Related papers: A zonotopic framework for functional abstractions
We introduce the notion of functionally compact sets into the theory of nonlinear generalized functions in the sense of Colombeau. The motivation behind our construction is to transfer, as far as possible, properties enjoyed by standard…
An afinne-invariant view of generating functions of symplectic transformations of an affine symplectic space is discussed. More generally, it works for symmetric symplectic spaces. The note is completely elementary, but it yields some nice…
Scientists often infer abstract procedures from specific instances of problems and use the abstractions to generate new, related instances. For example, programs encoding the formal rules and properties of a system have been useful in…
Modeling worlds and actions under uncertainty is one of the central problems in the framework of decision-theoretic planning. The representation must be general enough to capture real-world problems but at the same time it must provide a…
We state and prove a simple Theorem that allows one to generate invariant quantities in Metric-Affine Geometry, under a given transformation of the affine connection. We start by a general functional of the metric and the connection and…
The postulates of comprehension and extensionality in set theory are based on an inversion principle connecting set-theoretic abstraction and the property of having a member. An exactly analogous inversion principle connects functional…
Categorical semantics of type theories are often characterized as structure-preserving functors. This is because in category theory both the syntax and the domain of interpretation are uniformly treated as structured categories, so that we…
Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
In this paper, we unify the study of classical and non-classical algebra-valued models of set theory, by studying variations of the interpretation functions for identity and set-membership. Although, these variations coincide with the…
Among the most general structures extending the framework by Dung are the abstract dialectical frameworks (ADFs). They come equipped with various types of semantics, with the most prominent - the labeling-based one - analyzed in the context…
This article shows a correspondence between abstract interpretation of imperative programs and the refinement calculus: in the refinement calculus, an abstract interpretation of a program is a specification which is a function. This…
In this report proofs are presented for a method for abstracting continuous dynamical systems by timed automata. The method is based on partitioning the state space of dynamical systems with invariant sets, which form cells representing…
We show how geometric methods from the general theory of fractal dimensions and iterated function systems can be deployed to study symbolic dynamics in the zero entropy regime. More precisely, we establish a dimensional characterization of…
A theory of recursive definitions has been mechanized in Isabelle's Zermelo-Fraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
One of the most prominent tools for abstract argumentation is the Dung's framework, AF for short. It is accompanied by a variety of semantics including grounded, complete, preferred and stable. Although powerful, AFs have their…
We describe a type system for a synchronous pi-calculus formalising the notion of affine usage in signal-based communication. In particular, we identify a limited number of usages that preserve affinity and that can be composed. As a main…
In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted…
Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.