arXiv AI
Aug 3
Stratified Negation in RDF Rules: A Correct Approach (Extended Version)
arXiv:2607. 28778v1 Announce Type: cross Abstract: Combining RDF rule languages, such as N3 or SHACL Rules, with default negation is challenging.
Hybrid MKNF with Classical Negation in the Rule Component
arXiv:2607. 21202v1 Announce Type: cross Abstract: Hybrid MKNF knowledge bases under the well-founded semantics integrate Description Logics with Logic Programming.
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arXiv AI
Sep 1
Formal Concept Analysis with Three Types of Negation
arXiv:2608.29311v1 Announce Type: new Abstract: Classic Formal Concept Analysis (FCA) primarily focuses on the positive relationships between objects and attributes and does not have mechanisms for h...
arXiv AI
Sep 24
Not What You Meant: Can LLMs Follow a Specified Negation Semantics?
The paper investigates how large language models (LLMs) interpret negation across different logical semantics—open‑world vs. closed‑world, two‑ vs. three‑valued, and credulous vs. skeptical reasoning. Using the newly introduced NAFBench, a procedural generator that creates solver‑certified logic programs and their natural‑language verbalizations, the authors evaluate LLMs on four semantic viewpoints (SLDNF, well‑founded semantics, and stable‑model semantics). Results show a persistent gap: even the strongest models achieve only 59–74% accuracy, with many models sensitive to rule ordering and prone to overcommitment on undefined cases, though some frontier models reach near‑perfect performance on a fixed‑complexity set. "whyItMatters":"The study highlights that current LLMs struggle to reliably follow explicitly specified negation semantics, underscoring a limitation in their logical reasoning capabilities."
arXiv AI
Sep 10
Three Types of Negation of Triple and its Elements and an Extension of Triple
arXiv:2609.08271v1 Announce Type: new Abstract: In various data models, the classical triple is a typical semantic data model. However, due to the design of the triple as a simple structure for repre...
arXiv AI
Aug 12
sLTN: Structural Logic Tensor Networks
arXiv:2608. 11136v1 Announce Type: new Abstract: Logic Tensor Networks (LTN) provide a neurosymbolic framework in which first-order logic is interpreted through tensor operations, enabling logical constraints to be integrated with differentiable learning.
arXiv AI
Jul 24
A New Well-Supported Semantics for Description Logic Programs
arXiv:2607. 21203v1 Announce Type: new Abstract: Description logic programs are a powerful formalism for combining rules with ontologies.
Hugging Face Trending Papers
Jul 23
A New Well-Supported Semantics for Description Logic Programs
Description logic programs are a powerful formalism for combining rules with ontologies. The well-supported semantics for description logic programs ensures that no answer sets rely on cyclic dependencies.
Hugging Face Trending Papers
Jun 23
Tractable Reasoning and Conjunctive Query Answering for Defeasible DL-Lite under Rational Closure
In Description Logics (DLs), reasoning under Rational Closure (RC) is a well-known and widely accepted non-monotonic formalism to handle defeasible knowledge. In this paper, we study the application of RC to the core and horn variants of the DL-Lite family of lightweight description logics.
arXiv AI
Jun 9
Sound and Complete Neurosymbolic Reasoning with LLM-Grounded Interpretations
arXiv:2507. 09751v3 Announce Type: replace Abstract: Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but exhibit problems with logical consistency in their output.
arXiv AI
Jun 24
Tractable Reasoning and Conjunctive Query Answering for Defeasible DL-Lite under Rational Closure
arXiv:2606. 24279v1 Announce Type: new Abstract: In Description Logics (DLs), reasoning under Rational Closure (RC) is a well-known and widely accepted non-monotonic formalism to handle defeasible knowledge.
arXiv AI
Jun 9
Standpoint Logics with Defeasible Beliefs
arXiv:2606. 08503v1 Announce Type: new Abstract: In this paper, we integrate the defeasible logic of Kraus, Lehmann and Magidor (KLM) with the standpoint logic framework of G\'omez \'Alvarez and Rudolph.
arXiv AI
Jun 3
Towards Non-Monotonic Entailment in Propositional Defeasible Standpoint Logic
arXiv:2606. 03655v1 Announce Type: new Abstract: Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al.