Условия применимости классической логики в рамках языков неклассических логик.

Abstract

C lassical logic can not be applied in some philosophical reasonings, especially in those which contain contradictory, antinomical, paradoxical (true and false), senseless (neither true nor false), nonproved statements. So the problem o f applicability o f the classical logic and other logics to various statem ents may be important.

Let $L_1$ and $L_2$ be two defined in usual way propositional logics such that the language fo r $L_1$ is a sublanguage fo r $L_2$.

Logic $L_1$ with its connectives $\{C_1,...,C_n\}$ is called applicable to w ff A in $L_2$, {symbolically: Ap($L_1\{C_1,…,C_n\}$, A, $L_2$)) ifffo r any theorem $T$ in $L_1$ each formula $T_i$: obtained by substitution o f $A$ fo r all occurences same variables in $T$ is deducible in $L_2$.

The conditions o f applicability o f propositional classical logic will be defined in the languages o f the intuitionistic logic, Lukasiewich's logic $L_3$, Kleene's logic, enriched by fu ll equivalence.

The conditions o f applicability o f propositional classical logic, Lukasiewich's logic, Kleene's logic will be defined in the language o f the logic $FL4$ with falsehood operator.