8 research outputs found
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
Knowledge, awareness, and bisimulation
We compare different epistemic notions in the presence of awareness of propositional variables: the logics of implicit knowledge (in which explicit knowledge is definable), explicit knowledge, and speculative knowledge. Different notions of bisimulation are suitable for these logics. We provide correspondence between bisimulation and modal equivalence on image-finite models for these logics. The logic of speculative knowledge is equally expressive as the logic of explicit knowledge, and the logic of implicit knowledge is more expressive than both. We also provide axiomatizations for the three logics — only the one for speculative knowledge is novel. Then we move to the study of dynamics by recalling action models incorporating awareness. We show that any conceivable change of knowledge or awareness can be modelled in this setting, we give a complete axiomatization for the dynamic logic of implicit knowledge. The dynamic versions of all three logics are, surprising, equally expressive
Arbitrary Announcements on Topological Subset Spaces
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