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:2609.07483v1 Announce Type: new Abstract: Modus Tollens (MT) is a classical logical inference rule, while counterfactuals are hypothetical statements that are contrary to facts, and counterfact...
arXiv:2607. 28778v1 Announce Type: cross Abstract: Combining RDF rule languages, such as N3 or SHACL Rules, with default negation is challenging.
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."
The paper introduces the Evidential-Based Higher-Order Set Argumentation Framework (EHSAF), a unified formalism that extends Dung’s abstract argumentation by incorporating evidential support, higher-order relations, and collective interactions. Two complete semantics are defined: an adjacent complete labelling semantics allowing multiple truth values for arguments in support cycles, and an extension-based complete semantics that accepts only well‑founded support chains. The authors provide a propositional encoding in three‑valued Łukasiewicz logic and extend it to continuous fuzzy logics, proving key properties and showing equivalence under support‑acyclicity.
arXiv:2608. 05228v1 Announce Type: new Abstract: The "decompose-then-verify" paradigm for LLM factuality evaluation faces a fundamental trade-off: atomic facts, i.
arXiv:2606. 15246v1 Announce Type: cross Abstract: Provenance-enhanced statements of the form "according to $X$, $\varphi$" are pervasive in contemporary knowledge graphs, especially in domains where graph content primarily represents claims, interpretations, and hypotheses (\emph{capta}) rather than observer-independent facts (\emph{data}).
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.
arXiv:2607. 10212v1 Announce Type: new Abstract: Knowledge Graphs (KGs) are increasingly constructed through automated extraction pipelines; however, such systems often introduce spurious or incomplete triples, which degrade downstream performance.
arXiv:2607. 21202v1 Announce Type: cross Abstract: Hybrid MKNF knowledge bases under the well-founded semantics integrate Description Logics with Logic Programming.
Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al. applied to modal logics.
arXiv:2607. 16715v1 Announce Type: new Abstract: We study Controlled Query Evaluation (CQE), a declarative approach to confidentiality-preserving data access, in the context of Description Logic (DL) ontologies, and for confidentiality policies expressed through Epistemic Dependencies (EDs).