Related papers: The Mathematical Syntax of Architectures

Communication between practitioners is essential for the system's quality in the DevOps context. To improve this communication, practitioners often use informal diagrams to represent the components of a system. However, as systems evolve,…

Homotopy type theory is a new branch of mathematics, based on a recently discovered connection between homotopy theory and type theory, which brings new ideas into the very foundation of mathematics. On the one hand, Voevodsky's subtle and…

This article explores a generic framework of well-typed and well-scoped syntaxes, with a signature-axiom approach resembling traditional abstract algebra. The boilerplate code needed in defining operations on syntaxes is identified and…

Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…

Classic problem-space theory models problem solving as a navigation through a structured space of states, operators, goals, and constraints. Systems Engineering (SE) employs analogous constructs (functional analysis, operational analysis,…

In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…

The fidelity and utility of synthetic network traffic are critically compromised by architectural mismatch across heterogeneous network datasets and prevalent scalability failure. This study addresses this challenge by establishing an…

Sharing, reusing, and synthesizing knowledge is central to the research process, both individually, and with others. These core functions are not supported by our formal scholarly publishing infrastructure: instead of the smooth functioning…

Linear Software Models is a systematic effort to formulate a theory of software systems neatly based upon standard mathematics, viz. linear algebra. It has appeared in a series of papers dealing with various aspects of the theory. But one…

Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…

In previous work ("From signatures to monads in UniMath"), we described a category-theoretic construction of abstract syntax from a signature, mechanized in the UniMath library based on the Coq proof assistant. In the present work, we…

The most important architectural problem in AI is not the size of the model but the absence of a layer that carries forward what the model has come to understand. Sessions end. Context windows fill. Memory APIs return flat facts that the…

Enterprise Architecture defines the overall form and function of systems across an enterprise involving the stakeholders and providing a framework, standards and guidelines for project-specific architectures. Project-specific Architecture…

Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…

The recent trend in mathematics is towards a framework of abstract mathematical objects, rather than the more concrete approach of explicitly defining elements which objects were thought to consist of. A natural question to raise is whether…

The rules in a shape grammar apply in terms of embedding to take advantage of the parts that emerge visually in the appearance of shapes. While the shapes are kept unanalyzed as a computation moves forward, part-structures for shapes can be…

There is growing acknowledgement within the software engineering community that a theory of software development is needed to integrate the myriad methodologies that are currently popular, some of which are based on opposing perspectives.…

A new model of symbol grounding is presented, in which the structures of natural language, logical semantics, perception and action are represented categorically, and symbol grounding is modeled via the composition of morphisms between the…

In dynamic architectures, component activation and connections between components may vary over time. With the emergence of mobile computing such architectures became increasingly important and several techniques emerged to support in their…

Categorical semantics of type theories are often characterized as structure-preserving functors. This is because in category theory both the syntax and the domain of interpretation are uniformly treated as structured categories, so that we…