Logica Universalis

, Volume 11, Issue 4, pp 421–437 | Cite as

Admissibility in Positive Logics

  • Alex Citkin


The paper studies admissibility of multiple-conclusion rules in positive logics. Using modification of a method employed by M. Wajsberg in the proof of the separation theorem, it is shown that the problem of admissibility of multiple-conclusion rules in the positive logics is equivalent to the problem of admissibility in intermediate logics defined by positive additional axioms. Moreover, a multiple-conclusion rule \(\mathsf {r}\) follows from a set of multiple-conclusion rules \(\mathsf {R}\) over a positive logic \(\mathsf {P}\) if and only if \(\mathsf {r}\) follows from \(\mathsf {R}\) over \(\mathbf {Int}+ \mathsf {P}\).


Inference rule multiple-conclusion rule admissible rule positive logic intermediate logic Brouwerian algebra 

Mathematics Subject Classification

Primary 03B55 Secondary 03B60 03C05 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Metropolitan TelecommunicationsNew YorkUSA

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