Compilation of static and evolving conditional knowledge bases for computing induced nonmonotonic inference relations

  • Christoph BeierleEmail author
  • Steven Kutsch
  • Kai Sauerwald


Several different semantics have been proposed for conditional knowledge bases \(\mathcal {R}\) containing qualitative conditionals of the form “If A, then usually B”, leading to different nonmonotonic inference relations induced by \(\mathcal {R}\). For the notion of c-representations which are a subclass of all ranking functions accepting \(\mathcal {R}\), a skeptical inference relation, called c-inference and taking all c-representations of \(\mathcal {R}\) into account, has been suggested. In this article, we develop a 3-phase compilation scheme for both knowledge bases and skeptical queries to constraint satisfaction problems. In addition to skeptical c-inference, we show how also credulous and weakly skeptical c-inference can be modelled as constraint satisfaction problems, and that the compilation scheme can be extended to such queries. We further extend the compilation approach to knowledge bases evolving over time. The compiled form of \(\mathcal {R}\) is reused for incrementally compiling extensions, contractions, and updates of \(\mathcal {R}\). For each compilation step, we prove its soundness and completeness, and demonstrate significant efficiency benefits when querying the compiled version of \(\mathcal {R}\). These findings are also supported by experiments with the software system InfOCF that employs the proposed compilation scheme.


Conditional Conditional knowledge base c-representation Skeptical c-inference Weakly skeptical c-inference Credulous c-inference Constraint satisfaction problem Knowledge base compilation Knowledge base modification Incremental compilation 

Mathematics Subject Classification (2010)

68T27 68T30 68T37 


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This work was supported by DFG Grant BE 1700/9-1 given to Christoph Beierle as part of the priority program “Intentional Forgetting in Organizations” (SPP 1921). Kai Sauerwald is supported by this Grant. We thank the anonymous reviewers for their valuable hints and comments that helped us to improve the paper.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Christoph Beierle
    • 1
    Email author
  • Steven Kutsch
    • 1
  • Kai Sauerwald
    • 1
  1. 1.Faculty of Mathematics and Computer ScienceFernUniversität in HagenHagenGermany

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