Abstract
The logic of an “ought” operator O is contranegative with respect to an underlying preference relation ≥ if it satisfies the property Op & (¬p)≥(¬q) →Oq. Here the condition that ≥ is interpolative ((p≥ (p∨q) ≥q) ∨ (q≥ (p∨q) ≥p)) is shown to be necessary and sufficient for all ≥-contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & Oq→O(p&q)) and disjunctive division (O(p&q) →Op ∨ Oq).
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Hanson, S.O. A New Representation Theorem for Contranegative Deontic Logic. Studia Logica 77, 1–7 (2004). https://doi.org/10.1023/B:STUD.0000034182.95695.cb
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DOI: https://doi.org/10.1023/B:STUD.0000034182.95695.cb