We define a model for computing probabilities of right-nested conditionals in terms of graphs representing Markov chains. This is an extension of the model for simple conditionals from Wójtowicz and Wójtowicz. The model makes it possible to give a formal yet simple description of different interpretations of right-nested conditionals and to compute their probabilities in a mathematically rigorous way. In this study we focus on the problem of the probabilities of conditionals; we do not discuss questions concerning (...) logical and metalogical issues such as setting up an axiomatic framework, inference rules, defining semantics, proving completeness, soundness etc. Our theory is motivated by the possible-worlds approach ; however, our model is generally more flexible. In the paper we focus on right-nested conditionals, discussing them in detail. The graph model makes it possible to account in a unified way for both shallow and deep interpretations of right-nested conditionals. In particular, we discuss the status of the Import-Export Principle and PCCP. We briefly discuss some methodological constraints on admissible models and analyze our model with respect to them. The study also illustrates the general problem of finding formal explications of philosophically important notions and applying mathematical methods in analyzing philosophical issues. (shrink)

The study of the autonomic nervous system (ANS) function has shown to provide useful indicators for risk stratification and early detection on a variety of cardiovascular pathologies. However, data gathered during different tests of the ANS are difficult to analyse, mainly due to the complex mechanisms involved in the autonomic regulation of the cardiovascular system (CVS). Although model-based analysis of ANS data has been already proposed as a way to cope with this complexity, only a few models coupling the (...) main elements involved have been presented in the literature. In this paper, a new model of the CVS, representing the ventricles, the circulatory system and the regulation of the CVS activity by the ANS, is presented. The models of the vascular system and the ventricular activity have been developed using the Bond Graph formalism, as it proposes a unified representation for all energetic domains, facilitating the integration of mechanic and hydraulic phenomena. In order to take into account the electro-mechanical behaviour of both ventricles, an electrophysiologic model of the cardiac action potential, represented by a set of ordinary differential equations, has been integrated. The short-term ANS regulation of heart rate, cardiac contractility and peripheral vasoconstriction is represented by means of continuous transfer functions. These models, represented in different continuous formalisms, are coupled by using a multi-formalism simulation library. Results are presented for two different autonomic tests, namely the Tilt Test and the Valsalva Manoeuvre, by comparing real and simulated signals. (shrink)

Legal analysis is a task underlying many forms of legal problem solving. In the Anglo-American legal system, legal analysis is based in part on legal precedents, previously decided cases. This paper describes a reduction-graph model of legal precedents that accounts for a key characteristic of legal precedents: a precedent's relevance to subsequent cases is determined by the theory under which the precedent is decided. This paper identifies the implementation requirements for legal analysis using the reduction-graph model (...) of legal precedents and describes GREBE, a program that satisfies these requirements. (shrink)

Thomas Richardson and Peter Spirtes. Scoring Ancestral Graph Models.

In this paper the existence or nonexistence of isomorphic mappings between graph models for the untyped lambda calculus is studied. It is shown that Engeler's D A is completely determined, up to isomorphism, by the cardinality of its `atom-set' A. A similar characterization is given for a collection of graph models of the Pω-type; from this some propositions regarding automorphisms are obtained. Also we give an indication of the complexity of the first-order theory of graph models by (...) showing that the second-order theory of first-order definable elements of a graph model is first-order expressable in the model. (shrink)

A new approach to policy analysis is formulated within the framework of the graph model for conflict resolution. A policy is defined as a plan of action for a decision maker (DM) that specifies the DM’s intended action starting at every possible state in a graph model of a conflict. Given a profile of policies, a Policy Stable State (PSS) is a state that no DM moves away from (according to its policy), and such that no (...) DM would prefer to change its policy given the policies of the other DMs. The profile of policies associated to a PSS is called a Policy Equilibrium. Properties of PSSs are developed, and a refinement is suggested that restricts DMs to policies that are credible in that they are in the DM’s immediate interest. Relationships with existing stability definitions in the graph model for conflict resolution are then explored. (shrink)

A comprehensive decision support system called GMCA (Graph Model for Conflict Analysis) implementing the multi-player graph model for analyzing conflicts is developed. GMCA contains algorithms for the rapid computation of a wide range of solution concepts, thereby enabling decision makers to take account of the diversity of human behavior. Using an engineering case study, the key features of GMCA are illustrated.

