Step-wise Explanations of Constraint Satisfaction Problems

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We explore the problem of step-wise explaining how to solve constraint satisfaction problems, with a use case on logic grid puzzles. More specifically, we study the problem of explaining the inference steps that one can take during propagation, in a way that is easy to interpret for a person. We aim to give the constraint solver explainable agency, which can help in building trust in the solver by being able to understand and even learn from the explanations. The main challenge is that of finding a sequence of simple explanations, where each explanation should aim to be as cognitively easy as possible for a human to verify and understand. This contrasts with the arbitrary combination of facts and constraints that the solver may use when propagating. We propose the use of a cost function to quantify how simple an individual explanation of an inference step is, and identify the explanation-production problem of finding the best sequence of explanations of a CSP. We propose an approach that is agnostic of the underlying constraint propagation mechanisms, and that can provide explanations even for inference steps resulting from combinations of constraints. Our proposed algorithm iteratively constructs the explanation sequence by using an optimistic estimate of the cost function to guide the search for the best explanation at each step. Our experiments on logic grid puzzles show the feasibility of the approach in terms of the quality of the individual explanations and the resulting sequences obtained.

Original languageEnglish
Title of host publicationECAI 2020 - 24th European Conference on Artificial Intelligence, including 10th Conference on Prestigious Applications of Artificial Intelligence, PAIS 2020 - Proceedings
EditorsGiuseppe De Giacomo, Alejandro Catala, Bistra Dilkina, Michela Milano, Senen Barro, Alberto Bugarin, Jerome Lang
PublisherIOS Press
Number of pages8
ISBN (Electronic)978-1-64368-100-9
ISBN (Print)978-1-64368-100-9
Publication statusPublished - 24 Aug 2020
EventEuropean Conference on Artificial Intelligence (ECAI 2020) - Santiago De Compostela, Spain
Duration: 29 Aug 20202 Sep 2020
Conference number: 24

Publication series

NameFrontiers in Artificial Intelligence and Applications
PublisherIOS Press


ConferenceEuropean Conference on Artificial Intelligence (ECAI 2020)
Abbreviated titleECAI
CitySantiago De Compostela
Internet address


  • Hybrid AI
  • Explainable AI
  • First-order logic


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