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We determine the strictly positive fragment $\mathsf{QPL}^+(\mathsf{HA})$ ofthe quantified provability logic $\mathsf{QPL}(\mathsf{HA})$ of HeytingArithmetic. We show that $\mathsf{QPL}^+(\mathsf{HA})$ is decidable and that itcoincides with $\mathsf{QPL}^+(\mathsf{PA})$, which is the strictly positivefragment of the quantified provability logic of of Peano Arithmetic. Thispositively resolves a previous conjecture of the authors.  On our way to proving these results, we carve out the strictly positivefragment $\mathsf{PL}^+(\mathsf{HA})$ of the provability logic$\mathsf{PL}(\mathsf{HA})$ of Heyting Arithmetic, provide a simpleaxiomatization, and prove it to be sound and complete for two types ofarithmetical interpretations.  The simple fragments presented in this paper should be contrasted with a 2022result by Mojtahedi, where an axiomatization for $\mathsf{PL}(\mathsf{HA})$ isprovided. This axiomatization, although decidable, is of considerablecomplexity.

Strictly Positive Fragments of the Provability Logic of Heyting Arithmetic