PP-2011-30: The Dynamics of Awareness

PP-2011-30: van Benthem, Johan and Velázquez-Quesada, Fernando (2011) The Dynamics of Awareness. [Report]

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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 use a static base from the existing awareness literature,
extending it into a dynamic system that includes traditional acts of
observation, but also adding and dropping formulas from the current
‘awareness’ set. We give a completeness theorem, and we show how this
dynamics updates explicit knowledge. Then we extend our approach to
multi-agent scenarios where awareness changes may happen
privately. Finally, we mention further directions and related
approaches. Our contribution can be seen as a ‘dynamification’ of
existing awareness logics.

Item Type: Report
Report Nr: PP-2011-30
Series Name: Prepublication (PP) Series
Year: 2011
Uncontrolled Keywords: Epistemic logic, Considering, Dropping, Observation, Awareness, Dynamic epistemic logic
Subjects: Logic
Depositing User: Johan van Benthem
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/434

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