My beliefs about your beliefs: a case study in theory of mind and epistemic logic

We model three examples of beliefs that agents may have about other agents’ beliefs, and provide motivation for this conceptualization from the theory of mind literature. We assume a modal logical framework for modelling degrees of belief by partially ordered preference relations. In this setting, we describe that agents believe that other agents do not distinguish among their beliefs (‘no preferences’), that agents believe that the beliefs of other agents are in part as their own (‘my preferences’), and the special case that agents believe that the beliefs of other agents are exactly as their own (‘preference refinement’). This multi-agent belief interaction is frame characterizable. We provide examples for introspective agents. We investigate which of these forms of belief interaction are preserved under three common forms of belief revision.     

An epistemic and dynamic approach to abductive reasoning: Abductive problem and abductive solution

We propose a study of abductive reasoning addressing it as an epistemic process that involves both an agent?s information and the actions that modify this information. More precisely, we present and discuss definitions of an abductive problem and an abductive solution in terms of an agent?s information, that is, in terms of knowledge and beliefs. The discussion is then formalised by ‘implementing’ our definitions in a dynamic epistemic logic framework, where the properties of these definitions are studied, an epistemic action that represents the application of an abductive step is introduced, and an illustrative example is provided. A number of the most interesting properties of abductive reasoning (those highlighted by Peirce) are shown to be better modelled within this approach.