Johnson, Fred (Frederick A.), authorKluwer Academic Publishers, publisher2007-01-032007-01-031994Johnson, Fred, Syllogisms with Fractional Quantifiersk, Journal of Philosophical Logic 23, no. 4 (August 1994): [401]-422. http://dx.doi.org/10.1007/BF01048688http://hdl.handle.net/10217/39025Aristotle's syllogistic is extended to include denumerably many quantifiers such as more than 2/3' and exactly 2/3'. Syntactic and semantic decision procedures determine the validity, or invalidity, of syllogisms with any finite number of premises. One of the syntactic procedures uses a natural deduction account of deducibility, which is sound and complete. The semantics for the system is non-classical since sentences may be assigned a value other than true or false. Results about symmetric systems are given. And reasons are given for claiming that syllogistic validity is relevant validity.born digitalarticleseng© 1994 Kluwer Academic Publishers.Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.quantifiermodellogicfractionsyllogismTexthttps://dx.doi.org/10.1007/BF01048688