Non-monotonic Extensions to Formal Concept Analysis via Object Preferences

Lucas CarrLucas Carr, Nicholas LeisegangNicholas Leisegang, Thomas MeyerThomas Meyer, Sebastian RudolphSebastian Rudolph

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Lucas Carr, Nicholas Leisegang, Thomas Meyer, Sebastian Rudolph
Non-monotonic Extensions to Formal Concept Analysis via Object Preferences
Proceedings of the 5th Southern African Conference on AI Research (SACAIR'24), to appear

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KurzfassungAbstract
Formal Concept Analysis (FCA) is an approach to creating a conceptual hierarchy in which a concept lattice is generated from a formal context. That is, a triple consisting of a set of objects, G, a set of attributes, M , and an incidence relation I on G × M . A concept is then modelled as a pair consisting of a set of objects (the extent), and a set of shared attributes (the intent). Implications in FCA describe how one set of attributes follows from another. The semantics of these implications closely resemble that of logical consequence in classical logic. In that sense, it describes a monotonic conditional. The contributions of this paper are two-fold. First, we introduce a non-monotonic conditional between sets of attributes, which assumes a preference over the set of objects. We show that this conditional gives rise to a consequence relation that is consistent with the postulates for non-monotonicty proposed by Kraus, Lehmann, and Magidor (commonly referred to as the KLM postulates). We argue that our contribution establishes a strong characterisation of non-monotonicity in FCA. To our knowledge, this is a novel view of FCA as a formalism which supports non-monotonic reasoning. We then extend the influence of KLM in FCA by introducing the notion of typical concepts through a restriction placed on what constitutes an acceptable preference over the objects. Typical concepts represent concepts where the intent aligns with expectations from the extent, allowing for an exception-tolerant view of concepts. To this end, we show that the set of all typical concepts is a meet semi-lattice of the original concept lattice. This notion of typical concepts is a further introduction of KLM-style typicality into FCA, and is foundational towards developing an algebraic structure representing a concept lattice of prototypical concepts.
Projekt:Project: SECAI, ScaDS.AI
Forschungsgruppe:Research Group: Computational LogicComputational Logic

@inproceedings{CLMR2024,
  author    = {Lucas Carr and Nicholas Leisegang and Thomas Meyer and Sebastian
               Rudolph},
  title     = {Non-monotonic Extensions to Formal Concept Analysis via Object
               Preferences},
  booktitle = {Proceedings of the 5th Southern African Conference on {AI}
               Research (SACAIR'24)},
  year      = {2024}
}