(364) Proposal to provide a more direct definition of the term "gathering"

Taxon ◽  
2016 ◽  
Vol 65 (5) ◽  
pp. 1186-1186
Author(s):  
John H. Wiersema
Keyword(s):  
Direct Definition ◽  
Definition Of

Cubical Agda: A dependently typed programming language with univalence and higher inductive types

2021 ◽  
Vol 31 ◽  
Author(s):  
ANDREA VEZZOSI ◽  
ANDERS MÖRTBERG ◽  
ANDREAS ABEL
Keyword(s):  
Programming Language ◽  
Type Theory ◽  
Type Checking ◽  
Dependent Type Theory ◽  
Wide Range ◽  
General Schema ◽  
Direct Definition ◽  
Inductive Types ◽  
Definition Of ◽  
Cubical Type Theory

Abstract Proof assistants based on dependent type theory provide expressive languages for both programming and proving within the same system. However, all of the major implementations lack powerful extensionality principles for reasoning about equality, such as function and propositional extensionality. These principles are typically added axiomatically which disrupts the constructive properties of these systems. Cubical type theory provides a solution by giving computational meaning to Homotopy Type Theory and Univalent Foundations, in particular to the univalence axiom and higher inductive types (HITs). This paper describes an extension of the dependently typed functional programming language Agda with cubical primitives, making it into a full-blown proof assistant with native support for univalence and a general schema of HITs. These new primitives allow the direct definition of function and propositional extensionality as well as quotient types, all with computational content. Additionally, thanks also to copatterns, bisimilarity is equivalent to equality for coinductive types. The adoption of cubical type theory extends Agda with support for a wide range of extensionality principles, without sacrificing type checking and constructivity.

Tarski

Truth ◽  
2011 ◽  
Author(s):  
Alexis G. Burgess ◽  
John P. Burgess
Keyword(s):  
Mathematical Logic ◽  
Model Theory ◽  
The State ◽  
Truth Predicate ◽  
Object Language ◽  
French And English ◽  
Direct Definition ◽  
Definition Of ◽  
Basic Features ◽  
Self Reference

This chapter offers a simplified account of the most basic features of Alfred Tarski's model theory. Tarski foresaw important applications for a notion of truth in mathematics, but also saw that mathematicians were suspicious of that notion, and rightly so given the state of understanding of it circa 1930. In a series of papers in Polish, German, French, and English from the 1930s onward, Tarski attempted to rehabilitate the notion for use in mathematics, and his efforts had by the 1950s resulted in the creation of a branch of mathematical logic known as model theory. The chapter first considers Tarski's notion of truth, which he calls “semantic” truth, before discussing his views on object language and metalanguage, recursive versus direct definition of the truth predicate, and self-reference.

Realisability semantics of parametric polymorphism, general references and recursive types

2010 ◽  
Vol 20 (4) ◽  
pp. 655-703 ◽  
Author(s):  
LARS BIRKEDAL ◽  
KRISTIAN STØVRING ◽  
JACOB THAMSBORG
Keyword(s):  
Metric Spaces ◽  
Logical Relation ◽  
Data Types ◽  
General Reference ◽  
New Approach ◽  
Parametric Polymorphism ◽  
Abstract Data ◽  
Direct Definition ◽  
Semantic Types ◽  
Definition Of

We present a realisability model for a call-by-value, higher-order programming language with parametric polymorphism, general first-class references, and recursive types. The main novelty is a relational interpretation of open types that include general reference types. The interpretation uses a new approach to modelling references.The universe of semantic types consists of world-indexed families of logical relations over a universal predomain. In order to model general reference types, worlds are finite maps from locations to semantic types: this introduces a circularity between semantic types and worlds that precludes a direct definition of either. Our solution is to solve a recursive equation in an appropriate category of metric spaces. In effect, types are interpreted using a Kripke logical relation over a recursively defined set of worlds.We illustrate how the model can be used to prove simple equivalences between different implementations of imperative abstract data types.

scholarly journals ESSENCE OF THE SERVICE CATEGORY IN FORENSIC MERCHANDISING

2020 ◽  
Vol 2 ◽  
pp. 69-76
Author(s):  
I. Petrova ◽  
O. Dontsova
Keyword(s):  
Economic Value ◽  
Service Work ◽  
Structural Elements ◽  
Commercial Activity ◽  
Service Category ◽  
Direct Definition ◽  
Definition Of ◽  
Different Sources ◽  
Essential Service

