In this paper we investigate rst order common knowledge logics; i.e., modal epistemic logics based on rst order logic with common knowledge operators. It is shown that even rather weak fragments of rst order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the rst order part of wh...

What is public information in a multi-agent logic of knowledge such as Tn, S4n or S5n? Traditionally this notion has been captured by common knowledge, which is an epistemic operator Cφ given roughly

The usual justification foc Nash equilibrium behavior involves (at least implicitly) the assumption that it is common knowledge among the playecs both that the Nash equilibrium in question will be played by all and that all playecs ace expected utility maximizers. We show that in a large class of extensive form games, the assumption that rationality is common knowledge cannot be maintained thro...

What are the effects of forward guidance or, more generally, of news about the future? Workhorse macroeconomic models answer this question by imposing a strong form of common knowledge: every agent is, not only aware of, or attentive to, the news, but also confident that everyone is aware, that everyone is confident that everyone is aware, and so on. Once this assumption is relaxed, expectation...

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as xed-point type extensions and in nitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among these extensions are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the proposit...

Deduction chains represent a syntactic and in a certain sense constructive method for proving completeness of a formal system. Given a formula φ, the deduction chains of φ are built up by systematically decomposing φ into its subformulae. In the case where φ is a valid formula, the decomposition yields a (usually cut-free) proof of φ. If φ is not valid, the decomposition produces a countermodel...