By Dagfinn Føllesdal, Risto Hilpinen (auth.), Risto Hilpinen (eds.)
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Additional resources for Deontic Logic: Introductory and Systematic Readings
Vol. 3S (1961); reprinted in Perceiving, Sensing and Knowing (ed. by R. , New York, 1965, pp. 438-472.  Hanson, W. , 'Semantics for Deontic Logic', Logique et Analyse 8 (1965) 177-190.  Hansson, Bengt, 'An Analysis of Some Deontic Logics', Nous 4 (1970) 373-398. Reprinted in this volume, pp. 121-147.  Hilpinen, Risto, Rules of Acceptance and Inductive Logic (Acta Philosophica Fennica 22), North-Holland Publ. , Amsterdam, 1968.  Hilpinen, Risto, 'An Analysis of Relativised Modalities', in Philosophical Logic (ed.
1. 4 Cf. Anderson  and Castaneda . 5 Our notation here differs from Mally's; our u corresponds to Mally's U, n to n, w to V, and m to /\. g. on p. 29. 7 This is not the only possible explanation. In  Iaakko Hintikka has pointed out that if the material implication q ::::> r in the antecedent of (AI) is replaced by a deontic implication O(q ::::> r), we get an acceptable principle of deontic logic. Cf. also the formula (41) below. 8 These papers, as well as the paper by GrelIing mentioned below, are reviewed by Frederic B.
Is called a model system (by Hintikka) or a model structure (by Kripke). A set of deontic sentences is consistent (or satisfiable) if and only if there is a model system [/ satisfying (Fl)~F4) such that all members of the set are true in MeS. ) are easily defined. The standard system of deontic logic is complete with respect to the present semantical theory: f is valid according to this semantical theory if and only if it is a theorem of the standard system. It is possible to obtain stronger semantical systems of deontic logic by imposing certain structural requirements on the relation R.