N-ary Relations Research Articles

Exploring the Potential of k^n-tree for Efficient Representation of n-ary Relations

The objective of this experimental study was to investigate the scalability of -trees, a compact data structure designed for representing -ary relations, compared to a baseline based on a plain representation of adjacency lists. A literature review of compact data structures was conducted, focusing on -trees and their potential for efficient -ary data representation. To assess scalability, experiments comparing -trees performance against the baseline using set intersection as a benchmark were conducted. Results demonstrated superior -trees scalability in terms of time and memory, especially for high-dimensional and clustered datasets. On average, -trees were eight times faster and consumed times less memory than the baseline. The study also analyzed the impact of the order parameter on performance, revealing a trade-off between space efficiency and query time. This study provides valuable insights into the practical applicability of -trees for managing and querying high-dimensional data.

Structural, point-free, non-Hausdorff topological realization of Borel groupoid actions

Abstract We extend the Becker–Kechris topological realization and change-of-topology theorems for Polish group actions in several directions. For Polish group actions, we prove a single result that implies the original Becker–Kechris theorems, as well as Sami’s and Hjorth’s sharpenings adapted levelwise to the Borel hierarchy; automatic continuity of Borel actions via homeomorphisms and the equivalence of ‘potentially open’ versus ‘orbitwise open’ Borel sets. We also characterize ‘potentially open’ n-ary relations, thus yielding a topological realization theorem for invariant Borel first-order structures. We then generalize to groupoid actions and prove a result subsuming Lupini’s Becker–Kechris-type theorems for open Polish groupoids, newly adapted to the Borel hierarchy, as well as topological realizations of actions on fiberwise topological bundles and bundles of first-order structures. Our proof method is new even in the classical case of Polish groups and is based entirely on formal algebraic properties of category quantifiers; in particular, we make no use of either metrizability or the strong Choquet game. Consequently, our proofs work equally well in the non-Hausdorff context, for open quasi-Polish groupoids and more generally in the point-free context, for open localic groupoids.

Polyadic relational concept analysis

Formal concept analysis is a mathematical framework based on lattice theory that aims at representing the information contained in binary object-attribute datasets (called formal contexts) in the form of a lattice of so-called formal concepts. Since its introduction, it has been extended to more complex types of data. In this paper, we are interested in two of those extensions: relational concept analysis and polyadic concept analysis that allow to process, respectively, relational data and n-ary relations. We present a framework for polyadic relational concept analysis that extends relational concept analysis to relational datasets that are made of n-ary relations. We show its basic properties and that it is a valid extension of relational concept analysis.

Methods to compute interesting consequences

In modern deductive analysis, the main tasks include the following: finding proof of a given statement using axioms and rules of inference and checking the correctness of a given consequence from certain premises. Little is currently known about inference problems with predetermined properties (problems with interesting consequences). There are no clear answers to the following questions: what properties are inherent in an interesting consequence and how to calculate an interesting consequence? To solve these problems, it is proposed to use the methods of n-tuple algebra (NTA) based on properties of the Cartesian product of sets. The objects of NTA are arbitrary n-ary relations, which can be interpreted as the formulas of mathematical logic. They are matrix-like structures which cells do not contain elements, but subsets of the corresponding attributes. In NTA, operations (addition, generalized intersection and generalized union) in the tuple algebra correspond to logical connectives of mathematical logic (negation, conjunction, disjunction), and the generalized inclusion relation corresponds to the derivability relation. The calculation of quantifier operations is performed using operations on attributes (adding a dummy attribute, which corresponds to the generalization rule in predicate calculus, and eliminating an attribute). For two of the four types of NTA structures, the elimination of attributes corresponds to computing the projection of a relation. To derive interesting consequences in NTA, a structure called the minimal consequence is proposed, which is equal to the generalized intersection of premises. Interesting consequences are calculated as projections of the minimal consequence. As a result of calculations and checks, consequences are obtained with a reduced or a given composition of variables, as well as with a reduced amount of notation.

PosKHG: A Position-Aware Knowledge Hypergraph Model for Link Prediction

Link prediction in knowledge hypergraphs is essential for various knowledge-based applications, including question answering and recommendation systems. However, many current approaches simply extend binary relation methods from knowledge graphs to n-ary relations, which does not allow for capturing entity positional and role information in n-ary tuples. To address this issue, we introduce PosKHG, a method that considers entities’ positions and roles within n-ary tuples. PosKHG uses an embedding space with basis vectors to represent entities’ positional and role information through a linear combination, which allows for similar representations of entities with related roles and positions. Additionally, PosKHG employs a relation matrix to capture the compatibility of both information with all associated entities and a scoring function to measure the plausibility of tuples made up of entities with specific roles and positions. PosKHG achieves full expressiveness and high prediction efficiency. In experimental results, PosKHG achieved an average improvement of 4.1% on MRR compared to other state-of-the-art knowledge hypergraph embedding methods. Our code is available at https://anonymous.4open.science/r/PosKHG-C5B3/.

