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Categorization of business processes is an important part of auditing. Large amounts of transactional data in auditing can be represented as transactions between financial accounts using weighted bipartite graphs. We view such bipartite graphs as many-valued formal contexts, which we use to obtain explainable categorization of these business processes in terms of financial accounts involved in a business process by using methods in formal concept analysis. We use Dempster-Shafer mass functions to represent agendas showing different interest in different set of financial accounts. We also model some possible deliberation scenarios between agents with different interrogative agendas to reach an aggregated agenda and categorization. The framework developed in this paper provides a formal ground to obtain and study explainable categorizations from the data represented as bipartite graphs according to the agendas of different agents in an organization (e.g. an audit firm), and interaction between these through deliberation. We use this framework to describe a machine-leaning meta algorithm for outlier detection and classification which can provide local and global explanations of its result and demonstrate it through an outlier detection algorithm., Comment: arXiv admin note: substantial text overlap with arXiv:2210.17330

We propose Set2Seq Transformer, a novel sequential multiple instance architecture, that learns to rank permutation aware set representations of sequences. First, we illustrate that learning temporal position-aware representations of discrete timesteps can greatly improve static visual multiple instance learning methods that do not regard temporality and concentrate almost exclusively on visual content analysis. We further demonstrate the significant advantages of end-to-end sequential multiple instance learning, integrating visual content and temporal information in a multimodal manner. As application we focus on fine art analysis related tasks. To that end, we show that our Set2Seq Transformer can leverage visual set and temporal position-aware representations for modelling visual artists' oeuvres for predicting artistic success. Finally, through extensive quantitative and qualitative evaluation using a novel dataset, WikiArt-Seq2Rank, and a visual learning-to-rank downstream task, we show that our Set2Seq Transformer captures essential temporal information improving the performance of strong static and sequential multiple instance learning methods for predicting artistic success.

Hypergraphs serve as an effective model for depicting complex connections in various real-world scenarios, from social to biological networks. The development of Hypergraph Neural Networks (HGNNs) has emerged as a valuable method to manage the intricate associations in data, though scalability is a notable challenge due to memory limitations. In this study, we introduce a new adaptive sampling strategy specifically designed for hypergraphs, which tackles their unique complexities in an efficient manner. We also present a Random Hyperedge Augmentation (RHA) technique and an additional Multilayer Perceptron (MLP) module to improve the robustness and generalization capabilities of our approach. Thorough experiments with real-world datasets have proven the effectiveness of our method, markedly reducing computational and memory demands while maintaining performance levels akin to conventional HGNNs and other baseline models. This research paves the way for improving both the scalability and efficacy of HGNNs in extensive applications. We will also make our codebase publicly accessible.

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.

The variety and complexity of relations in multimedia data lead to Heterogeneous Information Networks (HINs). Capturing the semantics from such networks requires approaches capable of utilizing the full richness of the HINs. Existing methods for modeling HINs employ techniques originally designed for graph neural networks, and HINs decomposition analysis, like using manually predefined metapaths. In this paper, we introduce a novel prototype-enhanced hypergraph learning approach for node classification in HINs. Using hypergraphs instead of graphs, our method captures higher-order relationships among nodes and extracts semantic information without relying on metapaths. Our method leverages the power of prototypes to improve the robustness of the hypergraph learning process and creates the potential to provide human-interpretable insights into the underlying network structure. Extensive experiments on three real-world HINs demonstrate the effectiveness of our method.

Categorization of business processes is an important part of auditing. Large amounts of transnational data in auditing can be represented as transactions between financial accounts using weighted bipartite graphs. We view such bipartite graphs as many-valued formal contexts, which we use to obtain explainable categorization of these business processes in terms of financial accounts involved in a business process by using methods in formal concept analysis. The specific explainability feature of the methodology introduced in the present paper provides several advantages over e.g.~non-explainable machine learning techniques, and in fact, it can be taken as a basis for the development of algorithms which perform the task of clustering on transparent and accountable principles. Here, we focus on obtaining and studying different ways to categorize according to different extents of interest in different financial accounts, or interrogative agendas, of various agents or sub-tasks in audit. We use Dempster-Shafer mass functions to represent agendas showing different interest in different set of financial accounts. We propose two new methods to obtain categorizations from these agendas. We also model some possible deliberation scenarios between agents with different interrogative agendas to reach an aggregated agenda and categorization. The framework developed in this paper provides a formal ground to obtain and study explainable categorizations from the data represented as bipartite graphs according to the agendas of different agents in an organization (e.g.~an audit firm), and interaction between these through deliberation.

