Notre Dame Journal of Formal Logic

Anderson's Relevant Deontic and Eubouliatic Systems

Gert-Jan C. Lokhorst

Abstract

We present axiomatizations of the deontic fragment of Anderson's relevant deontic logic (the logic of obligation and related concepts) and the eubouliatic fragment of Anderson's eubouliatic logic (the logic of prudence, safety, risk, and related concepts).

Article information

Source
Notre Dame J. Formal Logic, Volume 49, Number 1 (2008), 65-73.

Dates
First available in Project Euclid: 6 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1199649901

Digital Object Identifier
doi:10.1215/00294527-2007-004

Mathematical Reviews number (MathSciNet)
MR2376851

Zentralblatt MATH identifier
1180.03026

Subjects
Primary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}
Secondary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}

Keywords
Anderson deontic logic eubouliatic logic relevant logic risk safety

Citation

Lokhorst, Gert-Jan C. Anderson's Relevant Deontic and Eubouliatic Systems. Notre Dame J. Formal Logic 49 (2008), no. 1, 65--73. doi:10.1215/00294527-2007-004. https://projecteuclid.org/euclid.ndjfl/1199649901


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References

  • [1] Anderson, A. R., and J. N. D. Belnap, "Modalities in Ackermann's `Rigorous Implication'", The Journal of Symbolic Logic, vol. 24 (1959), pp. 107--11.
  • [2] Anderson, A. R., "Some nasty problems in the formal logic of ethics", Noûs, vol. 1 (1967), pp. 345--60.
  • [3] Anderson, A. R., "A new square of opposition: Eubouliatic logic", pp. 271--84 in Akten des XIV. Internationalen Kongresses für Philosophie, Vol. 2, Herder, Vienna, 1968.
  • [4] Anderson, A. R., N. D. Belnap, Jr., and J. M. Dunn, Entailment. The Logic of Relevance and Necessity. Vol. II, Princeton University Press, Princeton, 1992.
  • [5] Goble, L., ``The Andersonian reduction and relevant deontic logic,'' pp. 213--46 in New Studies in Exact Philosophy: Logic, Mathematics and Science. Proceedings of the 1999 Conference of the Society of Exact Philosophy, edited by B. Brown and J. Woods, Hermes Science Publications, Paris, 2001.
  • [6] Lokhorst, G.-J. C., "Andersonian deontic logic, propositional quantification, and Mally", Notre Dame Journal of Formal Logic, vol. 47 (2006), pp. 385--95.
  • [7] The Oxford English Dictionary, 2d edition, Oxford University Press, Oxford, 1989.