From “what” to “how”: Extracting the Procedural Scientific Information Toward the Metric-optimization in AI

In response to the exponential growth of the volume of scientific publications, researchers have proposed a multitude of information extraction methods for extracting entities and relations, such as task, dataset, metric, and method entities. However, the existing methods cannot directly provide readers with procedural scientific information that demonstrates the path to the problem's solution. From the perspective of applied science, we propose a novel schema for the applied AI community, namely a metric-driven mechanism schema (Operation, Effect, Direction). Our schema depicts the procedural scientific information concerning “How to optimize the quantitative metrics for a specific task?” In this paper, we choose papers in the domain of NLP for our study, which is a representative branch of Artificial Intelligence (AI). Specifically, we first construct a dataset that covers the metric-driven mechanisms in single and multiple sentences. Then we propose a framework for extracting metric-driven mechanisms, which includes three sub-models: 1) a mechanism detection model, 2) a query-guided seq2seq mechanism extraction model, and 3) a task recognition model. Finally, a metric-driven mechanism knowledge graph, named MKGNLP, is constructed. Our MKGNLP has over 43K n-ary mechanism relations in the form of (Operation, Effect, Direction, Task). The human evaluation shows that the extracted metric-driven mechanisms in MKGNLP achieve 81.4% accuracy. Our model also shows the potential for creating applications to assist applied AI scientists to solve specific problems.

HyperGraphs.jl: representing higher-order relationships in Julia.

SummaryHyperGraphs.jl is a Julia package that implements hypergraphs. These are a generalization of graphs that allow us to represent n-ary relationships and not just binary, pairwise relationships. High-order interactions are commonplace in biological systems and are of critical importance to their dynamics; hypergraphs thus offer a natural way to accurately describe and model these systems.Availability and implementationHyperGraphs.jl is freely available under the MIT license. Source code and documentation can be found at https://github.com/lpmdiaz/HyperGraphs.jl.Supplementary information Supplementary data are available at Bioinformatics online.

Engineering uncertain time for its practical integration in ontologies

Ontologies are commonly used as a strategy for knowledge representation. However, they are still presenting limitations to model domains that require broad forms of temporal reasoning. This study is part of the Onto-mQoL project and was motivated by the real need to extend static ontologies with diverse time concepts, relations and properties, which go beyond the commonly used Allen’s Interval Algebra. Therefore, we use the n-ary relations as the basis for temporal structures, which minimally modify the original ontology, and extend these structures with a generic set of time concepts (moments and intervals), time concept properties (precise and uncertain), time relations (interval–interval, interval–moment, and moment–moment), and time relation properties (qualitative and quantitative). We divided the scientific contribution of this study into three parts. Firstly, we present the ontological temporal model (classes and properties) and how it is integrated into static ontologies. Secondly, we discuss the creation of axioms that give the semantics for precise temporal elements. Finally, as our main contribution, these ideas are extended with axioms for uncertain time. All these elements follow the Ontology Web Language (OWL) standards, so this proposal is still compatible with the main ontology editors and reasoners currently available. A case example demonstrates the use of this approach in the nutrition assessment domain.

TCM herbal prescription recommendation model based on multi-graph convolutional network

Ethnopharmacological relevanceThe recommendation of herbal prescriptions is a focus of research in traditional Chinese medicine (TCM). Artificial intelligence (AI) algorithms can generate prescriptions by analysing symptom data. Current models mainly focus on the binary relationships between a group of symptoms and a group of TCM herbs. A smaller number of existing models focus on the ternary relationships between TCM symptoms, syndrome-types and herbs. However, the process of TCM diagnosis (symptom analysis) and treatment (prescription) is, in essence, a “multi-ary” (n-ary) relationship. Present models fall short of considering the n-ary relationships between symptoms, state-elements, syndrome-types and herbs. Therefore, there is room for improvement in TCM herbal prescription recommendation models. PurposeTo portray the n-ary relationship, this study proposes a prescription recommendation model based on a multigraph convolutional network (MGCN). It introduces two essential components of the TCM diagnosis process: state-elements and syndrome-types. MethodsThe MGCN consists of two modules: a TCM feature-aggregation module and a herbal medicine prediction module. The TCM feature-aggregation module simulates the n-ary relationships between symptoms and prescriptions by constructing a symptom-‘state element’-symptom graph (Se) and a symptom-‘syndrome-type’-symptom graph (Ts). The herbal medicine prediction module inputs state-elements, syndrome-types and symptom data and uses a multilayer perceptron (MLP) to predict a corresponding herbal prescription. To verify the effectiveness of the proposed model, numerous quantitative and qualitative experiments were conducted on the Treatise on Febrile Diseases dataset. ResultsIn the experiments, the MGCN outperformed three other algorithms used for comparison. In addition, the experimental data shows that, of these three algorithms, the SVM performed best. The MGCN was 4.51%, 6.45% and 5.31% higher in Precision@5, Recall@5 and F1-score@5, respectively, than the SVM. We set the K-value to 5 and conducted two qualitative experiments. In the first case, all five herbs in the label were correctly predicted by the MGCN. In the second case, four of the five herbs were correctly predicted. ConclusionsCompared with existing AI algorithms, the MGCN significantly improved the accuracy of TCM herbal prescription recommendations. In addition, the MGCN provides a more accurate TCM prescription herbal recommendation scheme, giving it great practical application value.

