Suppose we replace "knowledge" by "belief with probability p" in standard definitions of common knowledge. Very different notions arise depending on the exact definition of common knowledge used in the substitution. This paper demonstrates those differences and identifies which notion is...

Recent contributions have questioned the meaningfulness of the Common Prior Assumption (CPA) in situations of incomplete information. We characterize the CPA in terms of the primitives (individuals' belief hierarchies) without reference to an ex ante stage. The key is to rule out "agreeing to...

Common knowledge can be defined in at least two ways: syntactically as the common knowledge of a set of formulas or semantically, as the meet of the knowledge partitions of the agents. In the multi-agent S5 logic with either finitely or countably many agents and primitive propositions, the...

Samet introduced a notion of hypothetical knowledge and showed how it could be used to capture the type of counterfactual reasoning necessary to force the backwards induction solution in a game of perfect information. He argued that while hypothetical knowledge and the extended information...

Formal Interactive Epistemology deals with the logic of knowledge and belief when there is more than one agent or "player." One is interested not only in each person's knowledge and beliefs about substantive matters, but also in his knowledge and beliefs about the others' knowledge and beliefs....

Formal Interactive Epistemology deals with the logic of knowledge and belief when there is more than one agent or "player." One is interested not only in each person's knowledge about substantive matters, but also in his knowledge about the others' knowledge. This paper examines two parallel...