New algorithms for the statement and class calculi.
Henry C. Byerly, Charles J. Merchant · Notre Dame Journal of Formal Logic · 1970
Efficient algorithms for making inferences in the statement calculus and in the calculus of classes may be developed with a fractional representation of statements.The idea is to take the transitivity of implication as the fundamental mode of inference.We seek then a representation in which hypothetical syllogism, which is an expression of this transitivity, appears in a convenient form.Both the inferences:work as if one "cancelled" the middle terms.This apparently simpleminded view can, as we shall show, be developed into a remarkably simple and perspicuous set of techniques for manipulation of logical relations between calsses and between statements.