Observing Interventions: A logic for thinking about experiments

Abstract

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 (Pearl 2009;Woodward 2003). In a first step we extend a causal model (Galles and Pearl 1998;Halpern 2000;Pearl 2009; Briggs 2012) with a simple Hintikka-style representation of the epistemic state of an agent. In the resulting setting, one can talk about the knowledge of an agent and information 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 principle of no learning for interventions. Therefore, in a second step we implement a more complex notion of knowledge (Nozick 1981) 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 logics, we provide a sound and complete axiomatization.