Universal truth tables and normal forms

Turksen´s (1995, 1986) fuzzy normal forms and Kandel et al.´s (1995) and Schwede and Kandel´s (1977) fuzzy maps are unified to establish universal truth tables and normal forms. After an introduction to the topic, we start out with a discussion on linguistic assertions. Next, we develop a new universal truth table construction in order to generate normal forms for both the 16 main concepts of two variables, as well as the subconcepts that can be generated from them. It is shown how fuzzy propositional and fuzzy predicate expressions can be generated with the universal truth table construction. Furthermore, it is shown that the laws of conservation hold in a general way on the “fuzzified laws of exclude middle and contradiction” generated by the class of t norms and their dual t conorms