Аналитические таблицы для позитивных логик, свободных от «парадоксов» материальной импликации.

Abstract

Method of analytic tableaux for implicative and positive relevant logics is developed. It is based on certain modification of the method of analytic tableaux elaborated by Beth, Hintikka, Smullyan and Fitting. This modification includes a simple signing of negative occurences of subformulae in a formula and corresponding definition of closed analytic tableau. The method proposed is used to construct decidable propositional relevant calculi without negation, namely the systems $RA_\supset$ and $RA_{pos}$.