# Deriving Bounds and Inequality Constraints Using LogicalRelations Among Counterfactuals

arXiv: https://arxiv.org/abs/2007.00628 · HTML: https://mlsanity.com/paper/2007.00628/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 8 of 8)

- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Towards Bounding Causal Effects under Markov Equivalence](https://mlsanity.com/paper/2311.07259/) (2023)
- [Scalable Computation of Causal Bounds](https://mlsanity.com/paper/2308.02709/) (2023)
- [The Causal Marginal Polytope for Bounding Treatment Effects](https://mlsanity.com/paper/2202.13851/) (2022)
- [The Limits of Predicting Agents from Behaviour](https://mlsanity.com/paper/2506.02923/) (2025)
- [Foundation Models for Partial Causal Identification](https://mlsanity.com/paper/2608.20841/) (2026)
- [Learning Counterfactual Outcomes Under Rank Preservation](https://mlsanity.com/paper/2502.06398/) (2025)

## Abstract (arXiv)

Causal parameters may not be point identified in the presence of unobserved confounding. However, information about non-identified parameters, in the form of bounds, may still be recovered from the observed data in some cases. We develop a new general method for obtaining bounds on causal parameters using rules of probability and restrictions on counterfactuals implied by causal graphical models. We additionally provide inequality constraints on functionals of the observed data law implied by such causal models. Our approach is motivated by the observation that logical relations between identified and non-identified counterfactual events often yield information about non-identified events. We show that this approach is powerful enough to recover known sharp bounds and tight inequality constraints, and to derive novel bounds and constraints.