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The weak completion semantics and equality. (English) Zbl 1415.68220
Barthe, Gilles (ed.) et al., LPAR-22. 22nd international conference on logic for programming, artificial intelligence and reasoning, Awassa, Ethiopia, November 17–21, 2018. Selected papers. Manchester: EasyChair. EPiC Ser. Comput. 57, 326-342 (2018).
Summary: The weak completion semantics is an integrated and computational cognitive theory which is based on normal logic programs, three-valued Łukasiewicz logic, weak completion, and skeptical abduction. It has been successfully applied – among others – to the suppression task, the selection task, and to human syllogistic reasoning. In order to solve ethical decision problems like – for example – trolley problems, we need to extend the weak completion semantics to deal with actions and causality. To this end, we consider normal logic programs and a set \(\mathcal{E}\) of equations as in the fluent calculus. We formally show that normal logic programs with equality admit a least \(\mathcal{E}\)-model under the weak completion semantics and that this \(\mathcal{E}\)-model can be computed as the least fixed point of an associated semantic operator. We show that the operator is not continuous in general, but is continuous if the logic program is a propositional, a finite-ground, or a finite datalog program and the Herbrand \(\mathcal{E}\)-universe is finite. Finally, we show that the weak completion semantics with equality can solve a variety of ethical decision problems like the bystander case, the footbridge case, and the loop case by computing the least \(\mathcal{E}\)-model and reasoning with respect to this \(\mathcal{E}\)-model. The reasoning process involves counterfactuals which is necessary to model the different ethical dilemmas.
For the entire collection see [Zbl 1407.68021].
MSC:
68T27 Logic in artificial intelligence
03A05 Philosophical and critical aspects of logic and foundations
68N17 Logic programming
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