Related papers: Domains, Information Frames, Rough Sets: An Equiva…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
Intelligent systems must deploy internal representations that are simultaneously structured -- to support broad generalization -- and selective -- to preserve input identity. We expose a fundamental limit on this tradeoff. For any model…
This paper introduces a declarative framework to specify and reason about distributions of data over computing nodes in a distributed setting. More specifically, it proposes distribution constraints which are tuple and equality generating…
In many combinatorial problems one may need to model the diversity or similarity of assignments in a solution. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this…
Tarski's semantic definition of truth is the composition of its extensional and intensional aspects. Abstract satisfaction, the core of the semantic definition of truth, is the basis for the theory of institutions (Goguen and Burstall). The…
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive…
Domain adaptation of embedding models, updating a generic embedding to the language of a specific domain, is a proven technique for domains that have insufficient data to train an effective model from scratch. Chemistry publications is one…
In this paper we generalize the fundamental equation of information to the symmetric cone domain and find general solution under the assumption of continuity of respective functions.
In this paper we study loops, neardomains and nearfields from a categorical point of view. By choosing the right kind of morphisms, we can show that the category of neardomains is equivalent to the category of sharply 2-transitive groups.…
In this article we present a new modelling framework for structured concepts using a category-theoretic generalisation of conceptual spaces, and show how the conceptual representations can be learned automatically from data, using two very…
Given a set $F$ of $n$ positive functions over a ground set $X$, we consider the problem of computing $x^*$ that minimizes the expression $\sum_{f\in F}f(x)$, over $x\in X$. A typical application is \emph{shape fitting}, where we wish to…
Semantic text similarity plays an important role in software engineering tasks in which engineers are requested to clarify the semantics of descriptive labels (e.g., business terms, table column names) that are often consists of too short…
The paper introduces a novel framework based on category theory to enhance the explainability of artificial intelligence systems, particularly focusing on word embeddings. Key topics include the construction of categories $\mathcal{L}_T$…
One of the consequences of the Compactness Principle in structural Ramsey theory is that the small Ramsey degrees cannot exceed the corresponding big Ramsey degrees, thereby justifying the choice of adjectives. However, it is unclear what…
Strong equivalence between knowledge bases ensures the possibility of replacing one with the other without affecting reasoning outcomes, in any given context. This makes it a crucial property in nonmonotonic formalisms. In particular, the…
To prove presence of chaos for fractals, a new mathematical concept of abstract similarity is introduced. As an example, the space of symbolic strings on a finite number of symbols is proved to possess the property. Moreover, Sierpinski…
It has been argued that semantic categories across languages reflect pressure for efficient communication. Recently, this idea has been cast in terms of a general information-theoretic principle of efficiency, the Information Bottleneck…
Strong Scott topology introduced by X. Xu and D. Zhao is a kind of new topology which is finer than upper topology and coarser than Scott topology. Inspired by the topological characterizations of continuous domains and hypercontinuous…
Motivated by questions from program transformations, eight notions of isomorphisms between term rewriting systems are defined, analysed, and classified. The notions include global isomorphisms, where the renaming of variables and function…
The use of semantic technologies is gaining significant traction in science communication with a wide array of applications in disciplines including the Life Sciences, Computer Science, and the Social Sciences. Languages like RDF, OWL, and…