Description

• Title:
  Core Type Theory
• Creator:
  van Dijk, Emma;
  Ripley, David;
  Gutierrez, Julian
• Contributor:
  Ripley, David - Monash University, Philosophy Department, SOPHIS, Building 11, Monash University, Clayton, VIC, Australia;
  Gutierrez, Julian - Monash University, Department of Data Science & AI, Woodside Building, Monash University, Clayton, VIC, Australia;
  van Dijk, Emma - emmavandijk168@gmail.com;
  Ripley, David - davewripley@gmail.com;
  Gutierrez, Julian - julian.gutierrez@monash.edu
• Description:
  Neil Tennant’s core logic is a type of bilateralist natural deduction system based on proofs and refutations. We present a proof system for propositional core logic, explain its connections to bilateralism, and explore the possibility of using it as a type theory, in the same kind of way intuitionistic logic is often used as a type theory. Our proof system is not Tennant’s own, but it is very closely related, and determines the same consequence relation. The difference, however, matters for our purposes, and we discuss this. We then turn to the question of strong normalization, showing that although Tennant’s proof system for core logic is not strongly normalizing, our modified system is.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nc-nd/4.0
• Date:
  2023.10.12;
  2023.08.16
• Type:
  Other
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Bulletin of the Section of Logic;2;
  52
• Subject:
  core logic;
  type theory;
  strong normalization
• Identifier:
  0138-0680;
  http://hdl.handle.net/11089/48070 ;
  2449-836X;
  10.18778/0138-0680.2023.19
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  check license
• Type:
  other