Rational Inference in Formal Concept Analysis
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910917726306304 |
|---|---|
| author | Carr, Lucas Leisegang, Nicholas Meyer, Thomas Obiedkov, Sergei |
| author_facet | Carr, Lucas Leisegang, Nicholas Meyer, Thomas Obiedkov, Sergei |
| contents | Defeasible conditionals are a form of non-monotonic inference which enable the expression of statements like "if $ϕ$ then normally $ψ$". The KLM framework defines a semantics for the propositional case of defeasible conditionals by construction of a preference ordering over possible worlds. The pattern of reasoning induced by these semantics is characterised by consequence relations satisfying certain desirable properties of non-monotonic reasoning. In FCA, implications are used to describe dependencies between attributes. However, these implications are unsuitable to reason with erroneous data or data prone to exceptions. Until recently, the topic of non-monotonic inference in FCA has remained largely uninvestigated. In this paper, we provide a construction of the KLM framework for defeasible reasoning in FCA and show that this construction remains faithful to the principle of non-monotonic inference described in the original framework. We present an additional argument that, while remaining consistent with the original ideas around non-monotonic reasoning, the defeasible reasoning we propose in FCA offers a more contextual view on inference, providing the ability for more relevant conclusions to be drawn when compared to the propositional case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16938 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rational Inference in Formal Concept Analysis Carr, Lucas Leisegang, Nicholas Meyer, Thomas Obiedkov, Sergei Artificial Intelligence Logic in Computer Science Defeasible conditionals are a form of non-monotonic inference which enable the expression of statements like "if $ϕ$ then normally $ψ$". The KLM framework defines a semantics for the propositional case of defeasible conditionals by construction of a preference ordering over possible worlds. The pattern of reasoning induced by these semantics is characterised by consequence relations satisfying certain desirable properties of non-monotonic reasoning. In FCA, implications are used to describe dependencies between attributes. However, these implications are unsuitable to reason with erroneous data or data prone to exceptions. Until recently, the topic of non-monotonic inference in FCA has remained largely uninvestigated. In this paper, we provide a construction of the KLM framework for defeasible reasoning in FCA and show that this construction remains faithful to the principle of non-monotonic inference described in the original framework. We present an additional argument that, while remaining consistent with the original ideas around non-monotonic reasoning, the defeasible reasoning we propose in FCA offers a more contextual view on inference, providing the ability for more relevant conclusions to be drawn when compared to the propositional case. |
| title | Rational Inference in Formal Concept Analysis |
| topic | Artificial Intelligence Logic in Computer Science |
| url | https://arxiv.org/abs/2504.16938 |