A logic for qualified syllogisms

Abstract

In various works, L.A. Zadeh has introduced fuzzy quantifiers, fuzzy usuality modifiers, and fuzzy likelihood modifiers. This paper provides these notions with a unified semantics and uses this to define a formal logic capable of expressing and validating arguments such as 'Most birds can fly; Tweety is a bird; therefore, it is likely that Tweety can fly'. In effect, these are classical Aristotelean syllogisms that have been 'qualified' through the use of fuzzy quantifiers. It is briefly outlined how these, together with some likelihood combination rules, can be used to address some well-known problems in the theory of nonmonotonic reasoning. © 2014 Springer International Publishing Switzerland.