Although logical settings are typically concerned with trackingalethicconsiderations, frameworks exist in whichtopic-theoreticconsiderations—e.g., trackingsubject-matterortopic—are given equal importance. Intuitions about extending topic through a propositional language are generally straightforward forextensionalcases. For a number of reasons, arriving at a compelling account of the subject-matter ofintensional operators—such as intensionalconditionals—is a more difficult task. In particular, the framework oftopic-sensitive intentional modals(TSIMs) championed by Francesco Berto and his collaborators leave the topics of intensional formulaeundefined, which artificially constricts the expressivity of the theory. This paper proposes an approach to fill in this lacuna, emphasizing an analogous problem in Parry-style containment logics. In this setting, the approach receives a proof-of-concept through the introduction of a natural and general family of subsystems of Parry’s\documentclass[12pt]{minimal}
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				\begin{document}$${\textsf{PAI}}$$\end{document}PAI—with sound and complete axiomatizations—that allow a fine degree of control over the topics of intensional conditionals.