Rescue when causal inference fails: formalizing causal triangulation as a reasoning process based on formal logical systems and causal assumptions

Causal triangulation aims to learn about a target causal estimand by comparing multiple studies targeting the same or similar estimands with distinct identification strategies. It is useful when all studies have questionable assumptions, and allows us to learn more about the target than had we considered each study in isolation. We formalize causal triangulation as a reasoning process that relies on formal logical systems and takes causal identification studies and falsification strategies as inputs. This reasoning aims to answer a triangulation query with specific goals, and requires different types of logical systems independent of questionable assumptions. We discuss two types of queries, their related propositional and probabilistic logical systems, and the reasoning based on them: (1) estimation, that only requires a system with deductive rules and unverifiable premises; and (2) explanation, that requires a system allowing abductive reasoning and often probabilistic. This formalization works under different causal models, provided they are complete and sound. We provide two querying and reasoning approaches that lead to (1) multi-source partial identification and (2) explanation of study estimate discordance or concordance.