Formal Concept Analysis with Three Types of Negation

Classic Formal Concept Analysis (FCA) primarily focuses on the positive relationships between objects and attributes and does not have mechanisms for handling negation.To overcome this limitation, we introduce three types of negation concepts (contradictory negation, opposite negation, intermediary negation) into FCA.Based on the set SCOI and logic LCOI+PLCOI with these three types negation, we define formal context, Galois connection operators, formal concept and concept lattice with three types of negation,this leads to the proposal of a FCACOI: Formal Concept Analysis with contradictory negation, opposite negation and intermediary negation.For the reasoning in FCACOI, this paper focuses on attribute implication reasoning. Based on the logic LCOI+PLCOI and its semantics, we introduce the notion of ICOI-entailment as the semantic implication for attribute implication reasoning in FCACOI. Through ICOI-entailment, a connection is established between attribute implication reasoning in FCACOI and inference in the logic LCOI+PLCOI, it indicate that formally proven inference rules (theorems) in LCOI+PLCOI are valid in the attribute implication reasoning of FCACOI, LCOI+PLCOI provides a logical foundation for attribute implication reasoning in FCACOI. To illustrate the capability of attribute implication reasoning in FCACOI, we discuss its application in a concrete example. Moreover, we explore attribute reduction of the formal context in FCACOI, propose two research frameworks for attribute reduction from different perspectives, and compare their characteristics.We believe that, based on richer logic and semantics, FCACOI elevates FCA from a theory that describes affirmations to one that can describe affirmations and its contradiction(either this or that), opposition(extreme negation) and intermediary (transitional states between oppositions).

Stratified Negation in RDF Rules: A Correct Approach (Extended Version)

Combining RDF rule languages, such as N3 or SHACL Rules, with default negation is challenging. Existing methods to stratify negation often fail for RDF rules, since individual triples do not carry enough information to meaningfully restrict potential dependencies. Blank nodes in rule heads further complicate the matter, since the order of rule applications may determine whether new values are created, which in turn can change the applicability of rules with negation. To solve these open problems, we propose chain stratification as a robust new condition that guarantees a well-behaved semantics for RDF rules with negation, and existential rules in general. Our condition combines an elaborate analysis of potential multistep derivations with a mechanism for using integrity constraints to discard impossible cases. Applying rules in any order that respects chain stratification is guaranteed to derive an RDF graph that is unique, lean, and justified under the usual negation-as-failure semantics. To show the practicality, we also provide a prototype implementation.

The Sound of Absence: Audio-Language Embedding Models Struggle with Negation

Audio-language embedding models such as CLAP are widely evaluated on matching present sound events, but rarely on negation. We show this affirmation-only evaluation hides a key limitation: these models fail to encode negated sound concepts, mapping affirmative and negated captions to nearly identical representations. To expose this blind spot, we introduce NegEval-Audio, a framework that converts existing datasets into two negation-aware tasks, Retrieval-Neg and Multiple-Choice Negation (MCQ-Neg), to probe whether models distinguish present from absent events. On AudioCaps and Clotho, performance degrades sharply under negation, with negation-type MCQ accuracy falling far below chance, and the failure persists even for a recent multimodal LLM-based embedding model. While a training-free steering method improves MCQ-Neg, it yields marginal gains for Retrieval-Neg. This indicates that affirmation bias is a fundamental flaw in the representation geometry, necessitating explicit negation-aware training objectives.

As Easy as Rocket Science: Assessing the Ability of Large Language Models to Interpret Negation in Figurative Language

Figurative language and negation are two areas that challenge current language models, however, both are widely used throughout written and spoken language. Large language models (LLMs) are also widely used in everyday contexts where they cannot necessarily be tuned for a specific dataset. It is therefore essential to understand the ability of LLMs to correctly interpret text that includes both negation and figurative language. To investigate this, we develop a set of new annotations to an existing dataset of figurative language, and test a range of language models on the dataset. We find that the combination of negation and figurativeness can present a particular challenge, and that performance overall and across different negation types is particularly dependent on the prompt style used.