Multi-level frameworks are increasingly used in knowledge representation to model scenarios involving not only types and their individuals, but also types of types, e.g. Species, Human, and me. Central to prominent approaches are powertypes and basetypes, which have not yet been analyzed for dependency. In this paper we analyze and formalize the dependence relations between these entities using Fine’s theory and logic of essence, derived notions for dependence, specialization, and rigidity, the Multi-Level Theory, and a geological use-case. Results reveal a web of dependencies that enhance understanding of these entities.

Processes are fundamental to enterprises, serving as significant engines of optimization and analysis. Understanding business processes is critical, yet integrating formal process ontologies with enterprise data and workflows remains difficult. We refer to this specific kind of ontology application, intended for practitioners working with enterprise data, as operational realization. The varied ontological commitments and highly expressive representation languages of process ontologies create barriers for operational realization, including issues of decidability, a lack of tooling, and operational constraints. This paper presents an architecture for the operational realization of process ontologies, driven by process mining needs. A key aspect of the architecture is the formalization of ontological commitments in tasks like data cleaning and analysis, which rely on implicit assumptions embedded in the interpretation of process data. Our approach builds on existing methodologies, notably ontology-based data access (OBDA), while going further by encoding domain knowledge required to interpret and reason with process data. This structure moves beyond an A-Box and T-Box distinction, explicitly capturing how the process ontology, domain data, and supporting data interpretation theories enable complex process reasoning. By structuring the dynamics of a process ontology, domain data, process data theories, and by characterizing reasoning scenarios, our approach provides a pragmatic foundation for integrating process ontologies into data-driven process workflows. We demonstrate this architecture with real enterprise data, challenge problems, and scenarios already widely used for benchmarking in process mining.

Graph clustering is a fundamental task in network analysis, aimed at uncovering meaningful groups of nodes based on structural and attribute-based similarities. Traditional Nonnegative Matrix Factorization (NMF) methods have shown promise in clustering tasks by providing low-dimensional representations of data. However, most existing NMF-based approaches are highly sensitive to noise and outliers, leading to suboptimal performance in real-world scenarios. Additionally, these methods often struggle to capture the underlying nonlinear structures of complex networks, which can significantly impact clustering accuracy. To address these limitations, this paper introduces Robust Self-Supervised Symmetric NMF (R3SNMF) to improve graph clustering. The proposed algorithm leverages a robust principal component model to handle noise and outliers effectively. By incorporating a self-supervised learning mechanism, R3SNMF iteratively refines the clustering process, enhancing the quality of the learned representations and increasing resilience to data imperfections. The symmetric factorization ensures the preservation of network structures, while the self-supervised approach allows the model to adaptively improve its clustering performance over successive iterations. In addition, R3SNMF integrates a graph-boosting method to improve how relationships within the network are represented. Extensive experimental evaluations on various real-world graph datasets demonstrate that R3SNMF outperforms state-of-the-art clustering methods in terms of both accuracy and robustness.

Process mining has emerged as a critical practice for understanding business processes through data-driven analysis. Practitioners necessarily apply diverse process and domain knowledge to guide their analyses. However, these practices are often ad-hoc and informal, failing to formalize the process knowledge being applied. While various formal methods including temporal logic have been applied to process mining, they fail to acknowledge fundamental ontological commitments of processes. Formal ontology for processes, on the other hand, are difficult to integrate into a process mining pipeline, lacking a data-driven grounding. We thus introduce process meaning patterns as a formal declarative framework to capture process knowledge being applied in process mining, based on first order logic ontology patterns. We demonstrate our framework's ability to semi-automatically infer process knowledge motivated by real applications from Volvo IT Belgium. This paper also accompanies a preliminary implementation of the framework using Python and Datalog.

Space, time, objects, and events are fundamental concepts in ontologies. For substantivalists that believe entities are located at regions (space or spacetime), a key issue to address is the relationship between entities and their located regions. There is rich literature on the ontologies of location and mereology of material objects, as well as their philosophical foundations, but relatively little on events and their location. Most existing event ontologies provide little beyond the signatures and simply associate an event entity to space and time. In this study, we propose a new location ontology for events that formalize the relationship between events and spacetime, where events and spacetime maintain their own mereologies. We also make ontological commitments to support the mereological harmony of events and spacetime and provide the rationale and axiomatization of these commitments.

Within knowledge representation in artificial intelligence, a first-order ontology is a theory in first-order logic that axiomatizes the concepts in some domain. Ontology verification is concerned with the relationship between the intended models of an ontology and the models of the axiomatization of the ontology. In particular, we want to characterize the models of an ontology up to isomorphism and determine whether or not these models are equivalent to the intended models of the ontology. Unfortunately, it can be quite difficult to characterize the models of an ontology up to isomorphism. In the first half of this article, we review the different metalogical relationships between first-order theories and identify which relationship is needed for ontology verification. In particular, we will demonstrate that the notion of logical synonymy is needed to specify a representation theorem for the class of models of one first-order ontology with respect to another. In the second half of the article, we discuss the notion of reducible theories and show we can specify representation theorems by which models are constructed by amalgamating models of the constituent ontologies.

The design of ontologies is a time-consuming and resource-intensive endeavour. Rather than (manually) design the ontology first and then associate it with data, can we (semiautomatically) design the ontology from the data itself? This paper presents a novel approach to the semi-automated design of ontologies that incorporates axiom generation from data models, semantic parsing, and ontology learning from examples and counterexamples via search through an ontology repository.

