Giacomo Bonanno, A Kripke-Lewis semantics for belief update and belief revision.
We provide a new characterization of both belief update and belief
revision in terms of a Kripke-Lewis semantics. We consider frames
consisting of a set of states, a Kripke belief relation and a Lewis
selection function. Adding a valuation to a frame yields a model. Given
a model and a state, we identify the initial belief set K with the
set of formulas that are believed at that state and we identify
either the updated belief set or the revised belief set, prompted by
the input represented by formula A, as the set of formulas that are the
consequent of conditionals that (1) are believed at that state and (2)
have A as antecedent. We show that this class of models characterizes
both the Katsuno-Mendelzon (KM) belief update functions and the AGM
belief revision functions, in the following sense: (1) each model gives
rise to a partial belief function that can be completed into a full
KM/AGM update/revision function, and (2) for every KM/AGM
update/revision function there is a model whose associated belief
function coincides with it. The difference between update and revision
can be reduced to two semantic properties that appear in a stronger
form in revision relative to update, thus confirming the finding by
Peppas et al. (1996) that, "for a fixed theory K, revising K
is much the same as updating K".
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Giacomo Bonanno, Two lectures
on the epistemic foundations
of game theory.
These are the slides of two lectures on the Epistemic
of Game Theory, delivered at the Royal Netherlands Academy of Arts and
Sciences (KNAW), February 8, 2007.
To download the files in pdf format
here: Lecture 1.pdf
Giacomo Bonanno (with Klaus
to disagree: a survey.
To download the paper in pdf format
Some of the material in this paper was published in: Giacomo
and Klaus Nehring, “How to make sense of the common prior
incomplete information", International Journal
of Game Theory, 28 (3), August 1999, pp. 409-434 (To download
in pdf format click