Abstract
In this chapter, we will change the atmosphere of our topics and our logical methods a bit: Worlds will make place for objects, modal logic for first-order logic, and there will be differences in style as well. Eventually, however, all will fit back into one uniform paradigm for this book.
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Notes
- 1.
In Chapter 10, we will discuss cases where the syntactic view is really richer.
- 2.
Note that in optimality theory the optimal alternative is chosen unconsciously; we are thinking mostly of applications where conscious choices are made. Also, in optimality theory the application of the constraints to the alternatives lead to a clear and unambiguous result: either the constraint clearly is true of the alternative or it is not, and that is something that is not sensitive to change. We will loosen this condition and consider issues that arise when changes do occur.
- 3.
Unlike in Chapter 8 belief does not enter into this definition. This means that \({Pref}(x,y)\) can be read as x is superior to y, or under complete information x is preferable over y.
- 4.
This way of deriving an ordering from a priority sequence is the “leximin ordering” of [62].
- 5.
Note that, although we used n priorities in the proof to make the procedure easy to describe, in general \(^{2}log(n)+1\) priorities are sufficient for the purpose.
- 6.
References
Andréka, H., M. Ryan, and P-Y. Schobbens. 2002. Operators and laws for combining preferential relations. Journal of Logic and Computation 12:12–53.
Blackburn, P. 2000. Representation, reasoning, and relational structures: A hybrid logic manifesto. Logic Journal of the IGPL 8:339–365.
Coste-Marquis, S., J. Lang, P. Liberatore, and P. Marquis. 2004. Expressive power and succinctness of propositional languages for preference representation. In Proceedings of the 9th international conference on principles of knowledge representation and reasoning (KR 2004), eds. D. Dubois, C. Welty, and M.-A. Williams, 203–212. Menlo Park, CA: AAAI Press.
Grosof, B.N. 1991. Generalising prioritization. In Proceedings of the 2th international conference on principles of knowledge representation and reasoning (KR 91), eds. J. Allen, R. Fikes, and E. Sandewall, 289–300. San Fransisco, CA: Morgan Kaufmann.
Kratzer, A. 1981. Partition and revision: The semantics of counterfactuals. Journal of Philosophical Logic 10:201–216.
Lewis, D. 1973. Counterfactuals. Oxford: Blackwell.
Lewis, D. 1981. Ordering semantics and premise semantics for counterfactuals. Journal of Philosophical Logic 10:217–234.
von Wright, G.H. 1963. The logic of preference. Edinburgh: Edinburgh University Press.
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Liu, F. (2011). Preference from Priorities: Static Logic. In: Reasoning about Preference Dynamics. Synthese Library, vol 354. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1344-4_7
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