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Deontic logic gives rise to a number of paradoxes when applied to our reasoning about moral values. These days it is starting to be applied in computer science. My worry is: doesn't the presence of those paradoxes render deontic logic automatically inapplicable to computer science?

  • Perhaps Chisholm's Paradox. I only say so because I found this pdf. – user3164 Apr 15 '14 at 17:57
  • Would it be useful to use a logic which also contain paradoxes? – Johan Apr 15 '14 at 19:10
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Standard Deontic Logic (SDL) has a number of problems, which McNamara divides into two groups:

  • Group 1. Problems stemming from the assumption that the obligation operator is normal.
  • Group 2. Problems stemming from a lack of expressivity of the language of SDL.

The above mentioned Chisholm's Paradox belongs to the second group. It shows, among other things, that the unary modal operator O (read "it is obligatory that") and the material conditional → (the truth-conditional "if..then") aren't jointly sufficient for expressing certain claims about obligations. Among the solutions to this class of problems is the addition of a dyadic conditional obligation operator SDL.

Analogy with classical logic. Consider the analogous "paradox" of the material conditional in classical logic: a sentence of the form (⊥ → ψ) is true whatever the value of ψ may be. If we were to apply classical logic in computer science in a domain that allowed contradictory information to be present in the same context, we could derive any conclusion we wanted. Some solutions to this explosive situation include the use of paraconsistent or relevance logics instead of the classical one.

The first group of problems is also serious, because they indicate that O may not be a normal operator. The Free Choice Permission Paradox, Good Samaritan Paradox, Sartre-Lemmon Dilemma, and many others in the group derive paradoxical conclusions from the assumption that O is normal, i.e., that it is aggregative, monotonic, etc. Among the solutions to this class of problems is the abandonment of the assumption that O is normal and the adoption of what are called neighborhood models.

Given that SDL has all these problems, the question about its applicability inevitably arises. But, as is usually the case, the answer depends on the field of application and the assumptions about the logic. Even if we leave SDL as it is, that is: without adding conditional obligation to address problems in (Group 2) or without weakening normalcy assumptions to address problems in (Group 1), it is still difficult to say whether SDL can have applications in computer science. At least the overall description of the problem area needs to be specified so that we can judge whether SDL's problems will carry over.

In sum, we cannot conclude that the problems and paradoxes with SDL make it a priori inapplicable.


van Benthem, J. (2010) Modal Logic for Open Minds, Stanford, CSLI Lecture Notes #199.
Holliday, W.H. (2012) Modal Reasoning, Lecture Course (Spring), UC Berkeley.
McNamara, P. (2010) Deontic Logic, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition).

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