A Triple Correspondence in Canonical Calculi: Strong Cut-Elimination, Coherence, and Non-deterministic Semantics

  • Arnon Avron
  • Anna Zamansky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5010)


An (n,k)-ary quantifier is a generalized logical connective, binding k variables and connecting n formulas. Canonical systems with (n,k)-ary quantifiers form a natural class of Gentzen-type systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a quantifier is introduced. The semantics for these systems is provided using two-valued non-deterministic matrices, a generalization of the classical matrix. In this paper we use a constructive syntactic criterion of coherence to characterize strong cut-elimination in such systems. We show that the following properties of a canonical system G with arbitrary (n,k)-ary quantifiers are equivalent: (i) G is coherent, (ii) G admits strong cut-elimination, and (iii) G has a strongly characteristic two-valued generalized non-deterministic matrix.


Atomic Formula Predicate Symbol Structural Rule Sequent Calculus Canonical System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Arnon Avron
    • 1
  • Anna Zamansky
    • 1
  1. 1.School of Computer ScienceTel-Aviv University 

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