Related papers: Category-Theoretic Foundations of "STCLang: State …
Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes,…
We introduce a hierarchical categorical framework for Schema-Based Learning (SBL) structured across four interconnected levels. At the schema level, a free multicategory $Sch_{syn}$ encodes fundamental schemas and transformations. An…
This paper begins the discussion of how the Information Flow Framework can be used to provide a principled foundation for the metalevel (or structural level) of the Standard Upper Ontology (SUO). This SUO structural level can be used as a…
Functional languages as input specifications for High-Level Synthesis (HLS) tools allow to specify data dependencies but do not contain a notion of time nor execution order. In this paper, we propose a method to add this notion to the…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
A number of domain specific languages, such as circuits or data-science workflows, are best expressed as diagrams of boxes connected by wires. Unfortunately, functional languages have traditionally been ill-equipped to embed this sort of…
In previous work, we have introduced functional strategies, that is, first-class generic functions that can traverse into terms of any type while mixing uniform and type-specific behaviour. In the present paper, we give a detailed…
This paper describes the overlay protocol Chord using the formalism of Abstract State Machines. The formalization concerns Chord actions that maintain ring topology and manipulate distributed keys. We define a class of runs and prove the…
Classification of entanglement is an important problem in Quantum Resource Theory. In this paper we discuss an embedding of this problem in the context of Topological Quantum Field Theories (TQFT). This approach allows classifying…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the…
The ability to extract compact, meaningful summaries from large-scale and multimodal data is critical for numerous applications, ranging from video analytics to medical reports. Prior methods in cross-modal summarization have often suffered…
The sequential process of conceptualization and instantiation is essential to generalizable commonsense reasoning as it allows the application of existing knowledge to unfamiliar scenarios. However, existing works tend to undervalue the…
This work establishes a robust mathematical foundation for compositional System Dynamics modeling, leveraging category theory to formalize and enhance the representation, analysis, and composition of system models. Here, System Dynamics…
Tangent category theory is a well-established categorical framework for differential geometry. A long list of fundamental geometric constructions, such as the tangent bundle functor, vector fields, Euclidean spaces, and vector bundles have…
Reasoning about complex networks has in recent years become an important topic of study due to its many applications: the adoption of commercial products, spread of disease, the diffusion of an idea, etc. In this paper, we present the…
Rewriting logic is naturally concurrent: several subterms of the state term can be rewritten simultaneously. But state terms are global, which makes compositionality difficult to achieve. Compositionality here means being able to decompose…
Category computation theory deals with a web-based systemic processing that underlies the morphic webs, which constitute the basis of categorial logical calculus. It is proven that, for these structures, algorithmically incompressible…
Dynamic logic is a powerful framework for reasoning about imperative programs. An extension with a concurrent operator [18] was introduced to formalise programs running in parallel. In other direction, other authors proposed a systematic…
Text embeddings from Large Language Models (LLMs) have become foundational for numerous applications. However, these models typically operate on raw text, overlooking the rich structural information, such as hyperlinks or citations, that…