A three-valued propositional logic is presented, within which the three values are read as ?true?, ?false? and ?nonsense?. A three-valued extended functional calculus, unrestricted by the theory of types, is then developed. Within the latter system, Bochvar analyzes the Russell paradox and the Grelling-Weyl paradox, formally demonstrating the meaninglessness of both.

The Joint Non-Trivialization Theorem, two Definability Theorems and the generalized Quantifier Elimination Theorem are proved for J 3-theories. These theories are three-valued with more than one distinguished truth-value, reflect certain aspects of model type logics and can. be paraconsistent. J 3-theories were introduced in the author's doctoral dissertation.

his paper presents a unified treatment of the propositional and first-order many-valued logics through the method of tableaux. It is shown that several important results on the proof theory and model theory of those logics can be obtained in a general way. We obtain, in this direction, abstract versions of the completeness theorem, model existence theorem (using a generalization of the classical analytic consistency properties), compactness theorem and Lowenheim-Skolem theorem. The paper is completely self-contained and includes examples of application to (...) particular many-valued formal systems. (shrink)

This paper studies a class of infinite-valued predicate logics. A sufficient condition for axiomatizability of logics from that class is given.