Nonmonotonic Desires - A Possibility Theory Viewpoint

If an agent desires that ϕ and desires that ψ, this agent often also desires that ϕ and ψ hold at the same time (ϕ ∧ ψ). However, there are cases where ϕ ∧ ψ may be found less satisfactory for the agent than each of ϕ or ψ alone. This paper is a first attempt at modeling such nonmonotonic desires. The approach is developed in the setting of possibility theory, since it has been recently pointed out that guaranteed (or strong) possibility measures are a good candidate for modeling graded desires. Although nonmonotonic reasoning has been studied extensively for knowledge, and that preferential nonmonotonic consequence relations can be faithfully represented in the possibilistic setting, nonmonotonic desires appear to require a different approach.

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