Related papers: Types, equations, dimensions and the Pi theorem
Analysis of (partial) groundness is an important application of abstract interpretation. There are several proposals for improving the precision of such an analysis by exploiting type information, icluding our own work with Hill and King,…
We propose an axiomatic approach to the concept of an intrinsic dimension of a dataset, based on a viewpoint of geometry of high-dimensional structures. Our first axiom postulates that high values of dimension be indicative of the presence…
One-dimensional quantum optical models usually rest on the intuition of large scale separation or frozen dynamics associated with the different spatial dimensions, for example when studying quasi one-dimensional atomic dynamics, potentially…
Type systems as a way to control or analyze programs have been largely studied in the context of functional programming languages. Some of those work allow to extract from a typing derivation for a program a complexity bound on this…
Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can…
Free categorical constructions characterise quantum computing as the combination of two copies of a reversible classical model, glued by the complementarity equations of classical structures. This recipe effectively constructs a…
Humans continuously adapt their style and language to a variety of domains. However, a reliable definition of `domain' has eluded researchers thus far. Additionally, the notion of discrete domains stands in contrast to the multiplicity of…
Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…
String theory in d dimensions has n+1=11-d parameters that may be thought of as being inherited from the geometry of an n+1 torus which may be used to construct the theory using dimensional reduction from eleven dimensions. We give the…
Important variables of processes are often categorical, i.e. names or labels representing, e.g. categories of inputs, or types of reactors or a sequence of steps. In this work, we use Natural Language Processing Models to derive embeddings…
This paper explores ideas and provides a potential roadmap for the development and evaluation of physics-specific large-scale AI models, which we call Large Physics Models (LPMs). These models, based on foundation models such as Large…
A general theory of programs, programming and programming languages built up from a few concepts of elementary set theory. Derives, as theorems, properties treated as axioms by classic approaches to programming. Covers sequential and…
Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…
A central aim of theoretical physics is to account for the structure of matter at the most elementary level as underlying the Standard Model of particle physics, and ideally also as a basis for a substantial dark sector, as distributed in…
This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular…
In this paper we propose an approach to reasoning about properties of imperative programs. We assume in this context that the meanings of program constructs are described using rules in the natural semantics style with the additional…
Semantic parsing has made significant progress, but most current semantic parsers are extremely slow (CKY-based) and rather primitive in representation. We introduce three new techniques to tackle these problems. First, we design the first…
In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be…
Dimension theory lies at the heart of fractal geometry and concerns the rigorous quantification of how large a subset of a metric space is. There are many notions of dimension to consider, and part of the richness of the subject is in…
Relevance is an underlying concept in the field of Information Science and Retrieval. It is a cognitive notion consisting of several different criteria or dimensions. Theoretical models of relevance allude to interdependence between these…