Computational Intelligence: Extended Truth Tables and Fuzzy Normal Forms

Our native intelligence captures and encodes our knowledge into our biological neural networks, and communicates them to the external world via linguistic expressions of a natural language. These linguistic expressions are naturally constrained by syntax and semantics of a given natural language and its cultural base of abstractions. Next, an accepted scientific paradigm and its language further restricts these linguistic expressions when propositional and predicate expressions are formulated in order to express either assumed or observed relationships between elements of a given domain of concern. Finally the symbols are represented with numbers in order to enable a computational aparatus to execute those assumed or observed relationships within the uniqueness of a given numerical scale. In this manner, our knowledge of a particular system’s behavior patterns are first expressed in a linguistic form and then transformed into computational expressions through at least two sets of major transformations stated above, i.e., first from language to formulae next from formulae to numbers.In this context, fuzzy normal-form formulae of linguistic expressions are derived with the construction of “Extended Truth Tables”. Depending on the set of axioms exhibited and/or we are willing to impose on the linguistic expressions of our native intelligence, we might arrive at different computational intelligence expressions for purposeful goal-oriented control of systems. In particular, it is shown that derivation of normal-form formulae for “Fuzzy Middle” and “Fuzzy Contradiction” lead to unique and enriched interpretations in comparison to the classical “Excluded Middle” and “Crisp Contradiction” expressions.