A hybrid preference framework is proposed for strategic conflict analysis to integrate preference strength and preference uncertainty into the paradigm of the graph model for conflict resolution (GMCR) under multiple decision makers. This structure offers decision makers a more flexible mechanism for preference expression, which can include strong or mild preference of one state or scenario over another, as well as equal preference. In addition, preference between two states can be uncertain. The result is a preference framework that (...) is more general than existing models which consider preference strength and preference uncertainty separately. Within the hybrid preference structure, four kinds of stability are defined as solution concepts and a post-stability analysis, called status quo analysis, which can be used to track the evolution of a given conflict. Algorithms are provided for implementing the key inputs of stability analysis and status quo analysis within the extended preference structure. The new stability concepts under the hybrid preference structure can be used to model complex strategic conflicts arising in practical applications, and can provide new insights for the conflicts. The method is illustrated using the conflict over proposed bulk water exports from Lake Gisborne in Newfoundland, Canada. (shrink)

Christopher Meek. Related Graphical Frameworks: Undircted, Directed Acyclic and Chain Graph Models.

In this paper, I sketch a new model for the format of the content of understanding states, Compressible Graph Maximalism (CGM). In this model, the format of the content of understanding is graphical, and compressible. It thus combines ideas from approaches that stress the link between understanding and holistic structure (like as reported by Grimm (in: Ammon SGCBS (ed) Explaining Understanding: New Essays in Epistemollogy and the Philosophy of Science, Routledge, New York, 2016)), and approaches that emphasize (...) the connection between understanding and compression (like Wilkenfeld (Synthese 190(6):997–1016, 2018)). I argue that the combination of these ideas has several attractive features, and I defend the idea against some challenges. (shrink)

Effective knowledge management in organizations, universities, libraries, and research institutions requires optimizing the flow of information while accounting for uncertainty. We propose a probabilistic framework that models knowledge as a graph of facts, where each node represents a knowledge unit characterized by its entropy H(v), and edges indicate dependency or influence relationships. Transitions of information between nodes are represented as a Markov Jump Process (MJP), and transition probabilities are optimized using the Metropolis–Hastings algorithm to maximize knowledge flow. This framework (...) identifies low-cost, high-impact pathways of knowledge transfer, enabling strategic decision-making in organizational learning and research. Simulation results demonstrate that maximizing mutual information between nodes reduces operational cost while promoting efficient knowledge dissemination. (shrink)

This paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all DAG independence models. This class of graphs, called maximal ancestral graphs, has two attractive features: there is at most one edge between each pair of vertices; every missing edge corresponds to an independence relation. These features lead to a simple parameterization of the corresponding set of distributions in the Gaussian case.

The focus of this article is the view about fundamental natural properties known as dispositional monism. This is a holistic view about nature, according to which all properties are essentially interrelated. The general question to be addressed concerns what kinds of features relational structures of properties should be thought to have. I use Bird's graph-theoretic framework for representing dispositional structures as a starting point, before arguing that it is inadequate in certain important respects. I then propose a more parsimonious (...) graph-theoretic system, which, among other things, overhauls Bird's distinction between stimulus and manifestation relations. (shrink)

