A logic of belief.
Alex Blum · Notre Dame Journal of Formal Logic · 1976
Our object in this paper* is to construct a purely extensional firstorder system S adequate for the systematization of first-order belief sentences.V Any satisfactory systematization of belief sentences would have to fulfill, it would appear, the following conditions: One, that if (1) Ralph believes of Ortcutt, that he is a spy is true, so is (2) {3x) Ralph believes of x, that x is a spy and hence, (1) and(3) Ortcutt = the mayor of Hanoi entail (4) Ralph believes of the mayor of Hanoi that he is a spy.Two, that even if (3) and (5) Ralph believes that Ortcutt is a spy are true, (6) Ralph believes that the mayor of Hanoi is a spy need not be true.And three, that (2) entails (7) Ralph believes that (3x) x is a spy.2 To facilitate understanding, we begin with the semantic motivation for S.We view the universe as a set of domains (not all distinct) of individuals *I am deeply indebted to Professor Raziel Abelson and to my students, Judith Rosenberg and David Widerker, for very helpful discussions on the logic of belief.