Coherence-based probability logic: Rationality under uncertainty

这个项目位于形式认识论和推理的新范式心理学的交叉点。本文将进一步发展“基于连贯性的概率逻辑”（CPL），作为不确定性推理的形式和实证研究的新理性框架。在连贯性框架中，概率被认为是主观的信念程度，条件概率被定义为一个原始的概念。相干方法特别适合于处理零先验概率的问题。需要完成三个工作包（WP1-WP3），以建立SPP1516以下关键问题的新答案：定性（基于逻辑的）和定量（基于概率的）方法对人类思维建模有多大用处？不确定性下的理性是什么？在WP1中，我们将为直言三段论开发一个基于相干的概率语义。在哲学上，我们将开发新的三段论中心概念的概率解释（如量词，存在的重要性，对立方）。在心理学上，我们将对新的语义进行实验。心理上的合理性将进行实证研究。新的语义学将根据目前的直言三段论心理学理论进行批判性的讨论。在WP2中，我们将从哲学的角度分析非单调条件逻辑的各种定性和定量的合理性原则。此外，我们将通过实验测试哪些合理性原则是人们实际认可的，从而哪一个系统最好地解释了人们在不完全概率知识下的推理方式。在WP3中，我们将开发迭代条件的哲学解释，并在一系列实验中测试我们理论的经验充分性。特别是，我们将从理论和实验两方面研究学习条件信息（与解释左嵌套条件句相关）与解释推理之间的关系。此外，在右嵌套条件的背景下，我们将研究进出口原则的心理学合理性，这是哲学家们经常假设的，但在cpll中并不成立。最终（大胆的）目标是将CPL发展为不确定推理的统一理性框架，并将心理概率逻辑构建为哲学上有依据的、描述性充分的人类不确定推理能力理论。WP1和WP3描述了实现这一目标的重要步骤。

This project is located in the intersection of formal epistemology and the new paradigm psychology of reasoning. It will further develop "coherence based probability logic" (CPL) as a new rationality framework for formal and empirical studies on reasoning under uncertainty. In the coherence framework, probabilities are conceived as subjective degrees of belief and conditional probability is defined as a primitive concept. The coherence approach is especially suitable for dealing with zero antecedent probabilities. Three working packages (WP1-WP3) shall be accomplished to establish new answers to the following key questions of the SPP1516: How useful are qualitative (logic-based) and quantitative (probability-based) approaches for modeling human thinking? What is rationality under uncertainty? In WP1, we will develop a coherence-based probability semantics for categorical syllogisms. Philosophically, we will develop new probabilistic interpretations of central syllogistic concepts (like quantifiers, existential import, the square of opposition). Psychologically, we will run experiments on the new semantics. The psychological plausibility will be empirically investigated. The new semantics will be critically discussed in the light of current psychological theories of categorical syllogisms. In WP2, we will philosophically analyze various rationality principles of nonmonotonic conditional logics in their qualitative and quantitative versions within the framework of CPL. Furthermore, we will test experimentally which of the rationality principles are actually endorsed by people, and hence which system explains best how people reason under incomplete probabilistic knowledge. In WP3, we will develop a philosophical account of iterated conditionals and test the empirical adequacy of our theory in a series of experiments. In particular, we will study, both theoretically and experimentally, the relationship between learning a conditional information, which is associated with interpreting left-nested conditionals, and explanatory reasoning. Additionally, in the context of right-nested conditionals, we will investigate the psychological plausibility of the Import-Export Principle, which is frequently assumed by philosophers, yet it does not hold in CPL. The ultimate (bold) goal is to develop CPL as an unified rationality framework for uncertain reasoning and to construct Mental Probability Logic as a philosophically informed and descriptively adequate competence theory of human uncertain inference. WP1¿WP3 describe important steps towards this goal.