No Syllogisms for the Numerical Syllogistic

The numerical syllogistic is the extension of the traditional syllogistic with numerical quantifiers of the forms at least C and at most C. It is known that, for the traditional syllogistic, a finite collection of rules, similar in spirit to the classical syllogisms, constitutes a sound and complete proof-system. The question arises as to whether such a proof system exists for the numerical syllogistic. This paper answers that question in the negative: no finite collection of syllogism-like rules, broadly conceived, is sound and complete for the numerical syllogistic.

• Type: Conference
• Year: 2009
• Where: BIRTHDAY
• Authors: Ian Pratt-Hartmann
• Keywords: Applied Computing, BIRTHDAY 2009, Numerical Quantifiers, Numerical Syllogistic, finite Collection