KR2024Proceedings of the 21st International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 21st International Conference on Principles of Knowledge Representation and Reasoning

Hanoi, Vietnam. November 2-8, 2024.

Edited by

ISSN: 2334-1033
ISBN: 978-1-956792-05-8

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Copyright © 2024 International Joint Conferences on Artificial Intelligence Organization

Non-monotone Fixpoint Theory Based on the Structure of Weak Bilattices

  1. Angelos Charalambidis(Harokopio University of Athens)
  2. Giannos Chatziagapis(National and Kapodistrian University of Athens)
  3. Babis Kostopoulos(Harokopio University of Athens)
  4. Panos Rondogiannis(National and Kapodistrian University of Athens)

Keywords

  1. Non-monotonic logics-General
  2. Logic programming, answer set programming-General

Abstract

We extend the well-known representation theorem for interlaced bilattices to the broader class of weak interlaced bilattices. Based on this new theorem, we develop a fixpoint theory for non-monotone functions over weak infinitarily interlaced bilattices. Our theory generalizes classical fixpoint constructions introduced by Fitting, as-well-as recent results in the area of approximation fixpoint theory. We argue that the proposed theory has direct practical applications: we develop the semantics of higher-order logic programming with negation under an arbitrary weak infinitarily interlaced bilattice with negation, generalizing in this way recent work on the three-valued semantics of this formalism. We consider a line of research, initiated by Fitting, which investigates the structure of the consistent parts of bilattices in order to obtain natural generalizations of Kleene’s three-valued logic. We demonstrate that the consistent parts of bilattices are closely connected to weak bilattices, generalizing previous results of Fitting and Kondo.