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Relative Unification in Intuitionistic Logic: Towards the Provability Logic of Ha
Journal of Symbolic Logic:1-41 (forthcoming)
Abstract
This article studies relative unification and admissibility in intuitionistic logic. We generalize results of [3, 7] and prove them relative to ${\mathsf {N}}$ formulae, the class of forlmulae with No Nested Implications to the Left. The main application of this generalization is to characterize the provability logic of Heyting Arithmetic $\mathsf {HA}$ and prove its decidability [16].Other Versions
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References found in this work
Unification in intuitionistic logic.Silvio Ghilardi - 1999 - Journal of Symbolic Logic 64 (2):859-880.
On the admissible rules of intuitionistic propositional logic.Rosalie Iemhoff - 2001 - Journal of Symbolic Logic 66 (1):281-294.
Best solving modal equations.Silvio Ghilardi - 2000 - Annals of Pure and Applied Logic 102 (3):183-198.
Rules of inference with parameters for intuitionistic logic.Vladimir V. Rybakov - 1992 - Journal of Symbolic Logic 57 (3):912-923.
Concerning formulas of the types a →b ∨c, a →(ex)b(X).Ronald Harrop - 1960 - Journal of Symbolic Logic 25 (1):27-32.
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