Logics of knowledge and action: critical analysis and challenges

International audienceWe overview the most prominent logics of knowledge and action that were proposed and studied in the multiagent systems literature. We classify them according to these two dimensions, knowledge and action, and moreover introduce a distinction between individual knowledge and group knowledge, and between a nonstrategic an a strategic interpretation of action operators. For each of the logics in our classification we highlight problematic properties. They indicate weaknesses in the design of these logics and call into question their suitability to represent knowledge and reason about it. This leads to a list of research challenges

Group Belief

While logical formalizations of group notions of knowledge such as common and distributed knowledge have received considerable attention in the literature, most approaches being based on modal logic, group notions of belief have received much less attention. In this paper we systematically study standard notions of group knowledge and belief under different assumptions about which properties knowledge and belief have. In particular, we map out (lack of) preservation of knowledge/belief properties against different standard definitions of group knowledge/belief. It turns out that what is called group belief most often is not actually belief, i.e., does not have the properties of belief. In fact, even what is called group knowledge is sometimes not actually knowledge either. For example, under the common assumption that belief has the KD45 properties, distributed belief is not actually belief (it does not satisfy the D axiom). In the literature there is no detailed completeness proof for axiomatizations of KD45 with distributed belief that we are aware of, and there has been some confusion regarding soundness of such axiomatizations related to the mentioned lack of preservation. In this paper we also present a detailed completeness proof for a sound axiomatization of KD45 with distributed belief