Teleological Inference in Structural Causal Models via Intentional Interventions

Dario Compagno; Fabio Massimo Zennaro

cs.AIMar 19, 2026

Teleological Inference in Structural Causal Models via Intentional Interventions

Authors: Dario Compagno, Fabio Massimo Zennaro

Abstract

Structural causal models (SCMs) were conceived to formulate and answer causal questions. This paper shows that SCMs can also be used to formulate and answer teleological questions, concerning the intentions of a state-aware, goal-directed agent intervening in a causal system. We review limitations of previous approaches to modeling such agents, and then introduce intentional interventions, a new time-agnostic operator that induces a twin SCM we call a structural final model (SFM). SFMs treat observed values as the outcome of intentional interventions and relate them to the counterfactual conditions of those interventions (what would have happened had the agent not intervened). We show how SFMs can be used to empirically detect agents and to discover their intentions.

Figures & tables

Panel of Figure 1 — Figure 1: (a) Causal model for a heating system defined over variables $W,T,H$ (for Weather, room Temperature, Heater status); we collect the data in the adjacent table. (b) Causal model for smoking defined over variables $S,P,D$ (for Smoking, Pleasure, lung Damage).

Panel of Figure 2 — Figure 2: (a) The DAG for a generic SCM $\mathcal{M}$ ; solid nodes represent endogenous variables, dashed nodes represent exogenous variables. (b) The DAG after intervention $\textrm{do}(X=1)$ . (c) The twin graph for the counterfactual $\textrm{ctf}(\cdot_{X=0}|X=1)$ ; black nodes represent actual variables, gray nodes represent counterfactual variables. (d) The twin graph for the intentional intervention $\textrm{do}^{\star}(X^{\star}=f(y))$ .

Desiderata	Exogenous	Endogenous	Time-based	Final
(D1) Causal grounding	$\times$	$\times$	$\times$	$\checkmark$
(D2) State-awareness	$\times$	$\checkmark$	$\checkmark$	$\checkmark$
(D3) Goal-directedness	$\times$	$\checkmark$	$\checkmark$	$\checkmark$
(D4) Explaining data	$\times$	$\checkmark$	$\checkmark$	$\checkmark$
(D5) Discriminating intentions	$\times$	$\checkmark$	$\checkmark$	$\checkmark$
(D6) Acyclicity	$\checkmark$	$\times$	$\checkmark$	$\checkmark$

Table 1: List of desiderata for intention modeling

Panel of Figure 3 — Figure 3: Existing approaches to account for agents’ intentions: (a) factoring into exogenous variables; (b) factoring into endogenous variables; (c) time-based models.

Panel of Figure 4 — Figure 4: (a) SFM for heating. (b) SFM for smoking.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 5 — Figure 5: SFM for detecting intentional interventions in colliders.

Panel of Figure 6 — Figure 6: (a) SFM for intention discovery in forks. (b) SFM with intervention $\textrm{do}(Z=\bar{z})$ for intention discovery in forks. (c) SFM with intervention $\textrm{do}(Y=\bar{y})$ for intention discovery in forks.

Panel of Figure 7 — Figure 7: Probability mass functions computed during intention discovery: (a) $P_{\mathcal{M}_{fin}}(S^{\star})$ ; (b) $P_{\mathcal{M}_{fin}}(S^{\star}|\textrm{do}(D=0))$ ; (b) $P_{\mathcal{M}_{fin}}(S^{\star}|\textrm{do}(P=0))$ .

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Causal AI Lab, Department of Computer Science, Columbia University, NY, USA.

Structural Causal Models Causal Identifiability Causal Inference

Open paper AskPDF arXiv

An artificial intelligence must have a model of its environment that is causal, supporting reasoning about interventions and counterfactuals, and also combinatorial, supporting generalization to unseen combinations of objects. In this work, we formally study when and how such a model can be learned. We develop relational structural causal models, extending structural causal models (Pearl 2009) to settings where objects and their relations vary. First, we show how answers to not only causal but also observational queries about unseen combinations of objects can not be identified without further assumptions. To enable such identification--including in the presence of unobserved confounding--we define relational causal graphs and derive symbolic identification criteria. Finally, we propose relational neural causal models, a provably correct approach that outperforms non-relational baselines on simulated traffic scenes with varying cars, signals, and pedestrians.

Abstract

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