Strong Decidability and Strong Recognizability

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Abstract

Extensions of Johansson’s minimal logic J are considered. It is proved that families of negative and nontrivial logics and a series of other families are strongly decidable over J. This means that, given any finite list Rul of axiom schemes and rules of inference, we can effectively verify whether the logic with axioms and schemes, J + Rul, belongs to a given family. Strong recognizability over J is proved for known logics Neg, Gl, and KC as well as for logics LC and NC and all their extensions.

Original languageEnglish
Pages (from-to)370-385
Number of pages16
JournalAlgebra and Logic
Volume56
Issue number5
DOIs
Publication statusPublished - 1 Nov 2017

Keywords

  • admissible rule
  • decidability
  • Johansson algebra
  • minimal logic
  • recognizable logic
  • strong decidability

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