Abstract
A theorem due to Shoesmith and Smiley that axiomatizes two- valued multiple-conclusion logics is extended to partial logics. Rumfitt (1) extends Smiley's (3) discussion of rejection by axiomatizing a calculus where truth values of sentences are given by truth tables that admit truth-value gaps. The Smiley multiple-conclusion consequence for the calculus is defined over assertions and rejections. Rumfitt gives a complex Henkin-style proof of com- pleteness for this calculus. Our goal is to show that there is a simple procedure for axiomatizing calculi of the sort that he considers. We do this by imitating Shoesmith and Smiley's (2) proof of a similar result (their Theorem 18.1) where truth tables do not admit truth-value gaps and the consequence relation is defined without using re-
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
