Subject-matter and intensional operators I: conditional-agnostic analytic implication.

Although logical settings are typically concerned with tracking alethic considerations, frameworks exist in which topic- theoretic considerations-e.g., tracking subject-matter or topic -are given equal importance. Intuitions about extending topic through a propositional language are generally straightforward for extensional cases. For a number of reasons, arriving at a compelling account of the subject-matter of intensional operators -such as intensional conditionals -is a more difficult task. In particular, the framework of topic-sensitive intentional modals (TSIMs) championed by Francesco Berto and his collaborators leave the topics of intensional formulae undefined , 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 PAI -with sound and complete axiomatizations-that allow a fine degree of control over the topics of intensional conditionals.
(© The Author(s) 2023.)