Canonical signed calculi with multi-ary quantifiers

Anna Zamansky*, Arnon Avron

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Canonical Gentzen-type calculi are a natural class of systems, which in addition to the standard axioms and structural rules have only logical rules introducing exactly one connective. There is a strong connection in such systems between a syntactic constructive criterion of . coherence, the existence of a two-valued non-deterministic semantics for them and strong cut-elimination. In this paper we extend the theory of canonical systems to . signed calculi with multi-ary quantifiers. We show that the extended criterion of coherence fully characterizes strong . analytic cut-elimination in such calculi, and use finite . non-deterministic matrices to provide modular semantics for every coherent canonical signed calculus.

Original languageEnglish
Pages (from-to)951-960
Number of pages10
JournalAnnals of Pure and Applied Logic
Issue number7
StatePublished - Jul 2012


  • Cut-elimination
  • Generalized quantifiers
  • Non-deterministic matrices
  • Proof theory
  • Signed calculi


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