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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…
Software engineers typically interpret the domain description in natural language and translate it into a conceptual model. Three approaches are used in this domain modeling: textual languages, diagrammatic languages, and a mixed based of…
Dynamic Topological Logic ($\mathcal{DTL}$) is a combination of $\mathcal{S}${\em 4}, under its topological interpretation, and the temporal logic $\mathcal{LTL}$ interpreted over the natural numbers. $\mathcal{DTL}$ is used to reason about…
Large language models (LLMs) exhibit failure modes on seemingly trivial tasks. We propose a formalisation of LLM interaction using a deterministic multi-tape Turing machine, where each tape represents a distinct component: input characters,…
Conceptual models as representations of real-world systems are based on diverse techniques in various disciplines but lack a framework that provides multidisciplinary ontological understanding of real-world phenomena. Concurrently, systems…
Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared towards solving and modeling…
We present Diagrammatica, a symbolic computation extension to the HEPTAPOD agentic framework, which enables LLM agents to plan and execute multi-step theoretical calculations. Symbolic computation poses a distinctive reliability challenge…
Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more…
The distribution of human linguistic groups presents a number of interesting and non-trivial patterns. The distributions of the number of speakers per language and the area each group covers follow log-normal distributions, while population…
AlphaGeometry represents a milestone in neuro-symbolic reasoning, yet its architecture faces a log-linear scaling bottleneck within its symbolic deduction engine that limits its efficiency as problem complexity increases. Recent technical…
This paper presents a unified algebraic, topological, and logical framework for electrical one-port networks based on \v{S}are's $m$-theory. Within this formalism, networks are represented by $m$-words (jorbs) over an ordered alphabet,…
Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here we study the…
Defining semantics for UML is a difficult task. Disagreements in the meaning of UML constructs as well as the size of UML are major obstacles. In this report, we describe our approach to define the semantics for UML. Semantics is defined…
In this paper, we discuss how pure mathematics and theoretical physics can be applied to the study of language models. Using set theory and analysis, we formulate mathematically rigorous definitions of language models, and introduce the…
Synchronous languages are now a standard industry tool for critical embedded systems. Designers write high-level specifications by composing streams of values using block diagrams. These languages have been extended with Bayesian reasoning…
Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…
Formal/symbolic semantics can provide canonical, rigid controllability and interpretability to sentence representations due to their \textit{localisation} or \textit{composition} property. How can we deliver such property to the current…
In this report, semantics for Statecharts is defined based on a mathematical model of object systems called "system model". The semantics definition is detailed for UML/P Statecharts, a variant of Statecharts which restricts the use of a…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
The design of complex engineering systems is an often long and articulated process that highly relies on engineers' expertise and professional judgment. As such, the typical pitfalls of activities involving the human factor often manifest…