we proposed a new class of fuzzy high-level Petri nets for reasoning. We model Horn clauses as fragments of this net, propagate along the net tuples of variables corresponding to predicates, and calculate the fuzzy degree of truth of the goal clause. Fragments of our proposed net structure model the rules, and its dynamics reflects the generation of resolvents. In this case, the fuzzy degree of truth of the goal statement is calculated. The developed fuzzy logic models and algorithms of fuzzy inference in the predicate calculus on the basis of Petri nets have universality, the ability to take into account the uncertainty of different nature, structuredness and visibility. They can equally be successfully used in various industries for creating advisory systems, decision support algorithms. This will be able to automate the solution of a wide class of practical problems that are difficult to quantify, uncertain in knowledge and data. At the same time, technicians can work with models even they do not have special knowledge and skills in the field of fuzzy sets, logical programming or automatic proof of theorems. Due to the possibility to take into account both the fuzzy degree of truth of facts and the fuzzy degree of experts' confidence in the rules, one can obtain results that are not inferior to the recommendations of highly qualified subject specialists.
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References3
Egorov A. F., Shajkin A. N. Logical modeling under uncertainty based on fuzzy interval Petri nets, Journal of Computer and Systems Sciences International, Russia, vol. 41/issue 2, pp 295-299, 2002.
Lee R. C. T. Fuzzy Logic and the Resolution Principle // J. ACM, 19, no 1, pp 109- 112, 1979.
Jeffrey J., Lobo J., Murata T. A High-Level Petri Net for Goal-Directed Semantics of Horn Clause Logic. IEEE Transactions on Knowledge and Data Engineering, 8, pp 241-259, 1996.
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