The article states that market of services, as a field of economic activity, plays the role of a leading sector of the national economy is not without certain problems, among which was the possibility of evaluating the service within the forensic merchandising. It is noted that researchers of the concept of service paid attention to its direct definition, description of the characteristics inherent in services and identify differences between the concepts: Goods, service, work. It is established the essence of the concept of service remains debatable and insufficiently researched regarding its application in forensic merchandising. In view of this, various structural elements of the concept of service were systematized into a single holistic definition by studying scientific approaches, terminological analysis and refining the definitions of this concept from different sources. It is established that uncertainty of services is that they are processes, not material objects and do not fall under the traditional definition of goods; identified a number of properties that distinguish services from tangible goods, and identified specific features of intangible services. It is emphasized that researching on category essence of service in forensic merchandising, one cannot ignore the interpretation of this term by legislators and scholars. Analysis of the service definition in regulations has established that the generalizing concept of service for these acts is a service as an action that has a certain beneficial effect, i.e. has benefits for consumer. Scientists argue that the service usually is an intangible product, process, and ownership of it for its sale to the consumer does not arise; ownership may arise as a result of the provision of the service. The essential service characteristic is defined by scientists as economic value, which makes it an object of commercial activity, a subject of trade and an object of purchase and sale; it turns it into an economic good. It is established that service concept is most often associated with the action or activity of the service provider aimed at meeting the needs of the consumer and is realized at the time of its provision.

THE RENNER MONOIDS AND CELL DECOMPOSITIONS OF THE SYMPLECTIC ALGEBRAIC MONOIDS

2003 ◽  
Vol 13 (02) ◽  
pp. 111-132 ◽  
Author(s):  
ZHENHENG LI ◽  
LEX E. RENNER
Keyword(s):  
Cross Section ◽  
Borel Subgroup ◽  
Unit Group ◽  
Admissible Sets ◽  
Cell Decompositions ◽  
A Cell ◽  
Direct Definition ◽  
The Cross ◽  
Definition Of ◽  
Renner Monoid

In this paper we explicitly determine the Renner monoid ℛ and the cross section lattice Λ of the symplectic algebraic monoid MSpn in terms of the Weyl group and the concept of admissible sets; it turns out that ℛ is a submonoid of ℛn, the Renner monoid of the whole matrix monoid Mn, and that Λ is a sublattice of Λn, the cross section lattice of Mn. Cell decompositions in algebraic geometry are usually obtained by the method of [1]. We give a more direct definition of cells for MSpn in terms of the B × B-orbits, where B is a Borel subgroup of the unit group G of MSpn. Each cell turns out to be the intersection of MSpn with a cell of Mn. We also show how to obtain these cells using a carefully chosen one parameter subgroup.

scholarly journals Boundary Conditions that Remove Certain Ultraviolet Divergences

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 577
Author(s):  
Roderich Tumulka
Keyword(s):  
Boundary Condition ◽  
Wave Function ◽  
Boundary Conditions ◽  
Particle Creation ◽  
Quantum Field ◽  
Interior Boundary ◽  
Direct Definition ◽  
Definition Of ◽  
Particle Creation And Annihilation ◽  
Interior Boundary Conditions

In quantum field theory, Hamiltonians contain particle creation and annihilation terms that are usually ultraviolet (UV) divergent. It is well known that these divergences can sometimes be removed by adding counter-terms and by taking limits in which a UV cutoff tends toward infinity. Here, I review a novel way of removing UV divergences: by imposing a type of boundary condition on the wave function. These conditions, called interior-boundary conditions (IBCs), relate the values of the wave function at two configurations linked by the creation or annihilation of a particle. They allow for a direct definition of the Hamiltonian without renormalization or limiting procedures. In the last section, I review another boundary condition that serves to determine the probability distribution of detection times and places on a time-like 3-surface.

Decision Models in the Design of Adaptive Educational Hypermedia Systems

2012 ◽  
pp. 1-18 ◽  
Author(s):  
Demetrios G Sampson ◽  
Pythagoras Karampiperis
Keyword(s):  
Performance Evaluation ◽  
Decision Function ◽  
Decision Models ◽  
Rule Sets ◽  
Direct Definition ◽  
Adaptation Rules ◽  
Adaptation Decision ◽  
Definition Of ◽  
Adaptation Model ◽  
Educational Hypermedia

Several efforts have been reported in literature aiming to support the Adaptation Model (AM) design in Adaptive Educational Hypermedia Systems (AEHS) with either guidance for the direct definition of adaptation rules or semi-automated mechanisms that generate the AM through the implicit definition of such rules. The main drawback of the direct definition of adaptation rules is that there can be cases during the run-time execution of AEHS where no adaptation decision can be made, due to insufficiency and/or inconsistency of the pre-defined adaptation rule sets. The goal of the semi-automated, decision-based approaches is to generate a continuous decision function that estimates the desired AEHS response, aiming to overcome the above mentioned problem. However, such approaches still miss a commonly accepted framework for evaluating their performance. In this chapter, we review the design approaches for the definition of the AM in AEHS and discuss a set of performance evaluation metrics proposed by the literature for validating the use of decision-based approaches.

Sign in / Sign up

Export Citation Format

Share Document