Abstract
1. I shall propose the formalization of some nonstandard semantics in sequential form. On semantical level the problem of paraconsistency has the following aspects: First of all, what does it mean that “contradictions entails everything”? What kind of entailment is involved here? Below we are going to show that under the different presuppositions different notions of entailment relation can be formalized in the same system. Secondly, what is our interpretation of contradiction. This question is related to the treatment of negation. The notion of impossible worlds and its analogous are not admitted in semantics as considered to be less clear. Instead of this predicates of truth and falsity are considered to be partially defined. We develop the idea of the symmetry of concepts of truth and falsity (and this is very important). Falsity is considered to be an independent notion and not as absence or negation of the truth.
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