Inference Rules in Nelson’s Logics, Admissibility and Weak Admissibility

Logica Universalis 9 (1):93-120 (2015)
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Abstract

Our paper aims to investigate inference rules for Nelson’s logics and to discuss possible ways to determine admissibility of inference rules in such logics. We will use the technique offered originally for intuitionistic logic and paraconsistent minimal Johannson’s logic. However, the adaptation is not an easy and evident task since Nelson’s logics do not enjoy replacement of equivalences rule. Therefore we consider and compare standard admissibility and weak admissibility. Our paper founds algorithms for recognizing weak admissibility and admissibility itself – for restricted cases, to show the problems arising in the course of study

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References found in this work

Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
Constructible falsity and inexact predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.
Unification in intuitionistic logic.Silvio Ghilardi - 1999 - Journal of Symbolic Logic 64 (2):859-880.
One hundred and two problems in mathematical logic.Harvey Friedman - 1975 - Journal of Symbolic Logic 40 (2):113-129.

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