Toward a logic for fuzzy syllogisms
Daniel G. Schwartz · 2002
The author describes a formal logic that encodes the reasoning embodied in syllogisms of the form. 'Most birds can fly; Tweety is a bird; therefore, it is likely that Tweety can fly,' and of the form, 'Usually, if something is a bird, it can fly; Tweety is a bird; therefore, it is likely that Tweety can fly.' More exactly, he defines a formal language in which syllogisms of these and related forms can be expressed, and then this language is provided with a rigorously defined semantics in which such syllogisms are valid. In the process a general approach is established to formalize the notions of fuzzy quantification, usuality, and likelihood. Some of the interrelations between these concepts that are expressible in this formalism are also explored.>