ABSTRACT
A generic construction of a many-valued logic starts with the choice of the sentential language L which may be shown as an algebra L = (For, FI , . . . , Fm) freely generated by the set of sentential variables Var = {p, q, r,...}. Formulas, i.e. elements of For, are then built from variables using the operations FI, ..., Fm representing the sentential connectives. In most cases, either the language of the classical sentential logic
Lk = (For, -., -», V, A, «•>) with negation (-1), implication (->), disjunction (V), conjunction (A), and equivalence («-»•), or some of its reducts or extensions is considered. Subsequently, one
defines a multiple-valued algebra A similar to L and chooses a non-empty subset of the universe of A, D C A of designated elements. The interpretation structures
M = (A,D) are called logical matrices.
