Fuzzy Logic in Narrow Sense with Hedges

Classical logic has a serious limitation in that it cannot cope with the issues of vagueness and uncertainty into which fall most modes of human reasoning. In order to provide a foundation for human knowledge representation and reasoning in the presence of vagueness, imprecision, and uncertainty, fuzzy logic should have the ability to deal with linguistic hedges, which play a very important role in the modification of fuzzy predicates. In this paper, we extend fuzzy logic in narrow sense with graded syntax, introduced by Nova´k et al., with many hedge connectives. In one case, each hedge does not have any dual one. In the other case, each hedge can have its own dual one. The resulting logics are shown to also have the Pavelkastyle completeness.