Abstract
In this chapter, we resume the issue of “entanglement” of preference and information-based notions like knowledge and belief, that we have studied already in Chapter 5. How does this play when preference comes with richer priority structure? To plunge right in, let us consider a variation of Example 7.1: Alice is going to buy a house. For her there are several things to consider: the cost, the quality and the neighborhood, strictly in that order.
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- 1.
It would be interesting to consider what more a full doxastic predicate logic language can bring to our preference setting, but we will leave this question to other occasions.
- 2.
Readers who liked our plausibility models for belief in Chapters 4, 5, may also just continue thinking in these terms when reading what we have to say about the doxastic modality Bφ.
- 3.
It would be also interesting to look at non-factual priorities containing beliefs of the agents.
- 4.
Superiority is just defined as preference was in Chapter 7.
- 5.
Note that the \(V^{\prime}(p_i)\) are only relevant for the ordering ⊴ because the p i ’s only occur directly under the Pref in \(\varphi(p_1, \dots,p_n).\)
- 6.
In Chapter 10, we will return to the role of structured propositions in priority graphs, showing how their “internal algebra” can be relevant to preference reasoning after all.
References
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Halpern, J.Y. 1997. Defining relative likelihood in partially-ordered preferential structure. Journal of Artificial Intelligence Research 7:1–24.
Liu, F. 2009. Diversity of agents and their interaction. Journal of Logic, Language and Information 18(1):23–53.
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Liu, F. (2011). Belief-Based Preference. In: Reasoning about Preference Dynamics. Synthese Library, vol 354. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1344-4_8
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