Year: 1997
Type: article
Abstract: The categoricity problem and truth-value gaps Ian RumfittIn a recent paper, 1 T. J. Smiley has revived, and advanced a solution to, an important but neglected problem in logical theory -that of finding 'categorical' axiomatizations for logical calculi.Using rules of rejection, he 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 gapsbreaks 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.
Source: Analysis
Author: I. Rumfitt
Institution: University of Michigan
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2079077960