The worldwide economies are being seriously impacted by financial fraud, requiring proficient detection techniques able to spot changing and complex fraudulent activity. Conventional Machine Learning (ML) models and rule-based approaches among other traditional fraud detection systems find it difficult to scale, and adaptably capture relational fraud patterns in vast financial transaction networks, and we present a new Graph Neural Network (GNN)-based fraud detection model that improves both computational efficiency and detection accuracy in order to meet these issues. To (...) develop expressive node representations, our method combines multi-hop neighborhood aggregation with attention methods, hence providing strong fraud detection. We also provide a hybrid detection system using community-based anomaly detection (Yelp-inspired) for detecting behavioral similarities and transaction-based embeddings (Amazon-inspired) to identify subconscious fraud movements. We use adaptive filtering systems and reinforce- ment learning-based neighbor selection to get above the constraints of highly imbalanced datasets, thus enhancing fraud detection performance and decreas- ing false positives. With 95.00% accuracy, 93.10% precision, 93.15% recall, and 93.20% AUC, experimental evaluations on real-world Yelp and Amazon datasets show that our model beats currently used GNN-based models including GCN, GAT, and GraphSAGE considerably. These findings confirm the success of our model in identifying large-scale fraudulent activity, providing a very attractive alternative for the prevention of financial fraud. (shrink)

Modeling mechanisms is central to the biological sciences – for purposes of explanation, prediction, extrapolation, and manipulation. A closer look at the philosophical literature reveals that mechanisms are predominantly modeled in a purely qualitative way. That is, mechanistic models are conceived of as representing how certain entities and activities are spatially and temporally organized so that they bring about the behavior of the mechanism in question. Although this adequately characterizes how mechanisms are represented in biology textbooks, contemporary biological research practice (...) shows the need for quantitative, probabilistic models of mechanisms, too. In this paper we argue that the formal framework of causal graph theory is well-suited to provide us with models of biological mechanisms that incorporate quantitative and probabilistic information. On the ba-sis of an example from contemporary biological practice, namely feedback regulation of fatty acid biosynthesis in Brassica napus, we show that causal graph theoretical models can account for feedback as well as for the multi-level character of mechanisms. However, we do not claim that causal graph theoretical representations of mechanisms are advantageous in all respects and should replace common qualitative models. Rather, we endorse the more balanced view that causal graph theoretical models of mechanisms are useful for some purposes, while being insufficient for others. (shrink)

We study model companions of theories extending the graph axioms. First we prove general results concerning the existence of the model companion. Then, by applying these results to the case of graphs, we give a series of companionable and non‐companionable examples.

This paper examines the use of diagrams in linguistics, in order to analyze their diagrammatic features, as well as their data structures, in relation to the modeling process. It starts from defining the comparison parameters, from several seminal works on diagrams.The analysis begins from the classical IPA Consonants chart and its relative vowel graph; both are instances of quite orthodox use of visual representations, showing themselves as a mere visual account of relational data. In the syntax section, there is (...) a strong presence of trees with their hierarchical structure.Semantics offers a far more varied collection of diagrams. Based on many possible foci and on different tasks, there are several important diagrams in use. It will be considered Wordnet, Framenet, Generative Lexicon, DRT and UML-based semantics.All these examples will lead us to stress how data models play an essential role in determining the modelling potential of graphs and the possible tasks performed by means of them. The object-oriented paradigm and its graphical development will be asserted as the most interesting use of diagrams; it will display an outstanding potential in modelling tasks. (shrink)

The primary objective of this study was to propose a functional discrete mathematical model for analyzing folklore fairy tales. Within this model, characters are denoted as vertices, and explicit instances of communication – both verbal and non-verbal – within the text are depicted as edges. Upon examining a corpus of Eastern Slavic fairy tales in comparison to Chukchi fairy tales, unforeseen outcomes emerged. Notably, the constructed models seem to evade establishing certain connections between characters. Consequently, instances where the (...) interactions among fairy tale characters would result in a non-planar graph structure are notably absent. To put it differently, the models refrain from incorporating sub-graphs delineated by the Kuratowski theorem governing planar graphs, specifically the minimal non-planar graphs Κ5 and Κ3,3. Remarkably, even in more extensive texts featuring a larger cast of characters, connections that would yield a non-planar graph pattern are consistently avoided. This leads to the formulation of a hypothesis positing that traditional folk tales adhere to a “planar narrative” design – an identifiable narrative variant characterized by inherent limitations in complexity. This design, in turn, appears deeply entrenched within the societal framework of the cultures that produced these folk narratives. (shrink)

Let \ be an ab initio amalgamation class with an unbounded increasing concave function f. We show that if the predimension function has a rational coefficient and f satisfies a certain assumption then the generic structure of \ has a model complete theory.

