Related papers: The Mathematical Syntax of Architectures
Mathematical models are increasingly used in both academia and the pharmaceutical industry to understand how phenotypes emerge from systems of molecular interactions. However, their current construction as monolithic sets of equations…
Today's ubiquitous computing ecosystem involves various kinds of hardware and software technologies for different computing environments. As the result, computing systems can be seen as integrated system of hardware and software systems.…
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…
The FAIR Principles aim to make data and knowledge Findable, Accessible, Interoperable, and Reusable, yet current digital infrastructures often lack a unifying semantic framework that bridges human cognition and machine-actionability. In…
Algorithms like those for differentiating functional expressions manipulate the syntactic structure of mathematical expressions in a mathematically meaningful way. A formalization of such an algorithm should include a specification of its…
There are multiple ways to formalise the metatheory of type theory. For some purposes, it is enough to consider specific models of a type theory, but sometimes it is necessary to refer to the syntax, for example in proofs of canonicity and…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
Neural Architecture Search (NAS) enabled the discovery of state-of-the-art architectures in many domains. However, the success of NAS depends on the definition of the search space. Current search spaces are defined as a static sequence of…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
Over the past two decades, the Internet of Things (IoT) has become an underlying concept to a variety of solutions and technologies that it is now hardly possible to enumerate and describe all of them. The concept behind the Internet of…
Coherence is a central issue in category theory and multicategory theory, ensuring that formally distinct compositions of morphisms, such as tensor reorderings or diagrammatic rewiring, represent the same underlying transformation. In…
In the age of artificial intelligence, architectural practice faces a paradox of immense potential and creeping standardization. As humans are increasingly relying on AI-generated outputs, architecture risks becoming a spectacle of…
The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…
The cloud is a new paradigm that is paving the way for new approaches and standards. The architectural styles are evolving in response to the cloud's requirements. In recent years, microservices have emerged as the preferred architectural…
We prove a theorem stating that any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous. We then show that when compositional semantics is…
Microservices have been a key architectural approach for over a decade, transforming system design by promoting decentralization and allowing development teams to work independently on specific microservices. While loosely coupled…
Large language models (LLMs) offer a new empirical setting in which long-standing theories of linguistic meaning can be examined. This paper contrasts two broad approaches: social constructivist accounts associated with language games, and…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
Event-driven architecture has been widely adopted in the software industry, emerging as an alternative to modular development to support rapid adaptations of constantly evolving systems. However, little is known about the effects of…
While a great effort has concerned the development of fully integrated modular understanding systems, few researches have focused on the problem of unifying existing linguistic formalisms with cognitive processing models. The Situated…