Data science incorporates a variety of processes, concepts, techniques and domains, to transform data that is representative of real-world phenomena into meaningful insights and to inform decision-making. Data science relies on simple datatypes like strings and integers to represent complex real-world phenomena like time and geospatial regions. This reduction of semantically rich types to simplistic ones creates issues by ignoring common and significant relationships in data science including time, mereology, and provenance. Current solutions to this problem including documentation standards, provenance tracking, and knowledge model integration are opaque, lack standardization, and require manual intervention to validate. We introduce the meaningful type safety framework (MeTS) to ensure meaningful and correct data science through semantically-rich datatypes based on dependent types. Our solution encodes the assumptions and rules of common real-world concepts, such as time, geospatial regions, and populations, and automatically detects violations of these rules and assumptions. Additionally, our type system is provenance-integrated, meaning the type environment is updated with every data operation. To illustrate the effectiveness of our system, we present a case study based on real-world datasets from Statistics Canada (StatCAN). We also include a proof-of-concept implementation of our system in the Idris programming language.

Upper ontologies have traditionally arisen from the approach in which concepts that are common across a set of domains can be axiomatized at a general level. The rationale is that reuse across domains is to be supported through specialization of the general concepts from an upper ontology. Similarly, semantic integration between ontologies is to be achieved through the general concepts they specialize. The TUpper Ontology follows an alternative approach (referred to as the sideways approach) to the conventional upper ontology paradigm. Rather than think of an upper ontology as a monolithic axiomatization centred on a taxonomy, the sideways approach considers an upper ontology to be a modular ontology composed of generic ontologies that cover concepts including those related to time, process, and space. TUpper is therefore composed of a set of generic ontologies, and each generic ontology axiomatizes a particular set of generic concepts (e.g., the classes and relations relevant for time, process, and space). The TUpper Ontology is designed as a top-level ontology that contains modules from the ontologies within existing international standards.

In recent years there has been a resurgence of interest in our community in the shape analysis of 3D objects represented by surface meshes, their voxelized interiors, or surface point clouds. In part, this interest has been stimulated by the increased availability of RGBD cameras, and by applications of computer vision to autonomous driving, medical imaging, and robotics. In these settings, spectral coordinates have shown promise for shape representation due to their ability to incorporate both local and global shape properties in a manner that is qualitatively invariant to isometric transformations. Yet, surprisingly, such coordinates have thus far typically considered only local surface positional or derivative information. In the present article, we propose to equip spectral coordinates with medial (object width) information, so as to enrich them. The key idea is to couple surface points that share a medial ball, via the weights of the adjacency matrix. We develop a spectral feature using this idea, and the algorithms to compute it. The incorporation of object width and medial coupling has direct benefits, as illustrated by our experiments on object classification, object part segmentation, and surface point correspondence.

There has been a constant debate about how to integrate spatial and temporal representation together. Three-dimensionalists believe that objects only have spatial dimensions; thus, they take space and time as two separate domains, so-called ”three-plus-one” dimensional approach. Controversially, four-dimensionalists argue that objects extend on time just as they extend on space, in which space and time is one primitive domain. In this research, we attempt to harmonize both of these views and interlink the two;meanwhile we justify our choices through a set of motivating scenarios. We also present our axiomatization of spatiotemporal regions and their mereotopology using the product order of spatial and temporal mereotopologies.

Humans are excellent at perceiving illusory outlines. We are readily able to complete contours, shapes, scenes, and even unseen objects when provided with images that contain broken fragments of a connected appearance. In vision science, this ability is largely explained by perceptual grouping: a foundational set of processes in human vision that describes how separated elements can be grouped. In this paper, we revisit an algorithm called Stochastic Completion Fields (SCFs) that mechanizes a set of such processes -- good continuity, closure, and proximity -- through contour completion. This paper implements a modernized model of the SCF algorithm, and uses it in an image editing framework where we propose novel methods to complete fragmented contours. We show how the SCF algorithm plausibly mimics results in human perception. We use the SCF completed contours as guides for inpainting, and show that our guides improve the performance of state-of-the-art models. Additionally, we show that the SCF aids in finding edges in high-noise environments. Overall, our described algorithms resemble an important mechanism in the human visual system, and offer a novel framework that modern computer vision models can benefit from.

Although a variety of specialised formalisms have been proposed specifically for enterprise modelling, the use of existing modelling languages has not received as much attention. In this paper, we demonstrate that the systems modelling formalism SysML is in fact not sufficient to act as a standalone language for enterprise modelling. To demonstrate this claim, we show that there are four key enterprise modelling scenarios that cannot be addressed while adhering to SysML semantics: temporal representation, timing and scheduling, collaborations between two or more teams and decision trees .

Following Smith and Gasser’s work on embodied cognition, one can consider a robot as an intelligent agent that interacts with its external environment through sensorimotor activities, such as touching, lifting, standing, sitting, and walking. In this paper we explore the ontologies that are required to represent and reason about robot dynamics. We propose new ontologies for robotic components and poses, including a new nonclassical mereotopology for touch contact. The design of the ontologies is driven by semantic parsing of natural language instructions (e.g. “Lift the box that is beside the chair and place it on the table"), through which we identify the spatial and mereotopological relations among a robot’s components and the external world, as well as the activities that the robot can perform to change these relationships.