观察干预:思考实验的逻辑 (Observing Interventions: A logic for thinking about experiments)

from arxiv, This is the extended version of a paper that will appear in a special issue of the Journal of Logic and Computation dedicated to the 3rd DaL{\'i} Workshop on Dynamic Logic: New Trends and Applications. Different from the journal version, here the reader can find the full technical appendix

This paper makes a first step towards a logic of learning from experiments. For this, we investigate formal frameworks for modeling the interaction of causal and (qualitative) epistemic reasoning. Crucial for our approach is the idea that the notion of an intervention can be used as a formal expression of a (real or hypothetical) experiment. In a first step we extend the well-known causal models with a simple Hintikka-style representation of the epistemic state of an agent. In the resulting setting, one can talk not only about the knowledge of an agent about the values of variables and how interventions affect them, but also about knowledge update. The resulting logic can model reasoning about thought experiments. However, it is unable to account for learning from experiments, which is clearly brought out by the fact that it validates the no learning principle for interventions. Therefore, in a second step, we implement a more complex notion of knowledge that allows an agent to observe (measure) certain variables when an experiment is carried out. This extended system does allow for learning from experiments. For all the proposed logical systems, we provide a sound and complete axiomatization.

翻译：本文为从实验中学习的逻辑迈出了第一步。为此, 我们调查了用于模拟因果关系和( 定性的) 认知推理相互作用的正式框架。我们的方法的关键在于将干预的概念用作( 真实的或假设的)实验的正式表达。作为第一步, 我们扩展了已知的因果模型, 简单的Hintikka式的代理体特征代表。在由此形成的环境下, 人们不仅可以谈论代理人对变量的价值和干预措施如何影响这些变量的知识, 而且还可以谈论知识更新。由此产生的逻辑可以模拟思考实验的推理。但是, 我们无法解释从实验中学习的概念, 这一点显然是因为它证实了干预的学习原则。因此, 在第二步, 我们实施了一个更复杂的知识概念, 使代理人在进行实验时能够观察( 度 ) 某些变量。这个扩展的系统允许从实验中学习。对于所有拟议的逻辑系统, 我们提供一种正确和完整的轴心化。