Characterizing counterfactuals and dependencies over causal and generalized causal teams

TL;DR

This paper investigates the expressive power and proof systems of causal-observational languages within causal team semantics, including a generalized semantics for uncertainty, advancing formal understanding of interventionist counterfactuals and dependencies.

Contribution

It provides a systematic analysis of the expressive capabilities and complete natural deduction calculi for causal-observational languages, and introduces a generalized semantics for representing causal uncertainty.

Findings

Complete natural deduction calculi for each language.

Expressive power analysis over generalized semantics.

Framework for representing uncertainty in causal laws.

Abstract

We analyze the causal-observational languages that were introduced in Barbero and Sandu (2018), which allow discussing interventionist counterfactuals and functional dependencies in a unified framework. In particular, we systematically investigate the expressive power of these languages in causal team semantics, and we provide complete natural deduction calculi for each language. Furthermore, we introduce a generalized semantics which allows representing uncertainty about the causal laws, and analyze the expressive power and proof theory of the causal-observational languages over this enriched semantics.