arXiv AI
Three Types of Negation of Triple and its Elements and an Extension of Triple
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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
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Modus Tollens and Counterfactuals and Counterfactual Reasoning Based on Three Types of Negation
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 AI
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Stratified Negation in RDF Rules: A Correct Approach (Extended Version)
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arXiv AI
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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
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Evidential-Based Higher-Order Set Argumentation Framework
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 AI
Aug 7
TriQua: Reconciling Granularity and Context in Factuality Evaluation
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