Abstract This paper gives a fresh look at my previous work on “epistemic actions” and information updates in distributed systems, from a coalgebraic perspective. I show that the “relational” semantics of epistemic programs, given in [BMS2] in terms of epistemic updates, can be understood in terms of functors on the category of coalgebras and natural transformations associated to them. Then, I introduce a new, alternative, more refined semantics for epistemic programs: programs as “epistemic coalgebras”. I argue for the advantages of this second semantics, from a semantic, heuristic, syntactical and proof-theoretic point of view. Finally, as a step towards a generalization, I show these concepts make sense for other functors, and that apparently unrelated concepts, such as Bayesian belief updates and process transformations, can be seen to arise in the same way as our “epistemic actions”.
[1]
Ronald Fagin,et al.
Reasoning about knowledge
,
1995
.
[2]
A. Kurz,et al.
Coalgebras and modal logic for parameterised endofunctors
,
2000
.
[3]
Jelle Gerbrandy,et al.
Reasoning about Information Change
,
1997,
J. Log. Lang. Inf..
[4]
J. Gerbrandy.
Bisimulations on Planet Kripke
,
1999
.
[5]
Alexandru Baltag,et al.
A Logic for Suspicious Players: Epistemic Actions and Belief-Updates in Games
,
2000
.
[6]
S. Griffis.
EDITOR
,
1997,
Journal of Navigation.
[7]
Alexander Kurz,et al.
Definability, Canonical Models, and Compactness for Finitary Coalgebraic Modal Logic
,
2002,
CMCS.
[8]
Lawrence S. Moss,et al.
The Logic of Public Announcements and Common Knowledge and Private Suspicions
,
1998,
TARK.
[9]
Alexandru Baltag.
Logics for insecure communication
,
2001
.