Description

• Title:
  Informal Provability, First-Order BAT Logic and First Steps Towards a Formal Theory of Informal Provability
• Creator:
  Pawlowski, Pawel;
  Urbaniak, Rafal
• Description:
  BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting. To reach this stage it has to be extended to a first-order version. In this paper we provide such an extension. We do so by constructing non-deterministic three-valued models that interpret quantifiers as some sorts of infinite disjunctions and conjunctions. We also elaborate on the semantical properties of the first-order system and consider a couple of its strengthenings. It turns out that obtaining a sensible strengthening is not straightforward. We prove that most strategies commonly used for strengthening non-deterministic logics fail in our case. Nevertheless, we identify one method of extending the system which does not.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2021 Logic and Logical Philosophy
• Date:
  2021.11.29
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Language:
  English
• Source:
  Logic and Logical Philosophy; Vol. 31 No. 3 (2022): September; 501-527;
  Logic and Logical Philosophy; Tom 31 Nr 3 (2022): Wrzesień; 501-527;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Publisher:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relation: https://apcz.umk.pl/LLP/article/view/27607/30481
• Subject:
  non-deterministic logics;
  informal provability;
  BAT logic
• Identifier: https://apcz.umk.pl/LLP/article/view/27607
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  text