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T. J. Stepień, L. T. Stepień


The Pedagogical University of Cracow, ul. Podchorazych 2, 30 - 084 Krakow, Poland


In this paper we put forward a new solution of the well-known problem of relevant logics,i.e., we construct an atomic entailment. Hence, we construct a system of predicate calculus based on the atomic entailment. Next, we establish the definition of atomic inconsistency. The atomic inconsistency establishes an infinite class of inconsistent, but non-trivial systems. In this paper we construct the new definition of the classical entailment, into the bargain.


Atomic entailment, atomic inconsistency, classical entailment, relevance.

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