Understanding artworks requires multi-step reasoning over visual content and cultural, historical, and stylistic context. While recent multimodal large language models show promise in artwork explanation, they rely on implicit reasoning and internalized knowledge, limiting interpretability and explicit evidence grounding. We propose A-MAR, an Agent-based Multimodal Art Retrieval framework that explicitly conditions retrieval on structured reasoning plans. Given an artwork and a user query, A-MAR first decomposes the task into a structured reasoning plan that specifies the goals and evidence requirements for each step. Retrieval is then conditioned on this plan, enabling targeted evidence selection and supporting step-wise, grounded explanations. To evaluate agent-based multimodal reasoning within the art domain, we introduce ArtCoT-QA. This diagnostic benchmark features multi-step reasoning chains for diverse art-related queries, enabling a granular analysis that extends beyond simple final answer accuracy. Experiments on SemArt and Artpedia show that A-MAR consistently outperforms static, non-planned retrieval and strong MLLM baselines in final explanation quality, while evaluations on ArtCoT-QA further demonstrate its advantages in evidence grounding and multi-step reasoning ability. These results highlight the importance of reasoning-conditioned retrieval for knowledge-intensive multimodal understanding and position A-MAR as a step toward interpretable, goal-driven AI systems, with particular relevance to cultural industries. The code and data are available at: https://github.com/ShuaiWang97/A-MAR.

Real-world multimodal knowledge graphs (MKGs) are inherently heterogeneous, modeling entities that are associated with diverse modalities. Traditional knowledge graph embedding (KGE) methods excel at learning continuous representations of entities and relations, yet they are typically designed for unimodal settings. Recent approaches extend KGE to multimodal settings but remain constrained, often processing modalities in isolation, resulting in weak cross-modal alignment, and relying on simplistic assumptions such as uniform modality availability across entities. Vision-Language Models (VLMs) offer a powerful way to align diverse modalities within a shared embedding space. We propose Vision-Language Knowledge Graph Embeddings (VL-KGE), a framework that integrates cross-modal alignment from VLMs with structured relational modeling to learn unified multimodal representations of knowledge graphs. Experiments on WN9-IMG and two novel fine art MKGs, WikiArt-MKG-v1 and WikiArt-MKG-v2, demonstrate that VL-KGE consistently improves over traditional unimodal and multimodal KGE methods in link prediction tasks. Our results highlight the value of VLMs for multimodal KGE, enabling more robust and structured reasoning over large-scale heterogeneous knowledge graphs.

Visual art understanding requires joint modeling of multiple perspectives and contextual inference rooted in cultural, historical, and stylistic knowledge. Recent multimodal large language models (MLLMs) demonstrate strong performance in generic captioning, primarily based on object recognition and training on large-scale generic data. They struggle in providing captions incorporating the multiple perspectives that fine art demands. In this work, we introduce ArtRAG, a novel training-free framework that integrates structured knowledge into a retrieval-augmented generation (RAG) pipeline for multi-perspective artwork explanation. ArtRAG automatically constructs an Art Context Knowledge Graph (ACKG) from domain-specific textual sources, organizing entities such as artists, themes, movements, and historical events into a rich, interpretable knowledge graph. At inference time, a multi-granular structured context retriever selects semantically and topologically relevant subgraphs to guide explanation generation. This approach enables MLLMs to produce contextually grounded, multi-perspective descriptions. Experiments on the SemArt and Artpedia datasets demonstrate that ArtRAG outperforms existing heavily trained baselines. Human evaluations further confirm ArtRAG's ability to generate coherent, informative, and culturally enriched interpretations of artworks.

Based on the intuitive idea that sets of objects or entities can be categorized in very different ways, and that some ways to categorise objects are better than others, depending on the purpose of the categorization, in this paper, a formal framework is introduced for parametrically generating a space of possible categorizations of a set of objects, based on the features which individual agents or groups thereof regard as relevant (formally encoded in the notion of interrogative agenda ). This formal framework accounts both for two-valued (crisp), and for many-valued (fuzzy) judgments about the relevance of given features, and introduces ways to aggregate individual agendas to group agendas. As an application on this framework, we discuss a machine-learning meta-algorithm for outlier detection and classification which provides local and global explanations of its results. • Parametric framework to generate categorization systems aligned with agent goals and knowledge stance. • Formal model of interrogative agendas with crisp and fuzzy importance judgments for feature relevance. • Operators to aggregate individual agendas into coherent group-level prioritization of categories. • FCA-based foundation for hierarchical, explainable, and uncertainty-aware categorization structures. • Meta-algorithm that learns agendas for classification, outlier detection, and explainable decision-making.

Categorization is one of the basic tasks in machine learning and data analysis. Building on formal concept analysis (FCA), the starting point of the present work is that different ways to categorize a given set of objects exist, which depend on the choice of the sets of features used to classify them, and different such sets of features may yield better or worse categorizations, relative to the task at hand. In their turn, the (a priori) choice of a particular set of features over another might be subjective and express a certain epistemic stance (e.g. interests, relevance, preferences) of an agent or a group of agents, namely, their interrogative agenda. In the present paper, we represent interrogative agendas as sets of features, and explore and compare different ways to categorize objects w.r.t. different sets of features (agendas). We first develop a simple unsupervised FCA-based algorithm for outlier detection which uses categorizations arising from different agendas. We then present a supervised meta-learning algorithm to learn suitable (fuzzy) agendas for categorization as sets of features with different weights or masses. We combine this meta-learning algorithm with the unsupervised outlier detection algorithm to obtain a supervised outlier detection algorithm. We show that these algorithms perform at par with commonly used algorithms for outlier detection on commonly used datasets in outlier detection. These algorithms provide both local and global explanations of their results.

We propose ArtSAGENet, a novel multimodal architecture that integrates Graph Neural Networks (GNNs) and Convolutional Neural Networks (CNNs), to jointly learn visual and semantic-based artistic representations. First, we illustrate the significant advantages of multi-task learning for fine art analysis and argue that it is conceptually a much more appropriate setting in the fine art domain than the single-task alternatives. We further demonstrate that several GNN architectures can outperform strong CNN baselines in a range of fine art analysis tasks, such as style classification, artist attribution, creation period estimation, and tag prediction, while training them requires an order of magnitude less computational time and only a small amount of labeled data. Finally, through extensive experimentation we show that our proposed ArtSAGENet captures and encodes valuable relational dependencies between the artists and the artworks, surpassing the performance of traditional methods that rely solely on the analysis of visual content. Our findings underline a great potential of integrating visual content and semantics for fine art analysis and curation.

In this paper, we generalize the basic notions and results of Dempster-Shafer theory from predicates to formal concepts. Results include the representation of conceptual belief functions as inner measures of suitable probability functions, and a Dempster-Shafer rule of combination on belief functions on formal concepts.

The present article contributes to the development of the mathematical theory of epistemic updates using the tools of duality theory. Here, we focus on Probabilistic Dynamic Epistemic Logic (PDEL). We dually characterize the product update construction of PDEL-models as a certain construction transforming the complex algebras associated with the given model into the complex algebra associated with the updated model. Thanks to this construction, an interpretation of the language of PDEL can be defined on algebraic models based on Heyting algebras. This justifies our proposal for the axiomatization of the intuitionistic counterpart of PDEL.