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.

We discuss an ongoing line of research in the relational (non topological) semantics of non-distributive logics. The developments we consider are technically rooted in dual characterization results and insights from unified correspondence theory. However, they also have broader, conceptual ramifications for the intuitive meaning of non-distributive logics, which we explore., Comment: 36 pages

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.

This paper continues the investigation of the logic of competing theories, be they scientific, social, political etc. We introduce a many-valued, multi-type modal language which we endow with relational semantics based on enriched reflexive graphs, inspired by Plo\v{s}\v{c}ica's representation of general lattices. We axiomatize the resulting many-valued, non-distributive modal logic of these structures and prove a completeness theorem. We illustrate the application of this logic through a case study in which we model competition among interacting political promises and social demands within an arena of political parties social groups., Comment: 24 pages

We introduce a complete many-valued semantics for basic normal lattice-based modal logic. This relational semantics is grounded on many-valued formal contexts from Formal Concept Analysis. We discuss an interpretation and possible applications of this logical framework for categorization theory to the formal analysis of multi-market competition., Comment: 24 pages

The present paper proposes a novel way to unify Rough Set Theory and Formal Concept Analysis. Our method stems from results and insights developed in the algebraic theory of modal logic, and is based on the idea that Pawlak's original approximation spaces can be seen as special instances of enriched formal contexts, i.e. relational structures based on formal contexts from Formal Concept Analysis.

We introduce a complete many-valued semantics for two normal lattice-based modal logics. This semantics is based on reflexive many-valued graphs. We discuss an interpretation and possible applications of this logical framework in the context of the formal analysis of the interaction between (competing) scientific theories., Comment: To appear in the proceedings of EUSFLAT 2019. Pre-final version with expanded proofs

By 'informational entropy', we understand an inherent boundary to knowability, due e.g. to perceptual, theoretical, evidential or linguistic limits. In this paper, we discuss a logical framework in which this boundary is incorporated into the semantic and deductive machinery, and outline how this framework can be used to model various situations in which informational entropy arises., Comment: To appear in proceedings of WoLLIC 2019, Remark 1 added

Categorization systems are widely studied in psychology, sociology, and organization theory as information-structuring devices which are critical to decision-making processes. In the present paper, we introduce a sound and complete epistemic logic of categories and agents' categorical perception. The Kripke-style semantics of this logic is given in terms of data structures based on two domains: one domain representing objects (e.g. market products) and one domain representing the features of the objects which are relevant to the agents' decision-making. We use this framework to discuss and propose logic-based formalizations of some core concepts from psychological, sociological, and organizational research in categorization theory., Comment: In Proceedings TARK 2017, arXiv:1707.08250

The present paper 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, of which prove soundness and completeness with respect to algebraic probabilistic epistemic models., Comment: Final version of the paper

We introduce the logic LRC, designed to describe and reason about agents' abilities and capabilities in using resources. The proposed framework bridges two - up to now - mutually independent strands of literature: the one on logics of abilities and capabilities, developed within the theory of agency, and the one on logics of resources, motivated by program semantics. The logic LRC is suitable to describe and reason about key aspects of social behaviour in organizations. We prove a number of properties enjoyed by LRC (soundness, completeness, canonicity, disjunction property) and its associated analytic calculus (conservativity, cut elimination and subformula property). These results lay at the intersection of the algebraic theory of unified correspondence and the theory of multi-type calculi in structural proof theory. Case studies are discussed which showcase several ways in which this framework can be extended and enriched while retaining its basic properties, so as to model an array of issues, both practically and theoretically relevant, spanning from planning problems to the logical foundations of the theory of organizations.

RS-frames were introduced by Gehrke as relational semantics for substructural logics. They are two-sorted structures, based on RS-polarities with additional relations used to interpret modalities. We propose an intuitive, epistemic interpretation of RS-frames for modal logic, in terms of categorization systems and agents' subjective interpretations of these systems. Categorization systems are a key to any decision-making process and are widely studied in the social and management sciences. A set of objects together with a set of properties and an incidence relation connecting objects with their properties forms a polarity which can be `pruned' into an RS-polarity. Potential categories emerge as the Galois-stable sets of this polarity, just like the concepts of Formal Concept Analysis. An agent's beliefs about objects and their properties (which might be partial) is modelled by a relation which gives rise to a normal modal operator expressing the agent's beliefs about category membership. Fixed-points of the iterations of the belief modalities of all agents are used to model categories constructed through social interaction., Comment: References updated