Conditional Preferences Based on Triadic Modal Logic

We concern ourselves in this paper with formalization of conditional preferences based on modal logic. We indicate four basic requirements for the task and show that meeting them jointly presents a challenge to existing dyadic modal logics of preferences. As an alternative, we introduce a minimal system, MCP, of triadic modal logic, which is consistent and also frame sound and frame complete with respect to its neighborhood semantics. A simple yet powerful mechanism of preference optimization is also developed on the basis of MCP, which embodies the criteria of maximal partial satisfaction, specificity, and positive utility. Our investigation in the paper shows that this formalization meets all of the requirements to a certain extent.