The Dynamics of Group Knowledge and Belief

5th International Workshop On Philosophy and Logic of Social Reality. 15-17 November 2019.Hokkaido University, Sapporo, Japa

Knowledge and Blameworthiness

Blameworthiness of an agent or a coalition of agents is often defined in terms of the principle of alternative possibilities: for the coalition to be responsible for an outcome, the outcome must take place and the coalition should have had a strategy to prevent it. In this article we argue that in the settings with imperfect information, not only should the coalition have had a strategy, but it also should have known that it had a strategy, and it should have known what the strategy was. The main technical result of the article is a sound and complete bimodal logic that describes the interplay between knowledge and blameworthiness in strategic games with imperfect information

Blameworthiness in Strategic Games

There are multiple notions of coalitional responsibility. The focus of this paper is on the blameworthiness defined through the principle of alternative possibilities: a coalition is blamable for a statement if the statement is true, but the coalition had a strategy to prevent it. The main technical result is a sound and complete bimodal logical system that describes properties of blameworthiness in one-shot games

Logics for modelling collective attitudes

We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The proposed logics for modelling collective attitudes are based on a substructural propositional logic that allows for circumventing inconsistent outcomes. Individual and collective propositional attitudes, such as beliefs, desires, obligations, are then modelled by means of minimal modalities to ensure a number of basic principles. In this way, a viable consistent modelling of collective attitudes is obtained

Resolving Distributed Knowledge

Distributed knowledge is the sum of the knowledge in a group; what someone who is able to discern between two possible worlds whenever any member of the group can discern between them, would know. Sometimes distributed knowledge is referred to as the potential knowledge of a group, or the joint knowledge they could obtain if they had unlimited means of communication. In epistemic logic, the formula D_G{\phi} is intended to express the fact that group G has distributed knowledge of {\phi}, that there is enough information in the group to infer {\phi}. But this is not the same as reasoning about what happens if the members of the group share their information. In this paper we introduce an operator R_G, such that R_G{\phi} means that {\phi} is true after G have shared all their information with each other - after G's distributed knowledge has been resolved. The R_G operators are called resolution operators. Semantically, we say that an expression R_G{\phi} is true iff {\phi} is true in what van Benthem [11, p. 249] calls (G's) communication core; the model update obtained by removing links to states for members of G that are not linked by all members of G. We study logics with different combinations of resolution operators and operators for common and distributed knowledge. Of particular interest is the relationship between distributed and common knowledge. The main results are sound and complete axiomatizations.Comment: In Proceedings TARK 2015, arXiv:1606.0729