The Logic of Normative Systems
This paper exploits the properties of adjointness to develop a theory of norms. The adjoints are a pair of mappings between two logics, one called IMP, a logic of imperatives, and another called PROP, which is ordinary logic. In particular, L is a mapping form Prop to IMP and it has a right adjoint R from IMP to PROP. Norms are defined, formally, as statements that contain occurrences of RU where U is in IMP. A sample theorem (reminiscent of Kant’s “ought implies can”): Responsibility implies power and, moreover, incapacity implies immunity.
KeywordsTraffic Light Simple Norm Conjunctive Normal Form Deontic Logic Elementary Norm
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