A unified semantic framework for fully structural propositional sequent systems

Ori Lahav*, Arnon Avron

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We identify a large family of fully structural propositional sequent systems, which we call basic systems. We present a general uniform method for providing (potentially, nondeterministic) strongly sound and complete Kripke-style semantics, which is applicable for every system of this family. In addition, this method can also be applied when: (i) some formulas are not allowed to appear in derivations, (ii) some formulas are not allowed to serve as cut formulas, and (iii) some instances of the identity axiom are not allowed to be used. This naturally leads to new semantic characterizations of analyticity (global subformula property), cut admissibility and axiom expansion in basic systems. We provide a large variety of examples showing that many soundness and completeness theorems for different sequent systems, as well as analyticity, cut admissibility, and axiom expansion results, easily follow using the general method of this article.

Original languageEnglish
Article number27
JournalACM Transactions on Computational Logic
Volume14
Issue number4
DOIs
StatePublished - Nov 2013

Keywords

  • Analyticity
  • Axiom expansion
  • Cut admissibility
  • Kripke semantics
  • Logic
  • Nondeterministic semantics
  • Proof theory
  • Semantic characterization
  • Sequent calculi

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