Abstract
Preferences arise from comparisons between alternatives, say, outcomes, actions, or situations. Such a comparison is typically associated with some ordering, indicating that one alternative is “better” than another. For instance, when playing chess or other games, choosing a move π1 instead of π2 is determined largely by a consideration concerning the outcomes that π1 or π2 leads to. In general, individual preferences can be used to predict behavior by rational agents, as studied in game theory and decision theory. Preference logics in the literature study the abstract properties of different comparative structures [101].
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Notes
- 1.
In a different setting, [44] showed how such a language, extended with hybrid modalities, defines conditionals, Nash equilibrium, and Backward Induction solutions to games.
- 2.
We use two independent modalities here for weak and strict betterness. This may seem strange, since strict order was definable in terms of weak order. But the point is that this definition cannot be reproduced in a natural way inside our modal language, which therefore brings out reasoning with both modalities on a par.
- 3.
In this chapter, we use pre-orders since we want the generality of possibly non-total preferences. Total orders, the norm in areas like game theory, provide an interesting specialization for the results in this chapter. We will study total ordered preference in Chapter 7.
- 4.
One example are the added “intersection modalities” of Chapter 5.
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Liu, F. (2011). Preference over Worlds: Static Logic. In: Reasoning about Preference Dynamics. Synthese Library, vol 354. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1344-4_3
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