Giacomo Bonanno, Logics for belief as maximally plausible possibility.
We consider a basic logic with two primitive uni-modal operators: one for certainty and the other for plausibility.
The former is assumed to be a normal operator (corresponding -
semantically - to a binary Kripke relation), while the latter is merely
a classical operator (corresponding - semantically - to a neighborhood
structure). We then define belief, interpreted as ``maximally plausible
possibility'', in terms of these two notions: the agent believes A if (1) she cannot rule out A (that is, it is not the case that she is certain that not-A), (2) she judges A to be plausible and (3) she does not judge not-A
to be plausible. We consider several interaction properties between
certainty and plausibility and study how these properties translate
into properties of belief (positive and negative introspection, their
converses, conjunction, etc.). We then prove that all the logics
considered are minimal logics for the highlighted theorems. We also
consider a number of possible interpretations of plausibility and
identify the corresponding logics.
Giacomo Bonanno and Elias Tsakas, Qualitative analysis of common belief of rationality in strategic-form games.
study common belief of rationality in strategic-form games with ordinal
utilities, employing a model of qualitative beliefs. We characterize
the three main solution concepts for such games, viz., Iterated
Deletion of Strictly Dominated Strategies (IDSDS), Iterated Deletion of
Boergers-dominated Strategies (IDBS) and Iterated Deletion of Inferior
Strategy Profiles (IDIP), by means of gradually restrictive properties
imposed on the models of qualitative beliefs. As a corollary, we prove
that IDIP refines IDBS, which refines IDSDS.
To download the files in pdf format click here: Lecture 1.pdf , Lecture 2.pdf
Giacomo Bonanno (with Klaus Nehring), Agreeing to disagree: a survey.
To download the paper in pdf format click here: agree.pdf
Some of the material in this paper was published in: Giacomo Bonanno
and Klaus Nehring, “How to make sense of the common prior assumption under
incomplete information", International Journal
of Game Theory, 28 (3), August 1999, pp. 409-434 (To download the paper
in pdf format click here: common.pdf)