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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 allowedAuthor's Profile
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References found in this work
Formal Logic, or the Calculus of Inference, Necessary and Probable.Augustus de Morgan - 1847 - London, England: Taylor & Walton.
The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel.Ivor Grattan-Guinness - 2000 - Princeton, NJ, USA: Princeton University Press.
Logics for the relational syllogistic.Ian Pratt-Hartmann & Lawrence S. Moss - 2009 - Review of Symbolic Logic 2 (4):647-683.
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