Comparing Functional Dependences on Interventionist Counterfactual Causal Models

Formalizing causality into terms of (mathematical) logic can allow us to determine with greater precision (1) when it is appropriate to draw causal relationships, (2) whether we can express all the nuanced types of causality, and (3) how we can define the constituent parts of the machinery that drives causal reasoning, among other objectives. While work on (1) and (2) is plentiful and exemplified by Pearl’s structural causal model (SCM), the use of functional dependence logics like Vaananen’s DL based on team semantics to describe reasoning over SCMs is a relatively new tactic toward (3).

With this year’s advent of van Benthem and Baltag’s new functional dependence logic LFD, which takes a more local and modal approach to dependence relationships, I explore in this thesis the expressibility of causality in terms of SCMs in the new system of LFD, mirroring the work done using team semantics, the main result toward this end being the new logic CFD. Comparatively between the two forms of dependence logic discussed, I argue that using the more local CFD to analyze interactions between dependence and causality is more fundamental, fine-grained, and easily controllable, with respect to its global counterpart COD that is based on team semantics. However, I also show that localizing dependence in combined functional-counterfactual dependence logics still leaves various metaphysical problems for analyzing causality that lie outside the scope of said localization. Consequently, I then propose interventional analysis of sets of causal models, rather than singular models, might help solve some of these issues. All throughout, I will show how even in these localized settings, the stratification of causal inference tasks encapsulated in the Pearl Causal Hierarchy hold — and that, in general, logic still backs that correlation (almost) never implies causation.