Dynamic Logic of Preference Upgrade
Johan van Benthem, Fenrong Liu

Abstract:
Statements made to us not only update our current knowledge, but can
also have other dynamic effects. In particular, suggestions or
commands may 'upgrade' our current preferences. So far, much work has
been done on knowledge update, but little on explicit dynamic logics
of preference upgrade. We propose a logic of knowledge update plus
preference upgrade that works just like a dynamic-epistemic logic in
having a complete set of reduction axioms, but with some new twists in
changing the relevant relations. This system can model issues of
changing obligations, conflicting commands, or 'regret'. Moreover, it
has a product update version which allows for preferences between
actions, in addition to those between worlds, a move which has also
been proposed elsewhere in dynamic logic. At this stage, we also find
it convenient to look at the issues from a second perspective,
viz. upgrade of explicit utilities.  We also propose a dynamic logic
of utility upgrade, on the analogy of product update systems for
graded belief models. We show how this second system can deal with
update logics for defaults. Some delicate differences come up when
comparing our two kinds of preference upgrade. But construed either
way, given the ubiquity of preference relations in many settings
(deontic logic, games, conditional logic), we think understanding the
dynamics of preference is important. We present some illustrations
with defaults and obligations. And we conclude with what we have
achieved right now and what we want to do next.