Pairing Traditional and Generic Common Knowledge

摘要

Common Knowledge C is a standard tool in epistemic logics. Generic Common Knowledge J is an alternative which has desirable logical behavior such as cut-elmination and which can be used in place of C in the analysis of many games and epistemic senarios. In order to compare their deductive strengths directly we define the multi-agent logic S4_n~(CJ) built on a language with both C and J operators in addition to agents' K_is so that any finite prefix of modal operators is acceptable. We prove S4_n~(CJ) is complete, decidable, and that JΦ→CΦ though not CΦ → JΦ. Additional epistemic scenarios may be investigated which take advantage of this dual layer of common knowledge agents.