Dialogical Foundations of Semantics (DiFoS)

将交互作用融入到传统静态的逻辑图景中，是当前逻辑研究中最重要和最吸引人的话题之一。《逻辑与游戏》的广泛研究领域涉及关于游戏的推理，但也涉及在推理中使用游戏，看看目前研究人员对逻辑中交互的关注，很容易忘记逻辑中对话的使用至少可以追溯到洛伦森1958年的论文《Logik and Agon》，它的根源可以追溯到更古老的传统，可以追溯到前Socatic。我们的项目旨在(1)描述洛伦森对话逻辑的基本价值，(2)考虑到它的历史根源，将其嵌入到现代科学背景中。(1)基础性研究包括：(1)讨论和澄清对话语义学的技术要点；(2)评价对话语义学的哲学背景主张及其为数学、计算机科学和语言学的逻辑推理奠定基础的潜力。这些基础调查是项目的核心，将以两个主要项目的形式进行，这两个项目不是分配到特定地点，而是所有三个主要调查人员共同致力于的中心项目。(2)融入现代背景和历史根源是两个地点之间的三个合作项目的主题，以及五个单独的地方项目的主题。他们研究了否定和定义推理作为一般推理范例的作用，非正式和半正式数学证明中对话的使用，计算机科学中零知识证明和扩展逻辑程序的使用，以及语言学中命题类型方法的对话版本。关于历史根源，我们除了研究对话逻辑的现代历史外，还主要研究中世纪的义务理论。

Incorporating interaction into the traditionally static picture of logic is one of the most vital and fascinating topics in current logical research. The broad research area of "Logic and Games" deals with reasoning about games, but also with the use of games in reasoning, Looking at the current preoccupation of researchers with interaction in logic, it is easy to forget that the use of dialogues in logic goes back at least to Lorenzen's 1958 paper "Logik und Agon", and has its roots in much older traditions, going back to the pre-Socratics.Our project aims to (1) describe the foundational value of Lorenzen's dialogical logic, and (2) embed it into a modern scientific context taking into account its historical roots. (1) The foundational investigations consist in (i) discussing and clarifying technical points of dialogue semantics, and (ii) evaluating its philosophical background claims as well as its potential to lay the foundations for logical reasoning in mathematics, computer science and linguistics. These foundational investigations are the heart of the project and will be carried out in the form of two Master Projects, which are not assigned to a particular site, but are central projects which all three principal investigators are jointly committed to. (2) The embedding into a modern context and the historical roots are subjects of three collaborative projects between two sites each, as well as of five individual local projects. They investigate the role of negation and of definitional reasoning as paradigms for reasoning in general, the use of dialogues in informal and semi-formal mathematical proofs, the use of zero-knowledge proofs and extended logic programs in computer science and of dialogical versions of the propositions-as-types approach within linguistics. Concerning the historical roots we concentrate, besides studying the modern history of dialogical logic, mainly on medieval theories of obligations.