Summary This release marks the transition of the Idea Graph Framework from a internal concept to a public draft. It provides a foundational blueprint for describing visual compositions and modelling uncertainty. It includes a functional sandbox environment for testing. Key Features in this Draft Architectural Blueprint: Core concepts and structural definitions of the framework. Working Sandbox: A ready-to-use environment to explore the framework's capabilities. Initial Documentation: Overview of the intended workflows and data structures. Community Feedback & Goals The primary (...) goal of this v0.9.2 release is to gather community feedback. We are specifically looking for input on: The clarity of the framework's logic. Enhancements. workflow proposals. Potential edge cases. Note: As a "Public Draft", this version is intended for evaluation and discussion. Breaking changes may occur in future iterations based on feedback. (shrink)

We answer some questions about graphs that are reducts of countable models of Anti-Foundation, obtained by considering the binary relation of double-membership $x\in y\in x$. We show that there are continuum-many such graphs, and study their connected components. We describe their complete theories and prove that each has continuum-many countable models, some of which are not reducts of models of Anti-Foundation.

Automated moral inference is an emerging topic of critical importance in artificial intelligence. The contemporary approach typically relies on language models to infer moral relevance or moral properties of a concept. This approach demands complex parameterization and costly computation, and it tends to disconnect with existing psychological accounts of moralization. We present a simple cognitive model for moral inference, Moral Association Graph (MAG), inspired by psychological work on moralization. Our model builds on word association network for inferring (...) moral relevance and draws on rich psychological data. We demonstrate that MAG performs competitively to state-of-the-art language models when evaluated against a comprehensive set of data for automated inference of moral norms and moral judgment of concepts, and in-context moral inference. We also show that our model yields interpretable outputs and is applicable to informing short-term moral change. (shrink)

This paper explores the structural mismatch problem between physical and phenomenal properties, where the similarity relations we experience among phenomenal properties lack corresponding relations in the physical domain. I introduce a new understanding of this problem via the Uniformity Principle: for any set of dimensions used to determine phenomenal similarities, there must be a consistently applied set of physical dimensions generating the same pattern of similarity relations. I then assess the potential of recent machine learning models, specifically graph neural (...) networks, to resolve this problem, as proposed by Epstein. By examining how these models generate sensory maps, I argue that the dimensions they adopt violate the Uniformity Principle in two ways: impure dimensions, where subjective responses affect the physical dimensions used, and non-uniform dimensions, where the applied dimensions vary inconsistently. These issues show that current machine learning models fail to establish a systematic correspondence between physical and phenomenal properties. (shrink)

In this article the structure of the models of decidable monadic theories of planar graphs is investigated. It is shown that if the monadic theory of a class K of planar graphs is decidable, then the tree-width in the sense of Robertson and Seymour of the elements of K is universally bounded and there is a class T of trees such that the monadic theory of K is interpretable in the monadic theory of T.

Navigating and retrieving relevant excerpts of legislation is challenging, requiring time and effort, especially to fine-tune appropriate input search queries. Furthermore, the continuously growing, heterogeneous body of laws, combined with a deep interconnection among normative acts, adds a layer of complexity: some potentially relevant rules may be hidden in articles that, through multiple citations and references, might be relevant for the input query. Traditional search systems, based on keywords or more sophisticated approaches as BM25 or TF-IDF, do not support such (...) flexible exploration, being ineffective at handling contextual information. To address these challenges, recent research proposed using graph data models for legislative knowledge management, introducing a straightforward approach to handling network complexity. They adopted the Property Graph data structure, demonstrating how it provides semantics and navigation power, supporting advanced querying tools for legislative acts, and implemented it on the Italian legislation. In this paper, we build on recent results on legislative knowledge management with graphs by proposing LegisSearch, an effective navigation system that, combining the graph data model with pre-trained Large Language Models and universal text embeddings, allows users to conduct powerful searches within a legislative system. We implement LegisSearch within the Italian graph of national laws, and we test its performance across multiple domains by comparing its search results with those provided in specific thematic areas by Italian ministries on their official websites, demonstrating its superior retrieval performance over traditional search systems and testing the contribution of each component. (shrink)

