David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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 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.
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