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Decidable variables for constructive logics
Author(s) -
Niki Satoru
Publication year - 2020
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.202000022
Subject(s) - decidability , mathematics , class (philosophy) , intuitionistic logic , constructive , zeroth order logic , extension (predicate logic) , discrete mathematics , warrant , propositional calculus , propositional variable , atomic formula , intermediate logic , calculus (dental) , computer science , description logic , theoretical computer science , multimodal logic , programming language , artificial intelligence , process (computing) , financial economics , medicine , dentistry , economics
Ishihara's problem of decidable variables asks which class of decidable propositional variables is sufficient to warrant classical theorems in intuitionistic logic. We present several refinements to the class proposed by Ishii for this problem, which also allows the class to cover Glivenko's logic. We also treat the extension of the problem to minimal logic, suggesting a couple of new classes.