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Categorical Approximation Fixpoint Theory

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Logics in Artificial Intelligence (JELIA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14281))

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Abstract

Approximation fixpoint theory (AFT) is a powerful framework that has been widely used for defining the semantics of non-monotonic formalisms in artificial intelligence and logic programming. In particular, AFT is used to derive the fixed points of (potentially non-monotonic) operators over complete lattices. However, in certain application domains, there arise operators defined over structures that are not necessarily complete lattices. Therefore, the quest for a more general version of AFT has been lingering as an interesting research direction. We develop an extension of AFT, namely Categorical AFT, that allows us to study the fixed points of (potentially non-functorial) operators defined over categories. Since categories are more general structures than complete lattices, we argue that our approach provides a more general and unified framework for the study of non-monotonicity. The versatility of category theory creates the potential of new insights and applications.

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Authors and Affiliations

  1. Department of Informatics and Telematics, Harokopio University, Athens, Greece

    Angelos Charalambidis

  2. Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece

    Panos Rondogiannis

Authors
  1. Angelos Charalambidis
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  2. Panos Rondogiannis
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Correspondence to Angelos Charalambidis .

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Editors and Affiliations

  1. TU Dresden, Dresden, Germany

    Sarah Gaggl

  2. Artificial Intelligence Research Institute - IIIA CSIC, Barcelona, Spain

    Maria Vanina Martinez

  3. Umeå University, Umeå, Sweden

    Magdalena Ortiz

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Charalambidis, A., Rondogiannis, P. (2023). Categorical Approximation Fixpoint Theory. In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds) Logics in Artificial Intelligence. JELIA 2023. Lecture Notes in Computer Science(), vol 14281. Springer, Cham. https://doi.org/10.1007/978-3-031-43619-2_35

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  • DOI: https://doi.org/10.1007/978-3-031-43619-2_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-43618-5

  • Online ISBN: 978-3-031-43619-2

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