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Beyond the Doctrine of Double Effect: A Formal Model of True Self-sacrifice

Part of the Intelligent Systems, Control and Automation: Science and Engineering book series (ISCA,volume 95)


The doctrine of double effect (\(\mathcal {{DDE}}\)) is an ethical principle that can account for human judgment in moral dilemmas: situations in which all available options have large good and bad consequences. We have previously formalized \(\mathcal {{DDE}}\) in a computational logic that can be implemented in robots. \(\mathcal {{DDE}}\), as an ethical principle for robots, is attractive for a number of reasons: (1) Empirical studies have found that \(\mathcal {{DDE}}\) is used by untrained humans; (2) many legal systems use \(\mathcal {{DDE}}\); and finally, (3) the doctrine is a hybrid of the two major opposing families of ethical theories (consequentialist/utilitarian theories versus deontological theories). In spite of all its attractive features, we have found that \(\mathcal {{DDE}}\) does not fully account for human behavior in many ethically challenging situations. Specifically, standard \(\mathcal {{DDE}}\) fails in situations wherein humans have the option of self-sacrifice. Accordingly, we present an enhancement of our \(\mathcal {{DDE}}\)-formalism to handle self-sacrifice; we end by looking ahead to future work.


  • Doctrine of double effect
  • True self-sacrifice
  • Law and ethics
  • Logic

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  • DOI: 10.1007/978-3-030-12524-0_5
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Fig. 1


  1. 1.

    Full formalization of \(\mathcal {{DDE}}\) would include conditions expressing the requirement that the agent in question has certain emotions and lacks certain other emotions (e.g., the agent cannot have delectatio morosa). On the strength of Ghosh’s Felmë theory of emotion, which formalizes (apparently all) human emotions in the language of cognitive calculus as described in the present paper, we are actively working in this direction.

  2. 2.

    The blue/red terminology is common in wargaming and offers in the minds of many a somewhat neutral way to talk about politically charged situations.

  3. 3.

    We leave out the counterfactual condition \(\mathbf {C}_5\) as it is typically excluded in standard treatments of \(\mathcal {{DDE}}\).

  4. 4.

    Technically, in the inaugural [2, 3], the straight event calculus is not used, but is enhanced, and imbedded within common knowledge, the operator for which is C.

  5. 5.

    A overview of this list is given lucidly in [16].

  6. 6.

    Placing limits on the layers of any intensional operators is easily regimented. See [2, 3].

  7. 7.

    More precisely, we allow such formulae to be interpreted in this way. Strictly speaking, even the “meaning” of a material conditional such as \((\phi \wedge \psi ) \rightarrow \psi \), in our proof-theoretic orientation, is true because this conditional can be proved to hold in “background logic.” Readers interested in how background logic appears on the scene immediately when mathematical (extensional deductive) logic is introduced are encouraged to consult [8].

  8. 8.

    The prover is available in both Java and Common Lisp and can be obtained at: The underlying first-order prover is SNARK, available at:

  9. 9.

    The definition of \(\rhd \) is inspired by Pollock’s [19] treatment, and while similarities can be found to the approach in [18], we note that this definition requires at least first-order logic.

  10. 10.

    The code is available at For further experimentation with and exploration of \(\mathcal {{DDE}}\), we are working on physical, 3D simulations, rather than only virtual simulations in pure software. Space constraints make it impossible to describe the “cognitive polysolid framework” in question (which can be used for simple trolley problems), development of which is currently principally the task of Matt Peveler.


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The research described above has been in no small part enabled by generous support from ONR (morally competent machines and the cognitive calculi upon which they are based) and AFOSR (unprecedentedly high computational intelligence achieved via automated reasoning), and we are deeply grateful for this funding.

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Correspondence to Naveen Sundar Govindarajulu .

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Govindarajulu, N.S., Bringsjord, S., Ghosh, R., Peveler, M. (2019). Beyond the Doctrine of Double Effect: A Formal Model of True Self-sacrifice. In: Aldinhas Ferreira, M., Silva Sequeira, J., Singh Virk, G., Tokhi, M., E. Kadar, E. (eds) Robotics and Well-Being. Intelligent Systems, Control and Automation: Science and Engineering, vol 95. Springer, Cham.

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