Related papers: Domain Theory for Modeling OOP: A Summary

We survey the prospects for an Information Dynamics which can serve as the basis for a fundamental theory of information, incorporating qualitative and structural as well as quantitative aspects. We motivate our discussion with some basic…

Computation is commonly defined as the execution of abstract algorithms over symbolic representations, with physical systems treated as substrates that realise predefined operations. While effective for engineered machines, this separation…

The present work is dedicated to searching parameters, alternative to entropy, applicable for description of highly organized systems. The general concept has been offered, in which the system complexity and order are functions of the order…

The polarized SILL programming language uniformly integrates functional programming and session-typed message-passing concurrency. It supports general recursion, asynchronous and synchronous communication, and higher-order programs that…

Function is defined as the ensemble of tasks that enable the product to complete the designed purpose. Functional tools, such as functional modeling, offer decision guidance in the early phase of product design, where explicit design…

Throughout the history of functional programming, recursion has emerged as a natural method for describing loops in programs. However, there does often exist a substantial cognitive distance between the recursive definition and the simplest…

While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…

Neural operators extend data-driven models to map between infinite-dimensional functional spaces. These models have successfully solved continuous dynamical systems represented by differential equations, viz weather forecasting, fluid flow,…

From logical reasoning to mental simulation, biological and artificial neural systems possess an incredible capacity for computation. Such neural computers offer a fundamentally novel computing paradigm by representing data continuously and…

We propose an axiomatic foundation of mathematics based on the finite sequence as the foundational concept, rather than based on logic and set, as in set theory, or based on type as in dependent type theories. Finite sequences lead to 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…

We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…

Theory-guided machine learning has demonstrated that including authentic domain knowledge directly into model design improves performance, sample efficiency and out-of-distribution generalisation. Yet the process by which a formal domain…

Decomposing the domain of a function into parts has many uses in mathematics. A domain may naturally be a union of pieces, a function may be defined by cases, or different boundary conditions may hold on different regions. For any…

We develop a domain-theoretic framework for imprecise probability reasoning and inference on general topological spaces with a countably based continuous lattice of open sets. We address two distinct forms of uncertainty: partial or…

Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…

Theory revision integrates inductive learning and background knowledge by combining training examples with a coarse domain theory to produce a more accurate theory. There are two challenges that theory revision and other theory-guided…

During the last few years, a new approach to language processing has started to emerge, which has become known under various labels such as "data-oriented parsing", "corpus-based interpretation", and "tree-bank grammar" (cf. van den Berg et…

Pattern-matching programming is an example of a rule-based programming style developed in functional languages. This programming style is intensively used in dialects of ML but is restricted to algebraic data-types. This restriction limits…

Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…