Related papers: Non-negative Rational Semantic Numeration Systems
The foundational concepts of semantic numeration systems theory are briefly outlined. The action of cardinal semantic operators unfolds over a set of cardinal abstract entities belonging to the cardinal semantic multeity. The cardinal…
This work is the first to propose the concept of a semantic numeration system (SNS) as a certain class of context-based numeration methods. The development of the SNS concept required the introduction of fundamentally new concepts such as a…
The concept of fuzzy cardinal semantic transformation as a basis for creating fuzzy semantic numeration systems is introduced in this work. Both fuzziness of the initial data - cardinals of abstract entities - and fuzziness of the…
The notion of a k-automatic set of integers is well-studied. We develop a new notion - the k-automatic set of rational numbers - and prove basic properties of these sets, including closure properties and decidability.
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
A binary representation of complex rational numbers and their arithmetic is described that is not based on qubits. It takes account of the fact that $0s$ in a qubit string do not contribute to the value of a number. They serve only as place…
The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…
Nominal sets provide a foundation for reasoning about names. They are used primarily in syntax with binders, but also, e.g., to model automata over infinite alphabets. In this paper, nominal sets are related to nominal renaming sets, which…
Gradual semantics with abstract argumentation provide each argument with a score reflecting its acceptability, i.e. how "much" it is attacked by other arguments. Many different gradual semantics have been proposed in the literature, each…
The notions of real and user cardinality of a sign are introduced. Rank distributions can be extended to arbitrary sign objects, i.e., semiotic systems. The dynamics of the distribution of consumer durables, such as automobiles, is studied.
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
It is known that any rational abstract numeration system is faithfully, and effectively, represented by an N-rational series. A simple proof of this result is given which yields a representation of this series which in turn allows a simple…
Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…
For building question answering systems and natural language interfaces, semantic parsing has emerged as an important and powerful paradigm. Semantic parsers map natural language into logical forms, the classic representation for many…
In this paper, we further develop the framework of Modular Systems that lays model-theoretic foundations for combining different declarative languages, agents and solvers. We introduce a multi-language logic of modular systems. We define…
Modern answer set programming solvers such as CLINGO support advanced language constructs that improve the expressivity and conciseness of logic programs. Conditional literals are one such construct. They form "subformulas" that behave as…
This contribution deals with the creation of numerical models for the simulation of the dynamic characteristics of fractional-order control systems and their comparison with analytical models. We give the results of the comparison of…
We propose general principles for semantic networks allowing them to be implemented as dynamical neural networks. Major features of our scheme include: (a) the interpretation that each node in a network stands for a bound integration of the…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…