A Hybrid Calculus for the Validities and Invalidities of Classical Propositional Logic

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Abstract

I introduce a novel hybrid calculus H for the validities and invalidities of classical propositional logic. The calculus H is different in nature from other hybrid calculi that can be found in the literature in that it does not include specific anti-sequent rules. Instead, I add to the sequent rules of classical propositional logic only two structural rules that allow us to introduce and eliminate anti-sequents in our derivations. The resultant system is much simpler than the existing systems in the literature. For one thing, it does not suffer from a proliferation of rules. For another, it is structurally complete: its admissible rules are all derivable.

Original languageEnglish
Pages (from-to)1701-1716
Number of pages16
JournalJournal of Philosophical Logic
Volume53
Issue number6
DOIs
StatePublished - 1 Dec 2024

Keywords

  • Anti sequents
  • Metainferences
  • Structural completeness

ASJC Scopus subject areas

  • Philosophy

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