| Summary: | <p>In multi-agent epistemic logics, common knowledge has been a central consideration of study. A generic common knowledge (<i>G.C.K.</i>) system is one that yields iterated knowledge <i>I</i>(ϕ): 'any agent knows that any agent knows that any agent knows. . . ϕ' for any number of iterations. Generic common knowledge yields iterated knowledge <i> G.C.K.</i>(ϕ) → <i>I</i>(ϕ) but is not necessarily logically equivalent to it. This contrasts with the most prevalent formulation of common knowledge <i>C</i> as equivalent to iterated knowledge. A spectrum of systems may satisfy the <i>G.C.K.</i> condition, of which <i>C</i> is just one. It has been shown that in the usual epistemic scenarios, <i>G.C.K.</i> can replace conventional common knowledge and Artemov has noted that such standard sources of common knowledge as public announcements of atomic sentences generally yield <i>G.C.K. </i> rather than <i>C.</i> </p><p> In this dissertation we study mathematical properties of generic common knowledge and compare them to the traditional common knowledge notion. In particular, we contrast the modal <i>G.C.K.</i> logics of McCarthy (e.g. <tt>M4</tt>) and Artemov (e.g. [special characters omitted]) with <i>C</i>-systems (e.g. [special characters omitted]) and present a joint <i>C/G.C.K.</i> implicit knowledge logic [special characters omitted] as a conservative extension of both. We show that in standard epistemic scenarios in which common knowledge of certain premises is assumed, whose conclusion does not concern common knowledge (such as Muddy Children, Wise Men, Unfaithful Wives, etc.), a lighter <i>G.C.K.</i>can be used instead of the traditional, more complicated, common knowledge. We then present the first fully explicit <i>G.C.K.</i> system <tt>LP</tt><i><sub> n</sub></i>(<tt>LP</tt>). This justification logic realizes the corresponding modal system [special characters omitted] so that <i>G.C.K.</i>, along with individual knowledge modalities, can always be made explicit.</p>
|
|---|