Recursive linear structural equation models can be represented by directed acyclic graphs. When represented in this way, they satisfy the Markov Condition. Hence it is possible to use the graphical d-separation to determine what conditional independence relations are entailed by a given linear structural equation model. I prove in this paper that it is also possible to use the graphical d-separation applied to a cyclic graph to determine what conditional independence relations are entailed to hold by a given (...) non-recursive linear structural equation model. I also give a causal intepretation to the linear coefficients in a non- recursive structural equation models, and explore the relationships between cyclic graphs and undirected graphs, directed acyclic graphs with latent variables, and chain independence graphs. (shrink)

A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of (...) two deductive systems is an m-graph whose nodes are language expressions and the m-edges represent the inference rules of the two original systems. The sobriety of the approach is confirmed by proving that all the fibring notions are universal constructions. This graph-theoretic view is general enough to accommodate very different fibrings of propositional based logics encompassing logics with non-deterministic semantics, logics with an algebraic semantics, logics with partial semantics and substructural logics, among others. Soundness and weak completeness are proved to be preserved under very general conditions. Strong completeness is also shown to be preserved under tighter conditions. In this setting, the collapsing problem appearing in several combinations of logic systems can be avoided. (shrink)

This work presents a formal architectural model for complex systems based on a directed object–relation graph. In contrast to diagram-centric approaches, architecture is defined independently of representation, notation, or tooling. Objects and directed relations constitute the complete ontological core, while diagrams and viewpoints are treated as computable projections derived through canonical graph operators. -/- The paper introduces formal definitions of reachability, path analysis, and structural vulnerability as intrinsic architectural properties. Minimality and irreducibility of the object–relation model (...) are established with respect to canonical architectural views, demonstrating that storing diagrams as primary architectural artifacts introduces no additional structural information. -/- Grounded in the principles of the Architecture of Complex Systems (ACS), the proposed model enables invariant architectural reasoning across representations and supports rigorous analysis of architectural structure prior to implementation. A reference implementation illustrates the feasibility of executing architectural operators directly at the data layer, independent of visualization mechanisms. (shrink)

Biomimicry studies natural systems and attempts to use the gained knowledge and understanding to solve human problems. Can biomimicry, if applied in urban planning, help to make our cities more sustainable or, precisely, more friendly for walkable and 15-minute city models? Various researchers identify the following features of natural systems as form fits function, catalysis of cooperation, local contextuality, continuity of development, diversity, integrity, redundancy, decentralization, multifunctionality, and less energy consumption (e.g. TOD if the energy needed for transportation is considered), (...) hierarchy, fractality, etc. The presented research has two objectives: analyze the possibility of describing and evaluating the degree of expression of the features of natural systems in urban spatial structures to use them for comparison, benchmarking, or creation of a biomimicry index; evaluate if cities with more strongly expressed biomimicry features could be considered more walkable and close to the 15-minute city concept. To give answers to the above-presented questions Riga, Vilnius, and Tallinn were investigated. They represent both certain similarities and differences in terms of history, urban planning, political context, size, etc. A simulative mathematical graph model was used as the main tool to describe and analyze complex urban structures based on spatial configurations. Various graph centralities were employed to describe and compare the expression of natural systems’ features in the selected cities. OSM data was used to overlap graph models with such information as the density of inhabitants, concentrations of various points of interest in order to evaluate walkability and 15-minute city friendliness. The research results could be seen as an important step for better understanding of informal principles of biomimicry that can help transform urban areas. (shrink)

We prove that, given a planar embedding of a graph in the sphere, the expansion of the graph structure by predicates encoding vertex separation by simple graph cycles is dp-minimal. This provides a rich natural class of examples of unstable, dp-minimal, and also monadically NIP theories. We also show how to infer the existence of a distal expansion of the theory of the Farey graph.

