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) $P_{\mathcal{M}_{fin}}(S^{\star}|\textrm{do}(P=0))$ .

Explore similar work

Jun 12, 2026

Relational Structural Causal Models

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.

Adiba Ejaz, Elias Bareinboim

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

Structural Causal Models Causal Identifiability Causal Inference

Ask PDF

May 5, 2026

Partially Observed Structural Causal Models

Here we introduce Partially Observed Structural Causal Models (POSCMs) as an extension of structural causal models (SCMs) to settings where upstream contexts co-determine both the interaction structure and downstream mechanisms on observed variables. POSCMs thus provide a self-contained causal modeling framework for endogenous graphs, allowing for an intervention hierarchy spanning node- and edge-level contexts and endogenous variable interventions. To define edge interventions, we separate node mechanisms into edge-local transmission channels that can be modified without changing the source node or the rest of the target mechanism. We provide an identifiability theory that clarifies which intervention families would suffice to disentangle structure formation from mechanisms. We then empirically validate these theoretical results in two external simulators: a biophysically detailed virtual human retina and a gene-regulatory analogue. The experiments reproduce non-identifiability under latent context, expose structure-mechanism confounding under latent edges, and recover pathway-level input-output relationships under targeted interventions, consistent with our positive Markov kernel identifiability results. Together, POSCMs provide an intervention-oriented framework for causal systems in which contexts, graph structure, mechanisms, and measurements are jointly generated and only partially observed.

Turan Orujlu, Jordan Matelsky, Martin V. Butz +2

University of Tübingen · MPI for Biological Cybernetics · University of Pennsylvania +1

Structural Causal Models Causal Identifiability Causal Intervention

Ask PDF

May 5, 2026

ReplaySCM: A Benchmark for Executable Causal Mechanism Induction from Interventions

Most causal benchmarks for language models score local answers or graph structure. We introduce ReplaySCM, a 1,300 item benchmark for executable causal mechanism induction from finite interventional evidence. Each item contains binary worlds generated by a latent fully observed acyclic Boolean structural causal model (SCM). A system must output a mechanism map in a restricted Boolean DSL; the submission is parsed, checked for legality and acyclicity, and replayed on training and held-out intervention worlds. Scoring uses replay behavior rather than formula strings, so syntactically different mechanisms receive credit when they behave correctly. ReplaySCM varies the structural information disclosed to the model through Ordered, Block-order, Hidden-order, and Hidden-roots settings, and includes Alternative-SCM tasks that supply a valid reference SCM and ask for a semantically distinct alternative that fits the training worlds, together with a separating intervention and witness. Frontier LLMs infer parts of the functional-parent structure, but held-out replay drops sharply when order or root structure is hidden. We also evaluate a matched support-audit ladder: Original, Extra Worlds, and Counterexample Audit (CEx), that raises mean local predecessor-pattern coverage from 0.8949 to 0.9815 to 1.0; under the audited searches, no discovered semantic alternative remains consistent with the training worlds. The Ordered/Hidden-order gap persists under this stronger evidence. ReplaySCM complements answer-level causal reasoning and graph-discovery benchmarks by evaluating executable replay generalization from finite interventional evidence, without claiming unique identification of the latent SCM.

Serafim Batzoglou

LLM Evaluation Structural Causal Models Causal Interventions in Language Models

Ask PDF