Hanoi, Vietnam. November 2-8, 2024.

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ISSN: 2334-1033

ISBN: 978-1-956792-05-8

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Copyright © 2024 International Joint Conferences on Artificial Intelligence Organization

- Non-monotonic logics-General
- Logic programming, answer set programming-General

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.