Characterizability in Horn Belief Revision

• Published in: Logics in Artificial Intelligence pp. 497 - 511
• Main Authors: Yaggie, Jon, Turán, György
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing
• Series: Lecture Notes in Computer Science
• ISBN: 3319487574; 9783319487571
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-48758-8_32

Delgrande and Peppas characterized Horn belief revision operators obtained from Horn compliant faithful rankings by minimization, showing that a Horn belief revision operator belongs to this class if and only if it satisfies the Horn AGM postulates and the acyclicity postulate scheme. The acyclicity scheme has a postulate for every \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 3$$\end{document} expressing the non-existence of a certain cyclic substructure. We show that this class of Horn belief revision operators cannot be characterized by finitely many postulates. Thus the use of infinitely many postulates in the result of Delgrande and Peppas is unavoidable. The proof uses our finite model theoretic approach to characterizability, considering universal monadic second-order logic with quantifiers over closed sets, and using predicates expressing minimality. We also give another non-characterizability result and add some remarks on strict Horn compliance.