Abstract
A new possible world semantics for deontic logic is proposed. Its intuitive basis is that prohibitive predicates (such as “wrong” and “prohibited”) have the property of negativity, i.e. that what is worse than something wrong is itself wrong. The logic of prohibitive predicates is built on this property and on preference logic. Prescriptive predicates are defined in terms of prohibitive predicates, according to the well-known formula “ought” = “wrong that not”. In this preference-based deontic logic (PDL), those theorems that give rise to the paradoxes of standard deontic logic (SDL) are not obtained. (E.g., O(p & q) → Op & Oq and Op → O(p v q)) are theorems of SDL but not of PDL. The more plausible theorems of SDL, however, can be derived in PDL.
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Hansson, S.O. Preference-based deontic logic (PDL). J Philos Logic 19, 75–93 (1990). https://doi.org/10.1007/BF00211186
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DOI: https://doi.org/10.1007/BF00211186