Hyperintensional epistemic justification: a ground-theoretic topic-sensitive semantics

In recent years the study of topic or subject matter has found application in the analysis of epistemic attitudes such as knowledge and belief. To know or believe \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi ,$$\end{document} one needs to grasp \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}'s topic, i.e. what \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document} is about. This yields a hyperintensional treatment of epistemic attitudes: if two necessary equivalent sentences differ in subject matter, they cannot be substituted salva veritate in the context of those attitudes. In this paper, I aim to extend this approach to propositional justification. I argue that, in contrast to epistemic attitudes, having propositional justification for φ does not require grasping the totality of φ's topic, but only part of it. This is the case because one may possess evidence for even without grasping the totality of φ's topic. I define what it means to be evidence for a proposition, borrowing some notions from the logical grounding literature. Building on extant frameworks modelling evidential support and subject matter, I then put forward a modal clause for propositional justification. Finally, I prove-together with the failure of some undesired principles-a ground-theoretic closure principle for the justification operator and show how it entails closure under Strong Kleene logic.