2026-04-17T03:02:57Zhttps://recercat.cat/oai/request

oai:recercat.cat:2445/2286102026-04-08T07:33:00Zcom_2072_1057col_2072_478820col_2072_478917

00925njm 22002777a 4500 dc Almeida Borges, Ana de author Joosten, Joost J. author 2026-03-30T15:32:49Z 2026-03-30T15:32:49Z 2024-10-30 2026-03-30T15:32:49Z We determine the strictly positive fragment QPL+(HA) of the quantified provability logic QPL(HA) of Heyting Arithmetic. We show that QPL+(HA) is decidable and that it coincides with QPL+(PA), which is the strictly positive fragment of the quantified provability logic of of Peano Arithmetic. This positively resolves a previous conjecture of the authors described in [14]. On our way to proving these results, we carve out the strictly positive fragment PL+(HA) of the provability logic PL(HA) of Heyting Arithmetic, provide a simple axiomatization, and prove it to be sound and complete for two types of arithmetical interpretations. The simple fragments presented in this paper should be contrasted with a recent result by Mojtahedi [43], where an axiomatization for PL(HA) is provided. This axiomatization, although decidable, is of considerable complexity. Lògica Probabilitats Aritmètica Logic Probabilities Arithmetic Strictly Positive Fragments of the Provability Logic of Heyting Arithmetic