On the Model-Theoretic Semantics of Fuzzy Set Logic for Dealing with Inconsistency
Inconsistency is likely to exist in a knowledge base built up from various sources of information, especially in the presence of uncertainty and fuzziness. In such a case, inconsistency is often local and thus should not cause the entire knowledge base to collapse. For a fuzzy logic system to be able to deal with local inconsistency, an appropriate model-theoretic semantics is required. This paper analyses and shows that the model-theoretic semantics approach of possibilistic logic, which has recently become popular to be applied to the development of fuzzy set logic whose formulas can have fuzzy set constants, cannot deal with local inconsistency. We then introduce the annotated logic-based approach as a solution, and discuss on the difference and relation between the two approaches.