Admissibility in Positive Logics

TL;DR

This paper investigates the admissibility of multiple-conclusion rules in positive logics, showing their equivalence to admissibility in certain intermediate logics through a modified proof method.

Contribution

It introduces a new approach linking admissibility in positive logics to intermediate logics using a modified separation theorem method.

Findings

Admissibility in positive logics is equivalent to that in certain intermediate logics.

A modified method based on Wajsberg's separation theorem is developed.

The approach simplifies the analysis of admissibility in positive logics.

Abstract

The paper studies admissibility of multiple-conclusion rules in the positive logics. Using modification of a method used by M.~Wajsberg in the proof of the separation theorem, it is shown that the problem of admissibility in positive logics is equivalent to the problem of admissibility in intermediate logics defined by positive additional axioms.