1 research outputs found
From Lawvere to Brandenburger-Keisler: interactive forms of diagonalization and self-reference
We analyze the Brandenburger-Keisler paradox in epistemic game theory, which
is a `two-person version of Russell's paradox'. Our aim is to understand how it
relates to standard one-person arguments, and why the `believes-assumes'
modality used in the argument arises.
We recast it as a fixpoint result, which can be carried out in any regular
category, and show how it can be reduced to a relational form of the one-person
diagonal argument due to Lawvere. We give a compositional account, which leads
to simple multi-agent generalizations.
We also outline a general approach to the construction of assumption complete
models.Comment: To appear in the Proceedings of LOFT 201