Inference, Promotion, and the Dynamics of Awareness
Johan van Benthem, Fernando R. Velazquez-Quesada

Abstract:
Classical epistemic logic describes implicit knowledge of agents about
facts and knowledge of other agents, based on semantic
information. The latter is produced by acts of observation or
communication, that are described well by dynamic epistemic
logics. What these logics do not describe, however, is how significant
information is also produced by acts of inference - and key axioms of
the system merely postulate "deductive closure". In this paper, we
take the view that all information is produced by acts, and hence we
also need a dynamic logic of inference steps showing what effort on
the part of the agent makes a conclusion explicit knowledge. Strong
omniscience properties of agents should be seen not as static
idealizations, but as the result of dynamic processes that agents
engage in.
  This raises two questions: (a) how to define suitable information
states of agents and matching notions of explicit knowledge, (b) how
to define natural processes over these states that generate new
explicit knowledge. To this end, we extend earlier epistemic
"awareness models" into a dynamic system that includes acts of public
observation, but also adding and dropping formulas from the currently
'entertained' set, we give a completeness theorem, and we show how
this dynamics updates explicit knowledge. Similar ideas have been
proposed before, but they were restricted to update with factual
propositions; our new dynamic system applies to arbitrary formulas.
  We also extend our approach to multi-agent scenarios where awareness
changes may happen privately. Finally, we mention further directions
and related approaches.

Keywords: inference;  observation;  awareness;  dynamic epistemic logic