Abstract
In Part III of this book,we presented a modal logic approach to preference and preference change via betterness relations. Then, in Part IV, we developed what might be seen as a competing priority-based view of preference. These two perspectives had different intuitions, both plausible and attractive. Even so, the question naturally arises how the two are related. The aim of the present chapter is to draw a comparison, connect them, and try to integrate them.
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Notes
- 1.
There are a few differences here with the general approach in [6] that we do not spell out. In particular, to make things comparable, note that each unary property P is naturally associated with the binary relation P such that for all x and y, x P y iff Px implies Py.
- 2.
This choice of direction is just a convention – but we need to fix one in our proof.
- 3.
Again, these should be read keeping in mind the close connection between priority graphs and algebraic terms formed with the operations ;, ║.
- 4.
We will discuss possible co-existence of extrinsic graph-based with intrinsic primitive betterness relations in Section 10.4.2 below.
- 5.
There is a translation into the decidable two-variable fragment of first-order logic.
- 6.
The main idea is that, like with distributive normal forms in propositional logic, one can effectively transform any given priority graph into an equivalent one where the propositions are complete conjunctions of literals for all relevant proposition letters.
- 7.
One obvious connection is with the dynamic betterness logics of Chapter 4.
- 8.
Reference [190] extends current semantic dynamic epistemic logic to systems that can deal with syntactic acts of inference.
- 9.
This can also be used in an alternative proof for Theorem 10.22: In particular, the flat-format definable relations are closed under taking intersections.
- 10.
Similar difficulties with deletion were found for “agenda dynamics” in [83].
- 11.
It is an interesting open problem if all PDL-flat-format-definable betterness transformers that always generate pre-orders are definable by syntactic graph updates.
- 12.
A nice illustration is deontic logic. If I obey the command of a higher moral authority, I may acquire an extrinsic preference, whose reason is obeying a superior. But for that higher agent, that same preference may be intrinsic: “The king’s whim is my law”.
- 13.
It is an interesting technical problem just when such definitions are possible.
- 14.
This dynamic take on what may be called the “act of representation” has independent logical interest: Representation constructions suggest language dynamics.
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Liu, F. (2011). A Two-Level Perspective on Preference. In: Reasoning about Preference Dynamics. Synthese Library, vol 354. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1344-4_10
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