Three logicians walk into a bar ...
Epistemic logics, called
also logics of knowledge, are
formal
logical systems which build on the ideas of
modal logics and allow to describe states of agents' knowledge and to
reason
about them. States of
knowledge described in such a way are static -- to our understanding,
before
1989 such logics were not
capable of describing how the knowledge changes as a result of
communications among
agents. To deal with the changes in knowledge resulting from
communications
among agents we introduced logics of knowledge and communications.
Applications of these systems include reasoning about knowledge in AI
and proofs of equivalence or correctness of computer
communication protocols. Different logical systems can be defined
depending on the properties of
agents and
communication methods they use. These considerations have grown
through the work of many logicians into a specialized area of formal
logic called Dynamic Epistemic Logics.
The second link below is to a paper in which we introduced public communications -- these are now commonly called public announcements, broadcasts or epistemic actions "tell". We considered propositional languages and provided both semantics and a sound and complete axiomatization. Formulas α + β of this paper are now commonly written as <α> β.
The third link below is to an abstract in which we defined semipublic
communications -- these are now commonly called epistemic actions "read". We
announced results of soundness, completeness and decidability and
considered applications in proving equivalence or correctness of
protocols.
The fourth reference below is to a paper by Hans van Ditmarsch which
comments on public communications in the context of the development of
dynamic epistemic logics.
The fifth reference below is to an advanced textbook / monograph on dynamic epistemic logics -- the best place to start reading if you want to familiarize yourself with the subject.
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