Linguistics and uncertainty in intelligent systems

Fuzzy set theories allow us to represent our knowledge under various interpretations and axiomatic foundations from linguistic to computational representations. There are at least four levels of knowledge representation: (i) linguistic, (ii) meta-linguistic, (iii) propositional, and (iv) computational. There are three transformations, which depend on the particular interpretations put on a knowledge representation schema. There are various choices, corresponding to one´s interpretation of: (a) type of set representation, (fuzzy or crisp), (b) type of propositional connectives and normal forms, and (c) type of computational connectives, i.e., weak or strong t-norms and co-norms. In the light of these selections, fuzzy disjunctive and conjunctive normal forms (FDNF, FCNF) are derived from fuzzy truth tables. It is shown that classical expressions such as excluded middle etc., when fuzzified, ought to be reinterpreted with a type II, second order, semantic uncertainty. The classical expressions should not be interpreted as to whether they are valid or not. One can only state that the well-known tautologies of classical logic are valid to many degrees specified by an interval defined by their FDNF and FCNF. FDNF and FCNF boundaries identify the nonspecificity measure associated with type II, second order, semantic uncertainty. Thus, those researchers who are not familiar or who are not concerned with type II semantic uncertainty work with a myopic understanding of fuzzy set and logic theories.