  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 Novak 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 Pavelka-style completeness

Artificial Intelligence;Logic in Computer Science