An Algebraic approach to the logic of information flow

Mehrnoosh Sadrzadeh (UQAM & Oxford Univ. ComLab)
Joint work with A. Baltag & B. Coecke (Oxford Univ.
ComLab)

In an interactive multi-agent system, agents
communicate with each other  and this communication
changes their information state.  In order to  reason
about information updates in such settings, one has to
take into account the dynamic as well as the epistemic
aspect of communication. The traditional approaches
only consider the epistemic aspect and dismiss the
dynamic one. Recent development of  Dynamic Epistemic
Logic integrates both in a  Dynamic Logic  with
kripke semantics.   We have shown how this
combinatorial setting  can be generalized to an  order
theoretic structure that has  a non-boolean
resource-sensitive nature.  The main mathematical
object of this structure is called a 'quantale' with
AMS subject classification '06F07'.  The quantale in
our setting is called an 'epistemic quantale' since it
is endowed with a family of endomorphisms that
represent information state of agents.  Closure-type
properties of these endomorphisms give rise to various
 notions of knowledge.  We have developed a  sound and
complete  sequent calculus  for  this setting.  I will
present the algebra and its sequent calculus and go
through the proof of a famous epistemic puzzle called
the muddy children puzzle and a cheating version of
it,  as well as  a security protocol.