2026-04-13T00:10:08Zhttps://recercat.cat/oai/request

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

urn:hdl:2445/228610 Strictly Positive Fragments of the Provability Logic of Heyting Arithmetic Almeida Borges, Ana de Joosten, Joost J. Lògica Probabilitats Aritmètica Logic Probabilities Arithmetic 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. 2026-03-30T15:32:49Z 2026-03-30T15:32:49Z 2024-10-30 2026-03-30T15:32:49Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Reproducció del document publicat a: https://doi.org/10.1007/s11225-024-10152-y Studia Logica, 2024 https://doi.org/10.1007/s11225-024-10152-y cc by (c) Almeida Borges, Ana de et al., 2024 https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Springer Articles publicats en revistes (Filosofia)