The Review of Symbolic Logic

Research Article

O IS NOT ENOUGH

J. B. PARISa1 c1 and R. SIMMONDSa1 c2

a1 School of Mathematics, University of Manchester

Abstract

We examine the closure conditions of the probabilistic consequence relation of Hawthorne and Makinson, specifically the outstanding question of completeness in terms of Horn rules, of their proposed (finite) set of rules O. We show that on the contrary no such finite set of Horn rules exists, though we are able to specify an infinite set which is complete.

(Received November 14 2008)

Correspondence:

c1 SCHOOL OF MATHEMATICS, UNIVERSITY OF MANCHESTER, MANCHESTER M13 9PL, UK. E-mail: jeff.paris@manchester.ac.uk

c2 SCHOOL OF MATHEMATICS, UNIVERSITY OF MANCHESTER, MANCHESTER M13 9PL, UK. E-mail: richard.simmonds@gmail.com