The emerging area of network biology is seeking to provide insights into organizational principles of life. However, despite significant collaborative efforts, there is still typically a weak link between biological and computational scientists and a lack of understanding of the research issues across the disciplines. This results in the use of simple computational techniques of limited potential that are incapable of explaining these complex data. Hence, the danger is that the community might begin to view the topological properties of network (...) data as mere statistics, rather than rich sources of biological information. A further danger is that such views might result in the imposition of scientific doctrines, such as scale-free-centric (on the modeling side) and genome-centric (on the biological side) opinions onto this area. Here, we take a graph-theoretic perspective on protein-protein interaction networks and present a high-level overview of the area, commenting on possible challenges ahead. (shrink)

Bipolar argument graphs represent the structure of complex pro and contra arguments for one or more standpoints. In this article, ampliative and exclusionary principles of evaluating argument strength in bipolar acyclic argumentation graphs are laid out and compared to each other. Argument chains, linked arguments, link attackers and supporters, and convergent arguments are discussed. The strength of conductive arguments is also addressed but it is argued that more work on this type of argument is needed to properly distinguish argument strength (...) from more general value-based components of such arguments. The overall conclusion of the article is that there is no justifiably unique solution to the problem of argument strength outside of a particular epistemological framework. (shrink)

This book develops a systematic and unified framework for the study of planar graph theory under uncertainty, integrating classical graph-theoretic concepts with fuzzy, intuitionistic fuzzy, neutrosophic, plithogenic, and uncertain graph models. The work revisits foundational graph classes—including planar, outerplanar, apex, quasi-planar, and related graph structures—and extends them into uncertainty-aware environments where vertices and edges may carry graded, indeterminate, or attribute-dependent information. Special attention is given to fuzzy planar graphs, intuitionistic fuzzy planar graphs, neutrosophic planar graphs, (...) plithogenic planar graphs, and uncertain planar graph formulations, emphasizing both structural consistency and model-independent interpretations of planarity. In addition, the book explores related extensions to hypergraphs and SuperHyperGraphs, thereby broadening the conceptual landscape of planar structures in higher-order settings. By combining rigorous definitions, examples, comparative perspectives, and theoretical analysis, the book establishes a coherent foundation for future investigations in uncertain network modeling, graph theory, artificial intelligence, graph neural networks, computer vision, VLSI design, and complex systems analysis. (shrink)

Many real-world systems involve uncertainty not only in individual attributes but also in the relationships between entities. To address this, a variety of graph-theoretic frameworks have been developed that incorporate uncertainty directly into vertices, edges, and higher-level structural properties. Among these, fuzzy graphs, intuitionistic fuzzy graphs, neutrosophic graphs, and plithogenic graphs represent key approaches to modeling uncertainty in network structures. This book presents a comprehensive and systematic survey of graph theory under uncertainty, with particular emphasis on the unifying (...) role of the uncertain graph framework. It reviews fundamental concepts, structural properties, graph classes, and graph parameters within fuzzy, neutrosophic, and related models, while also introducing a wide range of extensions such as uncertain digraphs, hypergraphs, superhypergraphs, and dynamic graphs. In addition to theoretical developments, the book explores practical applications, including uncertain molecular graphs, decision-making systems, graph neural networks, knowledge graphs, and cognitive maps. By organizing diverse uncertainty-aware graph models within a common perspective, this work provides a coherent framework for understanding their relationships, capabilities, and applications in complex systems. (shrink)

I argue that Frege Problems in thought are best modeled using graph-theoretic machinery; and that these problems can arise even when subjects associate all the same qualitative properties to the object they’re thinking of twice. I compare the proposed treatment to similar ideas by Heck, Ninan, Recanati, Kamp and Asher, Fodor, and others.

