Related papers: Canonical Selection of Colimits
Limits and colimits of diagrams, defined by maps between sets, are universal constructions fundamental in different mathematical domains and key concepts in theoretical computer science. Its importance in semantic modeling is described by…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
We give a necessary and sufficient condition on a $d$-dimensional affine subspace of $\mathbb{R}^n$ to be characterized by a finite set of patterns which are forbidden to appear in its digitization. This can also be stated in terms of local…
The vision of the Semantic Web (SW) is gradually unfolding and taking shape through a web of linked data, a part of which is built by capturing semantics stored in existing knowledge organization systems (KOS), subject metadata and resource…
Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. Generalizing results and methods from arXiv:1708.06782, we examine set-theoretic problems related to internal sizes and prove several…
We implement a novel representation of model search spaces as diagrams over a category of models, where we have restricted attention to a broad class of models whose structure is presented by \C-sets. (Co)limits in these diagram categories…
Canonical extension of finitary ordered structures such as lattices, posets, proximity lattices, etc., is a certain completion which entirely describes the topological dual of the ordered structure and it does so in a purely algebraic and…
Canonical inference rules and canonical systems are defined in the framework of non-strict single-conclusion sequent systems, in which the succeedents of sequents can be empty. Important properties of this framework are investigated, and a…
Clustering is a common technique for statistical data analysis, which is used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics. Clustering is the process of grouping similar…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
Large language models (LLMs) are increasingly used in group decision-making, but their influence risks fostering conformity and reducing epistemic vigilance. Drawing on the Argumentative Theory of Reasoning, we argue that confirmation bias,…
We show that the category of pastures has arbitrary limits and colimits of diagrams indexed by a small category.
The performance of vision-language models (VLMs), such as CLIP, in visual classification tasks, has been enhanced by leveraging semantic knowledge from large language models (LLMs), including GPT. Recent studies have shown that in zero-shot…
Clustering is a fundamental task in unsupervised learning. The focus of this paper is the Correlation Clustering functional which combines positive and negative affinities between the data points. The contribution of this paper is two fold:…
Safety constraints are crucial to the development of mission-critical systems. The practice of developing software for systems of this type requires reliable methods for identifying and analysing project artefacts. This paper proposes a…
The Distributed Ontology Language (DOL) is currently being standardized within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 3. It aims at providing a unified framework for (1) ontologies formalized in…
Codifying mathematical theories in a proof assistant or computer algebra system is a challenging task, of which the most difficult part is, counterintuitively, structuring definitions. This results in a steep learning curve for new users…
We develop a number of basic concepts in the theory of categories internal to an $\infty$-topos. We discuss adjunctions, limits and colimits as well as Kan extensions for internal categories, and we use these results to prove the universal…
In this work we introduce declarative statistics, a suite of declarative modelling tools for statistical analysis. Statistical constraints represent the key building block of declarative statistics. First, we introduce a range of relevant…
In this paper, we introduce CDL, a software library designed for the analysis of permutations and linear orders subject to various structural restrictions. Prominent examples of these restrictions include pattern avoidance, a topic of…