On the Relation Between Approximation Fixpoint Theory and Justification Theory
Authors: Simon Marynissen, Bart Bogaerts, Marc Denecker
IJCAI 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Approximation Fixpoint Theory (AFT) and Justification Theory (JT) are two frameworks to unify logical formalisms. AFT studies semantics in terms of fixpoints of lattice operators, and JT in terms of so-called justifications, which are explanations of why certain facts do or do not hold in a model. While the approaches differ, the frameworks were designed with similar goals in mind, namely to study the different semantics that arise in (mainly) non-monotonic logics. The first contribution of our current paper is to provide a formal link between the two frameworks. To be precise, we show that every justification frame induces an approximator and that this mapping from JT to AFT preserves all major semantics. The second contribution exploits this correspondence to extend JT with a novel class of semantics, namely ultimate semantics: we formally show that ultimate semantics can be obtained in JT by a syntactic transformation on the justification frame, essentially performing some sort of resolution on the rules. |
| Researcher Affiliation | Academia | 1KU Leuven 2Vrije Universiteit Brussel |
| Pseudocode | No | The paper presents theoretical definitions, theorems, and proofs but does not include any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | No | The paper does not mention releasing open-source code or provide any links to a code repository for the described methodology. |
| Open Datasets | No | This is a theoretical paper and does not involve datasets, training, or explicit statements about public dataset availability. |
| Dataset Splits | No | This is a theoretical paper and does not involve datasets or their splits for validation purposes. |
| Hardware Specification | No | This is a theoretical paper and does not describe any experimental setup or hardware used. |
| Software Dependencies | No | This is a theoretical paper and does not describe any experimental setup or software dependencies with version numbers. |
| Experiment Setup | No | This is a theoretical paper and does not describe any experimental setup, hyperparameters, or training settings. |