Incomplete Information and Justifications

• Published in: Language, Logic, and Computation Vol. 13206; pp. 258 - 278
• Main Authors: Doder, Dragan, Ognjanović, Zoran, Savić, Nenad, Studer, Thomas
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2022; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Justifcation logic; Probabilistic logic; Strong completeness; Upper and lower probabilities
• ISBN: 9783030984786; 3030984788
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-98479-3_13

We present a logic for reasoning about higher-order upper and lower probabilities of justification formulas. We provide sound and strongly complete axiomatization for the logic. Furthermore, we show that the introduced logic generalizes the existing probabilistic justification logic PPJ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {PPJ}$$\end{document}.