This paper develops and benchmarks the Relational Zero State (RZS) framework as an action-free, graph-dynamical model for pre-geometric cosmology. The starting point is not a spacetime Lagrangian, but a weighted relational network (graph) and node fields updated by explicit rules constrained by a stability principle (“Romero Law”). A reproducible workflow (“Universe Factory”) is provided to generate synthetic universes on a laptop and to track phase-transition diagnostics such as component unification (percolation), global communication onset (spectral connectivity growth), and (...) saturation (stability plateaus). -/- A core requirement is low-redshift validation. Mechanisms intended to amplify early rare events must remain compatible with the established low- and intermediate-redshift large-scale-structure (LSS) phenomenology. To isolate the specific RZS statistical effect—symmetric heavy-tail amplification of rare peaks with minimal impact on the two-point sector—controlled surrogate tests are performed using BOSS DR12 LOWZ and CMASS power-spectrum targets (NGC/SGC) and multiple k-windows. Iterative amplitude-adjusted Fourier transform (IAAFT) surrogates hold the target two-point spectrum fixed by construction while varying only the one-point distribution. Across catalogs and parameter sweeps, the heavy-tail prescription keeps skewness consistent with zero, increases excess kurtosis, and boosts tail exceedance in the high-sigma regime, consistent with an even-order (trispectrum-like) signature rather than a two-point modification. -/- All scripts, figures, and summary tables are included for reproducibility and direct scrutiny. -/- . (shrink)

This book provides a coherent and unifying view for logic and representation learning to contribute to knowledge graph (KG) reasoning and produce better computational tools for integrating both worlds. To this end, logic and deep neural network models are studied together as integrated models of computation. This book is written for readers who are interested in KG reasoning and the new perspective of neuro-symbolic integration and have prior knowledge to neural networks and deep learning. The authors first provide a (...) preliminary introduction to logic and background knowledge closely related to the surveyed techniques such as the introduction of knowledge graph and ontological schema and the technical foundations of first-order logic learning. Reasoning techniques for knowledge graph completion are presented from three perspectives, including: representation learning-based, logical, and neuro-symbolic integration. The book then explores question answering on KGs with specific focus on multi-hop and complex-logic query answering before outlining work that addresses the rule learning problem. The final chapters highlight foundations on ontological schema and introduce its usage in KG before closing with open research questions and a discussion on the potential directions in the future of the field. (shrink)

Legal Judgment Prediction (LJP) is a typical application of Artificial Intelligence in the intelligent judiciary. Current research primarily focuses on automatically predicting law articles, charges, and terms of penalty based on the fact description of cases. However, existing methods for LJP have limitations, such as neglecting document structure and ignoring case similarities. We propose a novel framework called Graph Contrastive Learning with Augmentation (GCLA) for legal judgment prediction to address these issues. GCLA constructs trainable document-level graphs for fact description, (...) capturing local and global context through sentence-level subgraphs. Graph augmentation enhances robustness. We introduce a comparison case relation perspective, using graph contrastive learning to model case-text label relationships effectively. Experimental results on real-world datasets demonstrate the competitive performance of GCLA. (shrink)

$${{{\mathcal {F}}}}$$ -systems are useful digraphs to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and the one of Yablo can be analyzed with that tool to find graph-theoretic patterns. In this paper we studied this general model consisting of a set of sentences and the binary relation ‘ $$\ldots $$ affirms the falsity of $$\ldots $$ ’ among them. The possible existence of non-referential sentences was also considered. To model the (...) sets of all the sentences that can jointly be valued as true we introduced the notion of conglomerate, the existence of which guarantees the absence of paradox. Conglomerates also enabled us to characterize referential contradictions, i.e., sentences that can only be false under a classical valuation due to the interactions with other sentences in the model. A Kripke-style fixed-point characterization of groundedness was offered, and complete (meaning that every sentence is deemed either true or false) and consistent (meaning that no sentence is deemed true and false) fixed points were put in correspondence with conglomerates. Furthermore, argumentation frameworks are special cases of $$\mathcal{F}$$ -systems. We showed the relation between local conglomerates and admissible sets of arguments and argued about the usefulness of the concept for the argumentation theory. (shrink)

When no single universal model for a set of structures exists at a given cardinal, then one may ask in which models of set theory does there exist a small family which embeds the rest. We show that for λ+-graphs (λ regular) omitting cliques of some finite or uncountable cardinality, it is consistent that there are small universal families and 2λ > λ+. In particular, we get such a result for triangle-free graphs.

