Introduction

Abstract

Abstract The vital part of the studies of logic seeks to determine structural criteria for propositional validity and deals with formal inference relations. A suitable starting point for any analysis of these problems consists in the selection of a set of propositions from among all grammatically well-formed sentences, the members of which satisfy some specified syntactical and semantical conditions. The assumption stating that to every proposition it may be ascribed exactly one of the two logical values, truth or falsity, called the principle of bivalence, constitutes the basis of classical logic. It determines both the subject matter and the scope of applicability of the logic, the main systems of which are the classical propositional calculus (CPC) and the (first-order) predicate calculus (quantifier calculus). CPC is a theory of all truth-functional propositional connectives, i.e. sentence-argument propositional functions having the property that the logical value of any complex sentence formed with their use is determined uniquely by the logical values of its components. The predicate calculus is formed by introducing to the language system, with its semantics adequately extended, the symbols of name-argument propositional functions representing the names of properties and relations and name quantifiers. It renders possible the profound analysis of propositions within the principle of bivalence paradigm.