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On the admissible rules of intuitionistic propositional logic

  • Rosalie Iemhoff (a1)

Abstract

We present a basis for the admissible rules of intuitionistic propositional logic. Thereby a conjecture by de Jongh and Visser is proved. We also present a proof system for the admissible rules, and give semantic criteria for admissibility.

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[1977] Citkin, A. I., On admissible rules of intuitionistic propositional logic, Mathematics of the USSR, Sbornik, vol. 31 (1977), pp. 314323.
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[to appear] Ghilhardi, S., Unification in intuitionistic and De Morgan Logic, this Journal, (to appear).
[1960] Harrop, R., Concerning formulas of the types A → B ⋁ C, A → (Ex)B(x) in intuitionistic formal systems, this Journal, vol. 25 (1960), pp. 2732.
[1976] Mints, G. E., Derimbility of admissible rules, Journal of Soviet Mathematics, vol. 6 (1976).
[1997] Rybakov, V. V., Admissibility of Logical Inference Rules, Elsevier, Amsterdam, 1997.
[1988] Troelstra, A. S. and van Dalen, D., Constructivism in Mathmatics I, Elsevier, Amsterdam, 1988.
[to appear] Visser, A., Rules and arithmetics, Notre Dame Journal of Formal Logic, (to appear).

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