Abstract
Lou Goble proposed powerful conditional deontic logics (CDPM) in that are able to deal with deontic conflicts by restricting the inheritance principle. One of the central problems for dyadic deontic logics is to properly treat the restricted applicability of the principle. “strengthening the antecedent”. In most cases it is desirable to derive from an obligation A under condition B, that A is also obliged under condition B and C. However, there are important counterexamples. Goble proposed a weakened rational monotonicity principle to tackle this problem. This solution is suboptimal as it is for some examples counter-intuitive or even leads to explosion. The chapter identifies also other problems of Goble’s systems. For instance, to make optimal use of the restricted inheritance principle, in many cases the user has to manually add certain statements to the premises. An adaptive logic framework on basis of CDPM is proposed which is able to tackle these problems. It allows for certain rules to be applied as much as possible. In this way counter-intuitive consequences as well as explosion can be prohibited and no user interference is required. Furthermore, for non-conflicting premise sets the adaptive logics are equivalent to Goble’s dyadic version of standard deontic logic.
A former version of the content of this chapter has been published under the name “An Adaptive Logic Framework for Conditional Obligations and Deontic Dilemmas” in the Journal “Logic and Logical Philosophy”, 2010, [1].
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Notes
- 1.
The permission operator is as usually defined by \(\mathsf {P}_{}(A\mid B) =_\mathrm{df }\lnot {\mathsf {O}}_{}(\lnot A\mid B)\).
- 2.
As in the monadic case in Chap. 10, we use a slight variation of Goble’s CDPM.2 which employs \(\vdash \bigl ({\mathsf {O}}_{}(A\mid C) \wedge {\mathsf {O}}_{}(B\mid C) \wedge \mathsf {P}_{}(A\wedge B\mid C)\bigr ) \supset {\mathsf {O}}_{}(A\wedge B\mid C)\) (CPAND) instead of our (CPAND\('\)). Using \({\mathbf{CDPM.2}}^{\prime}{\bf c}\) instead of CDPM.2c as lower limit logic leads to technically more elegant ALs. Furthermore, in contrast to CDPM.2c, \(\mathbf {{CDPM.2}}^{\prime}\!{\bf c}\), fulfills criterion \((C\star )\) that is going to be introduced in a moment.
- 3.
Some of the principles in \(\mathcal {P}\) will be defined later on (namely WRM\(_{\star }\), PS, CD and AWRM\(_{\star }\)).
- 4.
We slightly adjusted the criteria offered by Goble since his criteria were formulated in terms of theoremhood, while we focus on the consequences of premise sets. Models validating counter-instances of the criteria can be found in the proof of Theorem I.2.1 in Appendix I.
- 5.
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Acknowledgments
I thank Joke Meheus, Mathieu Beirlaen, Frederik Van De Putte, and the anonymous referees of the Journal of Logical Philosophy for valueable comments which helped to improve the paper.
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Straßer, C. (2014). An Adaptive Logic Framework for Conditional Obligations and Deontic Dilemmas. In: Adaptive Logics for Defeasible Reasoning. Trends in Logic, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-319-00792-2_11
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