On Strong and Weak Logics for Paraconsistent Computability
Journal
Journal of Applied Logics
ISSN
26319810
Publisher
College Publications
Date Issued
2025
Author(s)
Weber, Zach
Cano-Jorge, Fernando
Type
text::journal::journal article
Abstract
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.
License
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