Abstract
The usual axioms and inference rules of deontic logic employ as a new primitive term an operator for ‘obligatory’ or for ‘permitted’. These axioms and inference rules are here derived from a language which instead of the operator contains a predicate ‘admissible’ defined on the set of state descriptions of an assertoric language. This approach eliminates the problem of constructing a deontic formalism of its own. The predicate version requires fewer and weaker decisions and is closer to intuitive notions than the operator version. The solutions of some open problems of deontic logic flow automatically from the well-known rules of the assertoric predicate calculus. Special attention is given to the relations between deontic and assertoric statements.
The proposed formulation of deontic logic suggests a natural generalization by proceeding from two to any number of degrees of admissibility. When there is a continuum of degrees of desirability, deontic logic becomes identical with the calculus of utilities.
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Vetter, H. Deontic logic without deontic operators. Theor Decis 2, 67–78 (1971). https://doi.org/10.1007/BF00133139
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DOI: https://doi.org/10.1007/BF00133139