Review: "An Algebraic Study of Tense Logic with Linear Time," by R. A. Bull

Abstract

In these papers (the second of which is principally a correction and adumbration of the first) Bull constructs algebraic semantics which provide completeness theorems for three prepositional tense logics for linear time, depending on whether the linear ordering of moments is rational, real, or integral. It is also shown that the systems for time rational or real have the finite model property, but that the system for discrete (integral) time lacks this property. The notion of formulahood is the same for each of these propositional tense logics—in addition to the operators of the classical propositional calculus there are P, H, F, and G, which read, respectively, as "It has been the case that," "It has always been the case that," "It will be the case that," and "It will always be the case that." G and H are taken primitively with F and P defined as their respective duals.