The Logic & Structure project is about the language of mathematical logic and how it can be of use in the visual arts. It involves a conversation between a mathematical logician and a group of artists. The project is ongoing, and this is a report on its first two phases. This text has two parts. The first, “Logic”, is a short introduction to certain aspects of logic, as it was presented to the participants. The second part, “Structures”, describes some of the outcomes.The inspiration for the project comes from modern model theory whose advances revealed the extent to which formal methods may be helpful in describing and analysing mathematical structures. While the structures that are studied are often immensely complex, the formal language in which their properties can be expressed is simple. Its syntax is precisely defined and well understood, and this understanding often successfully guides us in our explorations of the rich world of mathematical objects. Our goal is to see the extent to which a similar approach could be of value when talking about works of art as structures. To this end, one could try to describe existing art objects in terms of suitably chosen formal languages, but we follow a reverse route. The language is described first, and the participating artists are asked to come up with artwork in which formal elements and their relations are chosen in advance, making it easier to identify those features of the created pieces that can be formally expressed. In other words, we are not thinking of applying formal methods to create art; rather we want to begin with samples that can serve as material for discussion.

中文翻译：

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逻辑与结构：一个艺术项目

逻辑与结构项目是关于数理逻辑的语言以及它如何在视觉艺术中使用。它涉及数学逻辑学家和一群艺术家之间的对话。该项目正在进行中，这是前两个阶段的报告。这段文字有两部分。第一个“逻辑”是对逻辑的某些方面的简短介绍，因为它已呈现给参与者。第二部分“结构”描述了一些成果。该项目的灵感来自现代模型理论，其进步揭示了形式方法在多大程度上有助于描述和分析数学结构。虽然研究的结构通常非常复杂，但可以表达其属性的形式语言却很简单。它的语法被精确定义和理解，这种理解常常成功地引导我们探索丰富的数学对象世界。我们的目标是了解在将艺术作品作为结构进行讨论时，类似方法在多大程度上具有价值。To this end, one could try to describe existing art objects in terms of suitably chosen formal languages, but we follow a reverse route. 首先描述语言，并要求参展艺术家提前选择形式元素及其关系的艺术作品，以便更容易识别创作作品中可以形式表达的特征。换句话说，我们不是在考虑应用形式化的方法来创造艺术；相反，我们想从可以作为讨论材料的样本开始。