Abstract
One way to model epistemic states of agents more realistically is to represent these states by sets of situations rather than possible worlds. In this paper we discuss representations of epistemic update in terms of situations. After linking epistemic update based on deleting epistemic accessibility arrows with update of situations, we discuss two specific kinds of public epistemic update; monotonic update in intuitionistic dynamic epistemic logic, and non-monotonic update in substructural dynamic epistemic logic. Our investigation is mainly conceptual, but leads to completeness results using reduction axioms, and lays the groundwork for future investigation into the concept of situated epistemic update.
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Notes
- 1.
Note that in the limiting case where \(Q_X st\) iff \(s = t\) and \(t \in X\) (suggesting that situations are “complete” and information cannot really be added to them), \(Q_X\) boils down to the test relation of Propositional Dynamic Logic and, abusing notation, epistemic update corresponds to the relation changer \(r_X: E_a \mapsto (E_a ; X?)\) in the style of dynamic logic with relation changers [27]. More liberal interpretations of \(Q_X\) link epistemic updates to various non-classical versions of dynamic logic with relation changers. The monotonic case outlined in the next section is related to intuitionistic relation changer logic studied in [9]; the non-monotonic case outlined in Sect. 4 is related to substructural dynamic logic with relation changers which, however, remains to be studied.
- 2.
In fact, modifying the satisfaction clause for \({ \texttt {[} A \texttt {]}}B\) to \((\mathfrak {C}, s) \models \!{ \texttt {[} A \texttt {]}}B\) iff \((\mathfrak {C}, s) \not \models A\) or \((\mathfrak {C}^{A}, s) \models B\) would make \({ \texttt {[} A \texttt {]}}B\) non-persistent, that is, we could have \(s \sqsubseteq t\) such that \({ \texttt {[} A \texttt {]}}B\) is satisfied in s but not in t.
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Acknowledgements
This work was supported by the Czech Science Foundation grant GJ18-19162Y for the project Non-Classical Logical Models of Information Dynamics. We are grateful to Vít Punčochář and two anonymous reviewers for valuable suggestions.
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Sedlár, I., Tedder, A. (2021). Situated Epistemic Updates. In: Ghosh, S., Icard, T. (eds) Logic, Rationality, and Interaction. LORI 2021. Lecture Notes in Computer Science(), vol 13039. Springer, Cham. https://doi.org/10.1007/978-3-030-88708-7_16
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