Number of the records: 1  

How Much Propositional Logic Suffices for Rosser's Undecidability Theorem?

  1. 1.
    0523434 - ÚI 2023 GB eng J - Journal Article
    Badia, G. - Cintula, Petr - Hájek, Petr - Tedder, Andrew
    How Much Propositional Logic Suffices for Rosser's Undecidability Theorem?
    Review of Symbolic Logic. -, Online 29 June 2020 (2022). ISSN 1755-0203. E-ISSN 1755-0211
    R&D Projects: GA ČR GA17-04630S
    Institutional support: RVO:67985807
    OECD category: Pure mathematics
    Impact factor: 1.000, year: 2020

    In this paper we explore the following question: how weak can a logic be for Rosser’s essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson’s Q is essentially undecidable in intuitionistic logic, and P. Hájek proved it in the fuzzy logic BL for Grzegorczyk’s variant of Q which interprets the arithmetic operations as non-total non-functional relations.We present a proof of essential undecidability in a much weaker substructural logic and for a much weaker arithmetic theory, a version of Robinson’s R (with arithmetic operations also interpreted as mere relations). Our result is based on a structural version of the undecidability argument introduced by Kleene and we show that it goes well beyond the scope of the Boolean, intuitionistic, or fuzzy logic.
    Permanent Link: http://hdl.handle.net/11104/0307787

     
     
Number of the records: 1