Related papers: A Relational Axiomatic Framework for the Foundatio…
This is a detailed and self-contained introduction to the real number system from a categorical perspective. We begin with the categorical definition of the natural numbers, review the Eudoxus theory of ratios as presented in Book V of…
Probabilistic relational models provide a well-established formalism to combine first-order logic and probabilistic models, thereby allowing to represent relationships between objects in a relational domain. At the same time, the field of…
Extending programming languages with stochastic behaviour such as probabilistic choices or random sampling has a long tradition in computer science. A recent development in this direction is a declarative probabilistic programming language,…
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…
We construct a family of globally defined dynamical systems for a nonlinear programming problem, such that: (a) the equilibrium points are the unknown (and sought) critical points of the problem, (b) for every initial condition, the…
This paper connects a vector-based composition model to a formal semantics, the Dependency-based Compositional Semantics (DCS). We show theoretical evidence that the vector compositions in our model conform to the logic of DCS.…
This paper rigorously and concisely defines, in the context of our (Elementary) Mathematical Data Model ((E)MDM), the mathematical concepts of dyadic relation, reflexivity, irreflexivity, symmetry, asymmetry, transitivity, intransitivity,…
Based on the principle of relativity and the postulate on universal invariant constants (c,l), all possible kinematics can be set up with sub-symmetries of the Umov-Weyl-Fock transformations for the inertial motions. Further, in the…
Given a finite and non-empty set $X$ and randomly selected specific functions and relations on $X$, we investigate the existence and non-existence of fixed points and reflexive points, respectively. First, we consider the class of…
In this paper, we propose a fresh perspective on argumentation semantics, to view them as a relational database. It offers encapsulation of the underlying argumentation graph, and allows us to understand argumentation semantics under a…
There are two approaches to computing the one-point functions for sine-Gordon model in infinite volume. One is a bootstrap type procedure based on the reflection relations. Another uses the fermionic basis which was originally found for the…
Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
We introduce a set of eight universal Rules of Inference by which computer programs with known properties (axioms) are transformed into new programs with known properties (theorems). Axioms are presented to formalize a segment of Number…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…
Synchronous languages are now a standard industry tool for critical embedded systems. Designers write high-level specifications by composing streams of values using block diagrams. These languages have been extended with Bayesian reasoning…
We introduce the new notion of epsilon-graded associative algebras which takes its root into the notion of commutation factors introduced in the context of Lie algebras. We define and study the associated notion of epsilon-derivation-based…
New concepts of rough natural number systems are introduced in this research paper from both formal and less formal perspectives. These are used to improve most rough set-theoretical measures in general Rough Set theory (\textsf{RST}) and…
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…