Related papers: Domains, Information Frames, Rough Sets: An Equiva…
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…
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…
Representations of domains mean in a general way representing a domain as a suitable family endowed with set-inclusion order of some mathematical structures. In this paper, representations of domains via CF-approximation spaces are…
Closure space has proven to be a useful tool to restructure lattices and various order structures.This paper aims to provide a novel approach to characterizing some important kinds of continuous domains by means of closure spaces. By…
Formal Concept Analysis has proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notions of attribute continuous formal context and continuous formal concept are introduced by…
Information systems with witnesses have been introduced in [D. Spreen. Generalised information systems capture L-domains. arXiv:1610.02260v2] as a logic-style representation of L-domains: The category of such information systems with…
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…
Basically information means selection within a domain (value or definition set) of possibilities. For objectifiable, comparable and precise information the domain should be the same for all. Therefore the global (online) definition of the…
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…
Web spaces, wide web spaces and worldwide web spaces (alias C-spaces) provide useful generalizations of continuous domains. We present new characterizations of such spaces and their patch spaces, obtained by joining the original topology…
Many real life optimization problems contain both hard and soft constraints, as well as qualitative conditional preferences. However, there is no single formalism to specify all three kinds of information. We therefore propose a framework,…
This monograph is an ongoing revision of "Lectures On A Mathematical Theory of Computation" by Dana Scott. Scott's monograph uses a formulation of domains called neighborhood systems in which finite elements are selected subsets of a master…
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…
Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched…
In this paper, concepts of (topological) FS-approximation spaces are introduced. Representations of FS-domains and BF-domains via (topological) FS-approximation spaces are considered. It is proved that the collection of CF-closed sets in an…
Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of $T_0$ spaces instead of restricting to posets. In this paper, we respond to this calling…
A concept of "evolving categories" is suggested to build a simple, scalable, mathematically consistent framework for representing in uniform way both data and algorithms. A state machine for executing algorithms becomes clear, rich and…
Scientific knowledge is constantly subject to a variety of changes due to new discoveries, alternative interpretations, and fresh perspectives. Understanding uncertainties associated with various stages of scientific inquiries is an…
In this paper, facts existing in different domains are explored, which are comparable by their end result. Properties of various domains and the facts that are part of such a unit are also presented, examples of comparison and methods of…
This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames $\mathcal{F} = \{f_i\}_{i \in I}$ and $\mathcal{E} =…