相关论文: Mathematics of Domains

Domain generalization (DG) focuses on transferring domain-invariant knowledge from multiple source domains (available at train time) to an, a priori, unseen target domain(s). This requires a class to be expressed in multiple domains for the…

We present an elementary account of mathematical cosmology through a series of important unsolved problems. We introduce the fundamental notion of `a cosmology' and focus on the issue of singularities as a theme unifying many current,…

Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…

We consider minimization problems in the calculus of variations set in a sequence of domains the size of which tends to infinity in certain directions and such that the data only depend on the coordinates in the directions that remain…

We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…

In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it…

We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an…

Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…

A construction of fully abstract typed models for PCF and PCF^+ (i.e., PCF + "parallel conditional function"), respectively, is presented. It is based on general notions of sequential computational strategies and wittingly consistent…

We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…

The Core Data Ontology (CDO) and the Informatics Domain Model represent a transformative approach to computational systems, shifting from traditional node-centric designs to a data-centric paradigm. This paper introduces a framework where…

Inspired by rational canonical forms, we introduce and analyze two decompositions of dynamic programming (DP) problems for systems with linear dynamics. Specifically, we consider both finite and infinite horizon DP problems in which the…

The authors lay the foundations for the study of normal families of holomorphic functions and mappings on an infinite-dimensional normed linear space. Characterizations of normal families, in terms of value distribution, spherical…

The purpose of this paper is to show that functions that derivate the two-variable product function and one of the exponential, trigonometric or hyperbolic functions are also standard derivations. The more general problem considered is to…

Probabilistic powerdomain in domain theory plays an important role in modeling the semantics of nondeterministic functional programming languages with probabilistic choice. In this paper, we extend the notion of powerdomain to directed…

Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…

Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…

In 20th century mathematics, the field of topology, which concerns the properties of geometric objects under continuous transformation, has proved surprisingly useful in application to the study of discrete mathematics, such as…

We introduce a notion of a noncommutative function defined on a domain of $d$-tuples of bounded operators on an infinite dimensional Hilbert space. Inverse and implicit function theorems in this setting are established. When these…

I have argued elsewhere that second order logic provides a foundation for mathematics much in the same way as set theory does, despite the fact that the former is second order and the latter first order, but second order logic is marred by…