Abstract
solves the problem for the classical propositional calculus, and for predicate and modal systems based upon it. As I show, however, his method of axiomatization breaks down over calculi that permit truth-value gaps breaks down, indeed, even over the central cases of compact calculi that classify sentences simply as true, as false, or as neither. I produce a method that handles these cases, and illustrate it by giving a categorical axiomatization for a propositional fragment of Smiley's own (1960) free predicate calculus. 1. The categoricity problem, and Smiley's solution to it
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