Related papers: Domain Theory: An Introduction
In domain theory every finite computable object can be represented by a single mathematical object instead of a set of objects, using the notion of finitary-basis. In this article we report on our effort to formalize domain theory in Coq in…
Two groups of naturally arising questions in the mathematical theory of domains for denotational semantics are addressed. Domains are equipped with Scott topology and represent data types. Scott continuous functions represent computable…
A generalisation of Scott's information systems \cite{sco82} is presented that captures exactly all L-domains. The global consistency predicate in Scott's definition is relativised in such a way that there is a consistency predicate for…
We give multiple descriptions of a topological universe of finitary sets, which can be seen as a natural limit completion of the hereditarily finite sets. This universe is characterized as a metric completion of the hereditarily finite…
We are interested in proving input-output properties of functions that handle infinite data such as streams or non-wellfounded trees. We provide a finitary refinement type system which is (sound and) complete for Scott-open properties…
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…
We present old and new characterizations of core spaces, alias worldwide web spaces, originally defined by the existence of supercompact neighborhood bases. The patch spaces of core spaces, obtained by joining the original topology with a…
A generalization of Scott's information systems~\cite{sco82} is presented that captures exactly all continuous domains. The global consistency predicate in Scott's definition is relativized. Now, for every atomic statement, there is a…
The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: - Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for…
Domain theory has its origins in Mathematics and Theoretical Computer Science. Mathematically it combines order and topology. Its central concepts have their origin in the idea of approximating ideal objects by their relatively finite or,…
Domain theory has a long history of applications in theoretical computer science and mathematics. In this article, we explore the relation of domain theory to probability theory and stochastic processes. The goal is to establish a theory in…
Classically domain theory is a rigourous mathematical structure to describe denotational semantics for programming languages and to study the computability of partial functions. Recently, the application of domain theory has also been…
In \cite{sp25}, continuous information frames were introduced that capture exactly all continuous domains. They are obtained from the information frames considered in \cite{sp21} by omitting the conservativity requirement. Information…
The purpose of this work is to find out how different library classification systems and linguistic ontologies arrange a particular domain of interest and what are the limitations for information retrieval. We use knowledge representation…
Scott's information systems provide a categorically equivalent, intensional description of Scott domains and continuous functions. Following a well established pattern in denotational semantics, we define a linear version of information…
Knowledge graphs store large numbers of relations efficiently, but they remain weak at representing a quieter difficulty: the meaning of a concept often shifts with the domain in which it is used. A triple such as Apple, instance-of,…
The so-called topos approach provides a radical reformulation of quantum theory. Structurally, quantum theory in the topos formulation is very similar to classical physics. There is a state object, analogous to the state space of a…
We discuss an infinitary refinement type system for input-output temporal specifications of functions that handle infinite objects like streams or infinite trees. Our system is based on a reformulation of Bonsangue and Kok's infinitary…
In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a…
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…