Condensed Representations of Association Rules in n-ary Relations

The problem of association rules mining has given rise to a rich literature, especially in classic binary bidimensional data. In particular, the representation of the set of rules without loss of information is well understood. This is not the case in multidimensional binary data. This paper shows that the knowledge of n-1 components of every closed n-sets of a multidimensional Boolean tensor, as well as the cardinality of the remaining dimension, is enough to allow for the derivation of the confidence of every multidimensional association rule. This generalises well-known results in the bidimensional case. This paper provides experimental comparisons between the numbers of closed n-sets and frequent associations.

Automatic Polygon Layout for Primal-Dual Visualization of Hypergraphs.

N-ary relationships, which relate $N$ entities where $N$ is not necessarily two, can be visually represented as polygons whose vertices are the entities of the relationships. Manually generating a high-quality layout using this representation is labor-intensive. In this paper, we provide an automatic polygon layout generation algorithm for the visualization of N-ary relationships. At the core of our algorithm is a set of objective functions motivated by a number of design principles that we have identified. These objective functions are then used in an optimization framework that we develop to achieve high-quality layouts. Recognizing the duality between entities and relationships in the data, we provide a second visualization in which the roles of entities and relationships in the original data are reversed. This can lead to additional insight about the data. Furthermore, we enhance our framework for a joint optimization on the primal layout (original data) and the dual layout (where the roles of entities and relationships are reversed). This allows users to inspect their data using two complementary views. We apply our visualization approach to a number of datasets that include co-authorship data and social contact pattern data.

A Semantic Knowledge-Based Framework for Information Extraction and Exploration

The availability of online documents that describe domain-specific information provides an opportunity in employing a knowledge-based approach in extracting information from web data. This research proposes a novel comprehensive semantic knowledge-based framework that helps to transform unstructured data to be easily exploited by data scientists. The resultant sematic knowledgebase is reasoned to infer new facts and classify events that might be of importance to end users. The target use case for the framework implementation was the financial domain, which represents an important class of dynamic applications that require the modelling of non-binary relations. Such complex relations are becoming increasingly common in the era of linked open data. This research in modelling and reasoning upon such relations is a further contribution of the proposed semantic framework, where non-binary relations are semantically modelled by adapting the semantic reasoning axioms to fit the intermediate resources in the N-ary relations requirements.

Biomedical cross-sentence relation extraction via multihead attention and graph convolutional networks

Most biomedical information extraction efforts are focused on binary relations, there is a strong need to extract drug–gene–mutation n-ary relations among cross-sentences. In recent years, end-to-end biomedical relation extraction with sequence-based or dependency-based method has gained increasing attention. However, handling global dependencies and structural information remains challenges for sequence-based and dependency-based models. Joint exploitation of sequence and graph information may improve biomedical cross-sentence relation extraction. In this paper, we present a hybrid model for extracting biomedical relation in a cross-sentence which aims to address these problems. Our models rely on the self-attention mechanism that directly draws the global dependency relation of the sentence. Furthermore, to preserve the dependency structural information between the words that contain the syntactic dependency relations, we employ graph convolutional networks that encode the dependency structural information to guide the multihead attention to learn the dependency relation. Through extensive experiments on benchmark datasets, we demonstrated the effectiveness of our method.

Digital Jordan Curves and Surfaces with Respect to a Closure Operator

In this paper, we propose new definitions of digital Jordan curves and digital Jordan surfaces. We start with introducing and studying closure operators on a given set that are associated with n-ary relations (n > 1 an integer) on this set. Discussed are in particular the closure operators associated with certain n-ary relations on the digital line ℤ. Of these relations, we focus on a ternary one equipping the digital plane ℤ2 and the digital space ℤ3 with the closure operator associated with the direct product of two and three, respectively, copies of this ternary relation. The connectedness provided by the closure operator is shown to be suitable for defining digital curves satisfying a digital Jordan curve theorem and digital surfaces satisfying a digital Jordan surface theorem.

