CRIS

Permanent URI for this communityhttps://scripta.up.edu.mx/handle/20.500.12552/1

Browse

Settings

Author: search.filters.author.Weber, ZachStart date: 2025

Search Results

Now showing 1 - 2 of 2
  • Loading...
    Thumbnail Image
    Some of the metrics are blocked by your 
    consent settings
    Item type:Publication,
    Inconsistent sets and how to compute them
    (Springer Science and Business Media LLC, 2026)
    Cano-Jorge, Fernando  
    ;
    Weber, Zach
    The idea of a paraconsistent computability theory has been proposed as a way to work effectively with inconsistent sets of numbers. The viability of such a theory, though—the very coherence of the idea of an ‘inconsistent recursive relation’—has been called into doubt, most recently in (Choi, Synthese 200(5):418, 2022). In this paper we remove some doubt, by setting out a simple model of (naïve) set theory in LP, showing how to compute inconsistent sets in terms of extensions and antiextensions, and establishing further representability results. This suggests a way that a longstanding and apparently impossible-to-answer question—how can inconsistency be computed?—can be answered. ©The author ©Springer.
  • Loading...
    Thumbnail Image
    Some of the metrics are blocked by your 
    consent settings
    Item type:Publication,
    On Strong and Weak Logics for Paraconsistent Computability
    (College Publications, 2025)
    Weber, Zach
    ;
    Cano-Jorge, Fernando
    One tradition in relevant and paraconsistent logics has been to develop systems intended for applications to arithmetic and computability theory. The aspiration, as in Meyer [38] and others, is to recover enough working mathematics for real computation, but without the limitative results of Turing, Gödel, etc.; or more cautiously, as in Dunn [22], to respect relevance and with that be insulated against the possibility of a genuine inconsistency. We distill these goals into GUIDING QUESTIONS, and study the options for logics within a range of relevant systems. We focus on strong truth functional logics RM3 and PAC [6] and their expansions, with application to inconsistent arithmetics [61, 62]. We argue that this approach, while having many virtues, does not fully answer our guiding questions. This points to weak relevant logics like Routley/Sylvan’s DKQ [54], Brady's MCQ [14], and Logan and Boccuni's DL2Q*f [31]. The recurring theme is that paraconsistent computability struggles with functionality [17, 41, 43]. A method for advancing on the ‘function problem' is sketched with Kleene's theorem as a worked example. ©The authors ©College Publications © Journal of Applied Logics.