Doherty, P., Driankov, D., and Hellendoorn, H. (1992). Fuzzy If-Then-Unless Rules and their Implementa tion. Technical Report LiTH-IDA-R-92-21, Department of Computer and Information Science, Linköping University, Sweden. Extended Version of a Paper accepted at InternationalConference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU'92 Palma de Mallorca, July 6-10, 1992. (bibtex),
Abstract: We consider the possibility of generalizing the notion of a fuzzy If-Then rule to take into account its context dependent nature. We interpret fuzzy rules as modeling a forward directed causal relationship between the antecedent and the conclusion, which applies in most contexts, but on occasion breaks down in exceptional contexts. The default nature of the rule is modeled by augmenting the original If-Then rule with an exception part. We then consider the proper semantic correlate to such an addition and propose a ternary relation which satisfies a number of intuitive constraints described in terms of a number of inference rules. In the rest of the paper, we consider implementational issues arising from the unless extension and propose the use of reason maintenance systems, in particular TMS's, where a fuzzy If-Then-Unless rule is encoded into a dependency net. We verify that the net satisfies the constraints stated in the inference schemes and conclude with a discussion concerning the integration of qualitative IN-OUT labelings of the TMS with quantitative degree of membership labelings for the variables in question. A generalization to the TMS relabeling algorithm is proposed which would permit the modeling of reasoning with ``generalized modus ponens''.
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