Qualitative-geometric ‘surrounds’ relations between disjoint regions

ABSTRACT This paper explores a class of qualitative-geometric relations between disjoint regions, embedded in the surface of a sphere or in the plane. These relations combine topological information about the configuration of the regions themselves as well as of the geometric Voronoi regions surrounding them. The method uses maptrees to construct a rigorous and exhaustive framework for n-ary relations between ensembles of regions. The resulting uniquely defined relations are akin to the verbal spatial relation ‘surrounds,’ in one common interpretation. The paper provides an exhaustive formal classification of such extended spatial relations between up to three regions. A further exhaustive computational exploration of up to seven regions in the sphere also provides an algorithm to enumerate all possible configurations. The results demonstrate how the approach can be used to provide fine-grained and salient descriptions of qualitative-geometric relations for complex scenes involving ensembles of multiple regions.

Atom canonicity and first order definability in classes of algebras of relations

AbstractFix 2 < n < ω and let CAn denote the class of cyindric algebras of dimension n. Roughly CAn is the algebraic counterpart of the proof theory of first order logic restricted to the first n variables which we denote by Ln. The variety RCAn of representable CAns reflects algebraically the semantics of Ln. Members of RCAn are concrete algebras consisting of genuine n-ary relations, with set theoretic operations induced by the nature of relations, such as projections referred to as cylindrifications. Although CAn has a finite equational axiomatization, RCAn is not finitely axiomatizable, and it generally exhibits wild, often unpredictable and unruly behavior. This makes the theory of CAn substantially richer than that of Boolean algebras, just as much as Lω,ω is richer than propositional logic. We show using a so-called blow up and blur construction that several varieties (in fact infinitely many) containing and including the variety RCAn are not atom-canonical. A variety V of Boolean algebras with operators is atom canonical, if whenever 𝔄 is atomic, then its Dedekind-MacNeille completion, sometimes referred to as its minimal completion, is also in V. From our hitherto obtained algebraic results we show, employing the powerful machinery of algebraic logic, that the celebrated Henkin-Orey omitting types theorem, which is one of the classical first (historically) cornerstones of model theory of Lω,ω, fails dramatically for Ln even if we allow certain generalized models that are only locallly clasfsical. It is also shown that any class K such that , where CRCAn is the class of completely representable CAns, and Sc denotes the operation of forming dense (complete) subalgebras, is not elementary. Finally, we show that any class K such that is not elementary, where Sd denotes the operation of forming dense subalgebra.

Conceptual and Logical Data Modeling: Detection and Configuration of P-types and n-ary Relationships in Domains

Conceptual and Logical Data Modeling: Detection and Configuration of P-types and n-ary Relationships in Domains

Incorporating representation learning and multihead attention to improve biomedical cross-sentence n-ary relation extraction

BackgroundMost biomedical information extraction focuses on binary relations within single sentences. However, extracting n-ary relations that span multiple sentences is in huge demand. At present, in the cross-sentence n-ary relation extraction task, the mainstream method not only relies heavily on syntactic parsing but also ignores prior knowledge.ResultsIn this paper, we propose a novel cross-sentence n-ary relation extraction method that utilizes the multihead attention and knowledge representation that is learned from the knowledge graph. Our model is built on self-attention, which can directly capture the relations between two words regardless of their syntactic relation. In addition, our method makes use of entity and relation information from the knowledge base to impose assistance while predicting the relation. Experiments on n-ary relation extraction show that combining context and knowledge representations can significantly improve the n-ary relation extraction performance. Meanwhile, we achieve comparable results with state-of-the-art methods.ConclusionsWe explored a novel method for cross-sentence n-ary relation extraction. Unlike previous approaches, our methods operate directly on the sequence and learn how to model the internal structures of sentences. In addition, we introduce the knowledge representations learned from the knowledge graph into the cross-sentence n-ary relation extraction. Experiments based on knowledge representation learning show that entities and relations can be extracted in the knowledge graph, and coding this knowledge can provide consistent benefits.

Methods of Clustering on Logical Models

This paper considers a model of a multidimensional space, in which variables are ordered and contain a finite number of values. Such a space may be analyzed with the n-tuple algebra developed by the authors as a natural combination of methods for the analysis of n-ary relations and logical structures. Some approaches enabling the application of some cluster analysis methods are proposed for this model.

Modeling Unified Language Templates for Designing Information Systems

Abstract—The most popular tools for developing object-oriented information systems are CASE-tools. More often, they do not support n-ary association relationships between classes. It is shown how, when describing a domain model, one can go from n-ary associations to binary ones, how to reduce the number of information system objects, and how to take into account the restrictions placed on objects. Situations that allow this kind of transformation are presented in the form of design patterns.