Journal of Philosophical Logic 42 (2):391-407 (2013)

Abstract
We extend the language of the classical syllogisms with the sentence-forms “At most 1 p is a q” and “More than 1 p is a q”. We show that the resulting logic does not admit a finite set of syllogism-like rules whose associated derivation relation is sound and complete, even when reductio ad absurdum is allowed
Keywords Syllogisms  Proof theory  Logic and natural language  Computational complexity
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DOI 10.1007/s10992-012-9229-3
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References found in this work BETA

What is a Syllogism?T. J. Smiley - 1973 - Journal of Philosophical Logic 2 (1):136 - 154.
Completeness of an Ancient Logic.John Corcoran - 1972 - Journal of Symbolic Logic 37 (4):696-702.
Logics for the Relational Syllogistic.Ian Pratt-Hartmann & Lawrence S. Moss - 2009 - Review of Symbolic Logic 2 (4):647-683.
The Hamiltonian Syllogistic.Ian Pratt-Hartmann - 2011 - Journal of Logic, Language and Information 20 (4):445-474.

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