In 1926, Mally proposed the first formal deontic system. As Mally
and others soon realized, this system had some rather strange
consequences. We show that the strangeness of Mally's system is not so
much due to Mally's informal deontic principles as to the fact that he
formalized those principles in terms of the propositional calculus. If
they are formalized in terms of relevant logic rather than classical
logic, one obtains a system which is related to Anderson's relevant
deontic logic and not nearly as strange as Mally's own system.
References
[1] Anderson, A. R., ``Some nasty problems in the formal logic of ethics,'' Noûs, vol. 1 (1967), pp. 345--60.
[2] Anderson, A. R., ``A new square of opposition: Eubouliatic logic,'' Akten des XIV. Internationalen Kongresses für Philosophie, vol. 2 (1968), pp. 271--84.
[3] Anderson, A. R., and N. D. Belnap, Jr., Entailment: The Logic of Relevance and Necessity, vol. 1, Princeton University Press, Princeton, 1975.
Mathematical Reviews (MathSciNet):
MR406756
[4] Bohnert, H. G., ``The semiotic status of commands,'' Philosophy of Science, vol. 12 (1945), pp. 302--15.
[5] Dunn, J. M., ``Relevance logic and entailment,'' pp. 117--224 in Handbook of Philosophical Logic, vol. 3, Alternatives to Classical Logic, edited by D. M. Gabbay and F. Günthner, D. Reidel, Dordrecht, 1986.
[6] Føllesdal, D., and R. Hilpinen, ``Deontic logic: An introduction,'' pp. 1--35 in Deontic Logic: Introductory and Systematic Readings, 2d edition, edited by R. Hilpinen, D. Reidel, Dordrecht, 1981.
[7] Mally, E., Grundgesetze des Sollens: Elemente der Logik des Willens, Leuschner and Lubensky, Graz, 1926. Reprinted in Mally, E., Logische Schriften: Großes Logikfragment---Grundgesetze des Sollens, pp. 227--324, edited by K. Wolf and P. Weingartner, D. Reidel, Dordrecht, 1971.
Mathematical Reviews (MathSciNet):
MR419154
[8] McArthur, R. P., ``Anderson's deontic logic and relevant implication,'' Notre Dame Journal of Formal Logic, vol. 22 (1981), pp. 145--54.
[9] Menger, K., ``A logic of the doubtful: On optative and imperative logic,'' pp. 53--65 in Reports of a Mathematical Colloquium, vol. 2, University Press, Notre Dame, 1939.
[10] Meyer, J. J., and R. J. Wieringa, `` Deontic logic: A concise overview,'' pp. 3--16 in Deontic Logic in Computer Science, edited by J.-J. Ch. Meyer and R. J. Wieringa, John Wiley, Chichester, 1993.
