Uniqueness of axiomatic extensions of cut-free classical propositional logic

Mario Piazza, Gabriele Pulcini

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

In this article, we prove that, for any cluster of extra-logical assumptions, there exists exactly one axiomatic (i.e. minimal) extension of classical propositional logic that admits cut elimination. As a corollary, it follows that classically equivalent formulas share the same axiomatization. The moral is that cut elimination "flattens" the specific information encoded by the logical structure of proper axioms.

Original languageEnglish
Pages (from-to)708-718
Number of pages11
JournalLogic Journal of the IGPL
Volume24
Issue number5
DOIs
Publication statusPublished - Oct 2016

Keywords

  • Axiomatic extensions
  • Cut elimination with proper axioms
  • Logic of pivotal assumptions
  • Proof theory

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