Системы натурального вывода для некоторых логик с истинностными провалами и логик с пресыщенными оценками

Abstract

In the paper we present Fitch-style natural deduction systems of some logics with truth-value gluts and truth-value gaps. We show that natural deduction systems of the logics in question can be set up with different formulations of either the disjunction elimination rule or the negation introduction rule. We give a constructive proof that for each natural deduction system N of a logic $\alpha$, a formula A is N-provable iff A is a $\alpha$-theorem.