The Syllogistic with Unity

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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    References found in this work BETA
    John Corcoran (1972). Completeness of an Ancient Logic. Journal of Symbolic Logic 37 (4):696-702.
    Wallace A. Murphree (1998). Numerical Term Logic. Notre Dame Journal of Formal Logic 39 (3):346-362.

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