Like many intensional logics, William Parry’s logic of analytic implication PAI admits extensions determined by imposing semantic conditions on its account of modality. PAI is unique, however, in its allowing a second dimension—a topic-theoretic dimension—along which extensions can be defined. The recent introduction by Francesco Berto of topic-sensitive intentional modals (TSIMs)—which disagree with PAI on this type of condition—provide further motivations to examine such topic-theoretic extensions. In this paper, we introduce, motivate, and characterize a number of such extensions of PAI, (...) paying special attention to applications to Berto’s framework and to ways in which the modal and topic-theoretic dimensions influence one another. (shrink)

Logical frameworks that are sensitive to features of sentences’ subject-matter—like Berto’s topic-sensitive intentional modals (TSIMs)—demand a maximally faithful model of the topics of sentences. This is an especially difficult task in the case in which topics are assigned to intensional formulae. In two previous papers, a framework was developed whose model of intensional subject-matter could accommodate a wider range of intuitions about particular intensional conditionals. Although resolving a number of counterintuitive features, the work made an implicit assumption that the subject-matter (...) of an intensional conditional is a function of the subject-matters of its subformulae. This assumption—which I will call a principle of topic sufficiency—runs counter to some natural intuitions concerning topic. In this paper, we will investigate topic sufficiency and offer a semantic account that is state-sensitive, providing an implementation through the introduction of topic-sensitive logics related to William Parry’s prototypical $\mathsf {PAI}$. (shrink)