Full characterization of Parikh's Relevance-Sensitive Axiom for Belief Revision

© 2019 AI Access Foundation. In this article, the epistemic-entrenchment and partial-meet characterizations of Parikh's relevance-sensitive axiom for belief revision, known as axiom (P), are provided. In short, axiom (P) states that, if a belief set K can be divided into two disjoint compartments, and the new information ' relates only to the first compartment, then the revision of K by ' should not affect the second compartment. Accordingly, we identify the subclass of epistemic-entrenchment and that of selection-function preorders, inducing AGM revision functions that satisfy axiom (P). Hence, together with the faithful-preorders characterization of (P) that has already been provided, Parikh's axiom is fully characterized in terms of all popular constructive models of Belief Revision. Since the notions of relevance and local change are inherent in almost all intellectual activity, the completion of the constructive view of (P) has a significant impact on many theoretical, as well as applied, domains of Artificial Intelligence

In Search of Homo Sociologicus

The subject of this dissertation is to build an epistemic logic system that is able to show the spreading of knowledge and beliefs in a social network that contains multiple subgroups. Epistemic logic is the study of logical systems that express mathematical properties of knowledge and belief. In recent years, there have been increasing number of new epistemic logic systems that are focused on community properties such as knowledge and belief adoption among friends. We are interested in revisable and actionable social knowledge/belief that leads to a large group action. Instead of centralized coordination, bottom-up approach is our focus. We explore multiple methods of belief revision in social networks. Such belief revision in groups represents social influence and power to some degree. Both influence from friends and from experts are explained. We define an intuitive concept of expected influence of a group. When different influence sources are suggesting conflicting actions, agents could make strategic decisions by analyzing expected influence of different subgroups. We then show some properties of expected influence in different network structures. We also simulate the strategic influence emerging in small-world networks which represents many real world networks