There are different meanings of the term "compositionality" within science: what one researcher would call compositional, is not at all compositional for another researcher. The most established conception is usually attributed to Frege, and is characterised by a bottom-up flow of meanings: the meaning of the whole can be derived from the meanings of the parts, and how these parts are structured together. Inspired by work on compositionality in quantum theory, and categorical quantum mechanics in particular, we propose the notions of Schrodinger, Whitehead, and complete compositionality. Accounting for recent important developments in quantum technology and artificial intelligence, these do not have the bottom-up meaning flow as part of their definitions. Schrodinger compositionality accommodates quantum theory, and also meaning-as-context. Complete compositionality further strengthens Schrodinger compositionality in order to single out theories like ZX-calculus, that are complete with regard to the intended model. All together, our new notions aim to capture the fact that compositionality is at its best when it is `real', `non-trivial', and even more when it also is `complete'. At this point we only put forward the intuitive and/or restricted formal definitions, and leave a fully comprehensive definition to future collaborative work.
翻译:科学中“ 组合” 一词的含义各有不同: 一位研究人员称其为“ 组合”, 完全不是另一研究人员的构成。 最固定的概念通常归Frege, 其特征是自下而上的含义流: 整体的含义可以来自各个部分的含义, 以及这些部分的结构。 受量子理论中“ 组合性”, 特别是绝对量子力学研究的启发, 我们提出“ Schrodinger ”, Whitehead, 和“ 完整的组合性” 的概念。 计算量子技术和人工智能中最近的重要发展, 其定义中没有自下而上的含义流动。 Schroding 构成性包含量子理论, 也包含“ 整体” 的含义。 完整的构成性进一步加强了Schrodinger 构成性, 以单挑出ZX- calculus 等理论, 与预期的模式是完全完整的。 我们的新概念的目的是要了解一个事实, 当它“ 真实的” 和“ 未来定义” 时, 也只是一个完全的“ 不完全的“ ” 定义, 和“ 未来” 。