О негативно эквивалентных расширениях минимальной логики.

Abstract

We define the relation of negative equivalence on the class of nontrivial extensions of minimal logic as follows. Logics are negatively equivalent if they define the same negative consequence relation or, equivalently, if they have the same class of inconsistent sets of formulas. We point out the least logic in any class of logics with fixed intuitionistic and negative counterparts and prove that each of such logics is closed under the rule $(\phi~\vee \perp)/\phi$. We prove also that negative counterparts of extensions of negative logics can be treated as theirs logics of contradictions.