1 Logic of preferences, a generalization
In the modern context, the logic of preferences was first formulated by von Wright in 1962 (then, see (von Wright 1972) etc.) as a “side-product” of his studies in the logics of values and norms. Indeed, both axiological and deontic preferences are the most evident kinds of preferences, and there is no need of arguing for necessity of their study. Since then, the logic of preferences was studied, also in axiological and deontic contexts, by Rescher (see now (Rescher 2004)) and Ivin (Iwin 1975); see, for a detailed review, (Hansson 2001).
Oddly enough, the role of the logic of preferences is so far ignored in narratology. However, it is obvious that the conflicts between different values and different duties belong to the basic motives of the literature and the human history (e.g., sacrifice of Abraham or that of Jephthah). Therefore, without going into the details, we are allowed legitimately to assume that the modalities of preferences are an important part of the whole logical structure of narrative.
A generalization of the logic of preferences to the logic of knowledge has been undertaken by Nicholas Rescher. The deontic and value logics deals with the “normative-evaluative facts,” while the epistemic logic with the “descriptive facts.” “Values and descriptive facts are both governed by norms.” However, “[o]ur knowledge of both sorts of facts, the descriptively informative and the normative-evaluative hinges on the criteriological bearing of the question: What merits approbation? To be sure, this overarching question bears a very different construction on each side of the issue, with approbation as acceptance on the side of descriptive information, and approbation as preference on the side of evaluative judgment. But acceptance too is a preference of sorts: an epistemic preference” (Rescher 2004, 54).
Presently I don’t know any study of preferences in the alethic modal logic. Nevertheless, a direct result of quantification with more than in the alethic modality is such categories as “more (im)possible” and “less (im)possible,” whose sense is self-evident (and not limited to the probabilistic interpretation).
Generally speaking, the logic of preference establishes relations between two sets of objects (in Mostowski’s sense: set is supposed not to have any relevant internal structure) sharing the same modal state but in a different extent. The comparison on which any preference is grounded makes sense within the same modal state only. Both compared sets must belong to either “good” or “bad,” “known” or “unknown”, etc.