Rational Inference in Formal Concept Analysis

Lucas CarrLucas Carr, Nicholas LeisegangNicholas Leisegang, Thomas MeyerThomas Meyer, Sergei ObiedkovSergei Obiedkov

Lucas Carr, Nicholas Leisegang, Thomas Meyer, Sergei Obiedkov
Rational Inference in Formal Concept Analysis
In Peggy Cellier, Bernhard Ganter, Rokia Missaoui, eds., Conceptual Knowledge Structures. CONCEPTS 2025, volume 15941 of Lecture Notes in Artificial Intelligence, 325–341, September 2025. Springer

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KurzfassungAbstract
Defeasible conditionals are a form of non-monotonic inference which enable the expression of statements like “if φ then normally ψ”. The KLM framework defines a semantics for the propositional case of defeasible conditionals by construction of a preference ordering over possible worlds. The pattern of reasoning induced by these semantics is characterised by consequence relations satisfying certain desirable properties of non-monotonic reasoning. In FCA, implications are used to describe dependencies between attributes. However, these implications are unsuitable to reason with erroneous data or data prone to exceptions. Until recently, the topic of non-monotonic inference in FCA has remained largely uninvestigated. In this paper, we provide a construction of the KLM framework for defeasible reasoning in FCA and show that this construction remains faithful to the principle of non-monotonic inference described in the original framework. We present an additional argument that, while remaining consistent with the original ideas around non-monotonic reasoning, the defeasible reasoning we propose in FCA offers a more contextual view on inference, providing the ability for more relevant conclusions to be drawn when compared to the classical case.
Projekt:Project: ScaDS.AI
Forschungsgruppe:Research Group: Wissensbasierte SystemeKnowledge-Based Systems

The final publication is available at Springer.

@inproceedings{CLMO2025,
  author    = {Lucas Carr and Nicholas Leisegang and Thomas Meyer and Sergei
               Obiedkov},
  title     = {Rational Inference in Formal Concept Analysis},
  editor    = {Peggy Cellier and Bernhard Ganter and Rokia Missaoui},
  booktitle = {Conceptual Knowledge Structures. {CONCEPTS} 2025},
  series    = {Lecture Notes in Artificial Intelligence},
  volume    = {15941},
  publisher = {Springer},
  year      = {2025},
  month     = {September},
  pages     = {325{\textendash}341}
}