THEORIES OF SET AND LOGIC : COMPUTING WITH WORDS AND NUMBERS

In this Kdynote address, two types of information granules are considered : (ⅰ) one for set assignments of a concept descriptor and (ⅱ) the other for truthood assignment to the concept description verifier. The first is, the process which specifies the assignment of an object to a clump, a class, a group, etc., and hence defines the set membership with a relational constraint. the second is the assignment of the degree of truthood or the membership specification of the abstract concept of truthood which specifies the " veristic" constraint associated with the concept descriptor. The combination of these two distinct assignments let us generate four set and logic theories. This then leads to the concern of normal forms and their derivation from truth tables for each of these theories. In this regard, some of the fundamental issues arising in this context are discussed and certain preliminary answers are provided in order to highlight the consequences of these theories.