The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The author not only provides (...) a thorough description of the theory, but also details its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory. (shrink)

The Four Books have shaped East Asian intellectual traditions, yet their multilayered interpretive complexity limits their accessibility in the digital age. While traditional bilingual commentaries provide a vital pedagogical bridge, computational frameworks are needed to preserve and explore this wisdom. This paper bridges AI and classical philosophy by introducing Graphilosophy, an ontology-guided, multilayered knowledge graph framework for modeling and interpreting The Four Books. Integrating natural language processing, multilingual semantic embeddings, and humanistic analysis, the framework transforms a bilingual Chinese–Vietnamese corpus (...) into an interpretively grounded resource. Graphilosophy encodes linguistic, conceptual, and interpretive relationships across interconnected layers, enabling cross-lingual retrieval and AI-assisted reasoning while explicitly preserving scholarly nuance and interpretive plurality. The system also enables nonexpert users to trace the evolution of ethical concepts across borders and languages, ensuring that ancient wisdom remains a living resource for modern moral discourse rather than a static relic of the past. Through an interactive interface, users can trace the evolution of ethical concepts across languages, ensuring ancient wisdom remains relevant for modern discourse. A preliminary user study suggests the system’s capacity to enhance conceptual understanding and cross-cultural learning. By linking algorithmic representation with ethical inquiry, this research exemplifies how AI can serve as a methodological bridge, accommodating the ambiguity of cultural heritage rather than reducing it to static data. (shrink)

The paper is concerned with the existence of a universal graph at the successor of a strong limit singular μ of cofinality ℵ0. Starting from the assumption of the existence of a supercompact cardinal, a model is built in which for some such μ there are $\mu^{++}$ graphs on μ+ that taken jointly are universal for the graphs on μ+, while $2^{\mu^+} \gg \mu^{++}$. The paper also addresses the general problem of obtaining a framework for consistency results at (...) the successor of a singular strong limit starting from the assumption that a supercompact cardinal κ exists. The result on the existence of universal graphs is obtained as a specific application of a more general method. (shrink)

User modeling is a key topic in many applications, mainly social networks and information retrieval systems. To assess the effectiveness of a user modeling approach, its capability to classify personal characteristics (e.g., the gender, age, or consumption grade of the users) is evaluated. Due to the fact that some of the attributes to predict are multiclass (e.g., age usually encompasses multiple ranges), assessing fairness in user modeling becomes a challenge since most of the related metrics work with binary attributes. As (...) a workaround, the original multiclass attributes are usually binarized to meet standard fairness metrics definitions where both the target class and sensitive attribute (such as gender or age) are binary. However, this alters the original conditions, and fairness is evaluated on classes that differ from those used in the classification. In this article, we extend the definitions of four existing fairness metrics (related to disparate impact and disparate mistreatment) from binary to multiclass scenarios, considering different settings where either the target class or the sensitive attribute includes more than two groups. Our work endeavors to bridge the gap between formal definitions and real use cases in bias detection. The results of the experiments, conducted on four real-world datasets by leveraging two state-of-the-art graph neural network-based models for user modeling, show that the proposed generalization of fairness metrics can lead to a more effective and fine-grained comprehension of disadvantaged sensitive groups and, in some cases, to a better analysis of machine learning models originally deemed to be fair. The source code and the preprocessed datasets are available at the following link: https://github.com/erasmopurif/toward-responsible-fairness-analysis. (shrink)