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The Weak Completion Semantics and Equality

17 pagesPublished: October 23, 2018


The weak completion semantics is an integrated and computational cognitive theory which is based on normal logic programs,three-valued Lukasiewicz 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 E of equations as in the fluent calculus. We formally show that normal logic programs with equality admit a least E-model under the weak completion semantics and that this 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 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 E-model and reasoning with respect to this E-model. The reasoning process involves counterfactuals which is necessary to model the different ethical dilemmas.

Keyphrases: cognitive reasoning, counterfactual reasoning, equational reasoning, ethical decision-making, Fluent Calculus, logic programming, Three-Valued Lukasiewicz Logic, Weak Completion

In: Gilles Barthe, Geoff Sutcliffe and Margus Veanes (editors). LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 57, pages 326--342

BibTeX entry
  author    = {Emmanuelle-Anna Dietz Saldanha and Steffen H\textbackslash{}"olldobler and Sibylle Schwarz and Lim Yohanes Stefanus},
  title     = {The Weak Completion Semantics and Equality},
  booktitle = {LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Gilles Barthe and Geoff Sutcliffe and Margus Veanes},
  series    = {EPiC Series in Computing},
  volume    = {57},
  pages     = {326--342},
  year      = {2018},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/pr47}}
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