Shared Common Grounds of Qualitative and Quantitative Rational Reasoning

理性的人类推理同时利用了定量和定性的论证，而人类似乎很容易将这两个方面结合起来。然而，尽管已经提出了一些同时依赖于定性和定量结构的方法(贝叶斯网络可能是最突出的一个)，但在科学上，追求定性方法的社区与那些利用定量框架捕捉理性推理的社区之间仍然存在着显著的差距。本项目旨在通过声称两者可以共享共同点，在非常深刻的水平上在定性和定量范式之间架起桥梁。这是基于这样的观察，即任何类型的规则都形成了推理的基本构件，这些构件通过推理范式(如MODUS PONNS或三段论)或通过贝叶斯网络中应用的特定技术而变得有效。从这个起点出发，在对条件句三值理解的基础上，我们通过专注于一种条件逻辑方法，在定性和定量框架中建立了理性推理的共同基础，该方法能够基本使用命题逻辑，而不会将语义限制在经典的二元论观点中。这允许我们在不同的语义框架中考虑遵循相同的一般原则的条件推理。在此背景下，我们讨论了哲学、心理学和计算机科学中提出的关于知识库的归纳推理、一致性和连贯性、似然性与概率以及人类因果推理的研究问题，并建立了与这些学科中提出的方法的联系。基于Spohn序数条件函数和基于最大熵原理的概率推理的所谓c-表示的形式调查，以及对它们的适当性和与其相关联的形式性质的经验评估，构成了这一交叉学科项目的核心，该项目联合了心理学和计算机科学的研究人员，并与哲学的研究人员密切合作。这些在语义上不同但具有共同逻辑基础的高质量推理方法，在形式深度和经验广度上得到了探索，这是第一次。我们期待着对人类理性的理解和形式回应的发展都有重要的见解。理性推理的规范体系。该项目基于第一个资助期的“条件和概率理性推理”和“非单调推理”项目的结果。

Rational human reasoning makes use of both quantitative and qualitative arguments, and human beings seem to combine easily both aspects. However, although some approaches have been put forward that rely both on qualitative and quantitative structures (with Bayesian networks being probably the most prominent one), scientifically, there is still a notable gap between the communities pursuing qualitative approaches and those that make use of quantitative frameworks to capture rational reasoning.This project aims at building bridges between qualitative and quantitative paradigms on a very profound level by claiming that both (can) share common grounds. This is based on the observation that rules of any kind form basic building blocks for reasoning which become effective via inference paradigms such as modus ponens or syllogism, or via the specific techniques applied in Bayesian networks. From this starting point, building on a three-valued understanding of conditionals, we establish common grounds for rational reasoning in qualitative and quantitative frameworks by focusing on a conditional-logical approach that is capable of making basic use of propositional logic without limiting semantics to the classical binary view. This allows us to consider conditional reasoning following the same general principles in various semantical frameworks. In this context, we address research questionsconcerning inductive reasoning from knowledge bases, consistency and coherence, plausibility vs. probability, and human causal reasoning that have been raised in philosophy, psychology, and computer science, and establish links to approaches which have been put forward in these disciplines. The formal investigation of so-called c-representations based on Spohn's ordinal conditional functions and probabilistic reasoning on the principle of maximum entropy, as well as the empirical evaluation of their appropriateness and of the formal properties that are associated with them for rational reasoning constitute the core of this interdisciplinary project that joins researchers from psychology and computer science and collaborates intensely with researchers from philosophy. It is for the first time that these high-quality approaches to reasoning which differ in semantics but share common logical grounds are explored in such formal depth and empirical breadth. We expect significant insights both for the understanding of human rationality and the development of formal resp. normative systems for rational reasoning.The project is based upon results from the projects "Rational reasoning with conditionals and probabilities" and "Non-monotonic Reasoning" of the first funding period.