Synchronizing Diachronic Uncertainty

Alistair M.C. Isaac, Tomohiro Hoshi

Research output: Contribution to journalArticlepeer-review


Diachronic uncertainty, uncertainty about where an agent falls in time, poses interesting conceptual difficulties. Although the agent is uncertain about where she falls in time, this uncertainty can only obtain at a particular moment in time. We resolve this conceptual tension by providing a transformation from models with diachronic uncertainty relations into “equivalent” models with only synchronic uncertainty relations. The former are interpreted as capturing the causal structure of a situation, while the latter are interpreted as capturing its epistemic structure. The models are equivalent in the sense that agents pass through the same information sets in the same order, In this paper, we investigate how such a transformation may be used to define an appropriate notion of equivalence, which we call epistemic equivalence. Although our project is motivated by problems which have arisen in a variety of disciplines, especially philosophy and game theory, our formal development takes place within the general and flexible framework provided by epistemic temporal logic.
Original languageEnglish
Pages (from-to)137-159
JournalJournal of Logic, Language and Information
Issue number2
Early online date6 Mar 2010
Publication statusPublished - 1 Apr 2011


  • Diachronic uncertainty
  • Sleeping beauty
  • Absent-mindedness
  • Epistemic temporal logic
  • The absent-minded driver


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