TxW Epistemic Modality

So far, T×W frames have been employed to provide a semantics for a language of tense logic that includes a modal operator that expresses historical necessity. The operator is defined in terms of quantification over possible courses of events that satisfy a certain constraint, namely, that of being alike up to a given point. However, a modal operator can as well be defined without placing that constraint. This paper outlines a T×W logic where an operator of the latter kind is used to express the epistemic property of definiteness. Section 1 provides the theoretical background. Sections 2 and 3 set out the semantics. Sections 4 and 5 show, drawing on established results, that there is a sound and complete axiomatization of the logic outlined.