Abstract
This paper shows that the Dawson technique of modelling deontic logics into alethic modal logics to gain insight into deontic formulas is not available for modelling a normal (in the spirit of Anderson) relevance deontic modal logic into either of the normal relevance alethic modal logics R□ S4or R□ M. The technique is to construct an extension of the well known entailment matrix set M 0and show that the model of the deontic formula P (A v B)→. PA v PB is excluded.
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References
A. R. Anderson, The formal analysis of normative systems, Technical Report No. 2, Contract No. SAR/Nonr-609(16), Office of Naval Research, Group Psychology Branch, New Haven 1956: reprinted in N. Rescher, The Logic of Decision, and Action, Pittsburgh, 1966.
A. R. Anderson and N. D. Belnap, Entailment: The Logic of Relevance and Necessity, Vol. 1, Princeton, 1975.
L. Aqvist, On Dawson-models for deontic logic, Logique et Analyse 7 (1964). pp. 14–21.
E. E. Dawson, A model for deontic logic, Analysis 19 (1959), pp. 73–78.
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Chidgey, J. On the non-availability of Dawson-modeling into certain relevance alethic modal logics. Stud Logica 38, 89–94 (1979). https://doi.org/10.1007/BF00370434
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DOI: https://doi.org/10.1007/BF00370434