存在与变化:现实操作形式主义的基础

Diederik Aerts
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引用次数: 51

摘要

本文的目的是通过实体的状态、上下文和属性来表示实体的一般描述。我们想要描述的实体不一定是一个物理实体,也可以是一个更抽象的实体,例如一个概念,或者一件文化制品,或者一个人的思想,等等。这意味着我们的目标是非常一般的描述。情境对实体状态的影响起着根本性的作用,这意味着我们的方法本质上是情境性的。该方法受到公理量子力学中发展起来的数学形式化的启发,其中对特定类型的量子上下文进行了建模。然而,因为一般情况下状态也会影响环境——这在量子力学中不是这样的——我们需要一个比这里使用的更一般的设置。我们将上下文作为一个基本概念,这使得统一“动态变化”和“测量影响下的变化”成为可能,这使得我们的方法也比传统的量子公理方法更普遍、更强大。因此,实验(或测量)是作为一种特定的背景引入的。在数学上,我们引入状态上下文属性系统作为结构,通过实体的状态、上下文和属性来描述实体。我们也从一开始就努力到一个分类设置,并从流变协方差原理推导出状态上下文属性系统之间的态射。我们引入范畴SCOP,将状态、上下文、属性系统作为元素,将从流变协方差原理导出的态射作为元素。引入属性完备性和状态完备性,研究了形式主义的运算基础
本文章由计算机程序翻译,如有差异,请以英文原文为准。
BEING AND CHANGE: FOUNDATIONS OF A REALISTIC OPERATIONAL FORMALISM
The aim of this article is to represent the general description of an entity by means of its states, contexts and properties. The entity that we want to describe does not necessarily have to be a physical entity, but can also be an entity of a more abstract nature, for example a concept, or a cultural artifact, or the mind of a person, etc..., which means that we aim at very general description. The effect that a context has on the state of the entity plays a fundamental role, which means that our approach is intrinsically contextual. The approach is inspired by the mathematical formalisms that have been developed in axiomatic quantum mechanics, where a specific type of quantum contextuality is modelled. However, because in general states also influence context -- which is not the case in quantum mechanics -- we need a more general setting than the one used there. Our focus on context as a fundamental concept makes it possible to unify `dynamical change' and `change under influence of measurement', which makes our approach also more general and more powerful than the traditional quantum axiomatic approaches. For this reason an experiment (or measurement) is introduced as a specific kind of context. Mathematically we introduce a state context property system as the structure to describe an entity by means of its states, contexts and properties. We also strive from the start to a categorical setting and derive the morphisms between state context property systems from a merological covariance principle. We introduce the category SCOP with as elements the state context property systems and as morphisms the ones that we derived from this merological covariance principle. We introduce property completeness and state completeness and study the operational foundation of the formalism
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