Canonical calculi with (n,k)-ary quantifiers

Propositional canonical Gentzen-type systems, introduced in [2], are systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a connective is introduced and no other connective is mentioned. [2] provides a constructive coherence criterion for the non-triviality of such systems and shows that a system of this kind admits cut-elimination iff it is coherent. The semantics of such systems is provided using two-valued non-deterministic matrices (2Nmatrices). [23] extends these results to systems with unary quantifiers of a very restricted form. In this paper we substantially extend the characterization of canonical systems to (n, k)-ary quantifiers, which bind k distinct variables and connect n formulas, and show that the coherence criterion remains constructive for such systems. Then we focus on the case of k ∈ {0, 1} and show that the following statements concerning a canonical calculus G are equivalent: (i) G is coherent, (ii) G has a strongly characteristic 2Nmatrix, and (iii) G admits strong cut-elimination. We also show that coherence is not a necessary condition for standard cut-elimination, and then characterize a subclass of canonical systems for which this property does hold.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 25,727
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Canonical Signed Calculi with Multi-Ary Quantifiers.Anna Zamansky & Arnon Avron - 2012 - Annals of Pure and Applied Logic 163 (7):951-960.

Add more citations

Similar books and articles

Monthly downloads

Sorry, there are not enough data points to plot this chart.

Added to index


Total downloads


Recent downloads (6 months)


How can I increase my downloads?

My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums