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The " -calculus" is a formal logical system, which as classical one, treats (true and false) assertions in the grounds, but unlike - in the semantic sense - their truth (falsity) values are differently set. Besides, here are of interest only (always) false formulas or negations etc. We formulate a number of formal theorems of the calculus within its "propositional", "predicate" and "arithmetical" versions and put forward the (meta-theoretical) requirements for completeness and consistency of these systems. It is shown that they largely "share fate" of classical formalizations: when it is about, say, completeness of the propositional calculus, or the (in)completeness of predicate calculus and formal number theory et al. Finally, we bring a version of this formalism as a sequential calculus, as well as a constructive proof of its consistency (after Gentzen).

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Dr Milan Tasi D. has degrees in mathematics, philosophy and classical languages (Greek and Latin). He obtained his PhD in the field of mathematical logic in Belgrade. He taught mathematics at the University of Skopje and Algiers and philosophy at the University of Ni . He is one of founders of the Biocosmological Association.

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