apply do-calculus

This work addresses the lack of a systematic approach to composing and ordering do-calculus rules, which hinders efficient exploration of the space of equivalent interventional queries. The paper introduces, for the first time, a derivation graph structure that formally captures the application and composition logic of do-calculus rules, systematically representing equivalence relations between observational and interventional probabilities under the do-calculus framework. Building upon this representation, the authors devise a streamlined identification procedure requiring at most four simplification steps. This approach not only reveals the intrinsic organizational structure underlying do-calculus reasoning but also enables the generation of multiple equivalent estimands for the same causal quantity, substantially improving estimation efficiency and facilitating practical applications of do-calculus.

This work addresses causal graph structure learning under hard interventions from multiple sources in the presence of latent variables, aiming to characterize intervention equivalence classes—i.e., distinct causal graphs that induce identical families of do-distributions. We propose the first systematic graphical characterization framework for such equivalence classes, grounded in do-calculus and d-separation theory, and establish sound edge orientation rules and graphical constraints. Our approach yields the first decidable criterion for intervention equivalence, unifying equivalence class characterization with structure learning. Furthermore, we design a provably sound hybrid algorithm that jointly leverages heterogeneous observational and interventional data for causal structure inference. Experiments demonstrate that our method significantly improves both accuracy and interpretability in identifying causal graphs under hard interventions.

This study addresses the problem of verifying whether a given observational formula correctly identifies a target interventional distribution in causal graphical models, going beyond mere identifiability assessment. To this end, it introduces a falsification-driven verification framework that decouples verification from identification for the first time: an efficient falsifier first eliminates incorrect formulas, and a verifier—provably almost surely correct under regular exponential family models—is then constructed atop this filter. As an application, the authors develop a “gateway test” that enumerates all valid variable sets satisfying the front-door criterion, with theoretical guarantees on verification reliability. This approach substantially enhances both the practicality and rigor of validating interventional distributions.

Existing causal identification methods rely heavily on probabilistic semantics, rendering them inapplicable to non-probabilistic causal systems such as databases, hardware description languages, distributed systems, and modern machine learning frameworks. Method: We propose the first purely syntactic causal identification framework grounded in symmetric monoidal categories, fully decoupling the syntactic structure of causal models from their semantic interpretation. By syntactically reconstructing ADMG graph structures, the ID algorithm, and backdoor/front-door adjustments, we eliminate reliance on probabilistic assumptions. Contribution/Results: Our framework enables categorical compositional transformations, yielding a verifiable and programmable general causal identification algorithm. Empirical validation confirms its effectiveness in complex non-probabilistic systems. This work establishes a foundational theoretical basis for formal and automated causal reasoning, advancing beyond probability-centric paradigms toward category-theoretic formalization of causality.

This paper uncovers the algebraic essence underlying convex analysis, Gaussian probability, and quadratic structure. To this end, we introduce Graphical Quadratic Algebra (GQA)—a novel algebraic framework based on chordal graphs—that uniformly models quadratic relations, Gaussian stochastic processes, and nondeterministic Gaussian processes via rotation-invariant quadratic generators. We provide the first sound and complete axiomatic characterization of three fundamental models: least-squares estimation, Gaussian randomness, and nondeterminism—revealing their shared conditional algebraic structure. Our method integrates string diagram theory, categorical semantics, and formal semantics of probabilistic programming. Theoretical contributions include soundness and completeness proofs for all three models within GQA. Applications demonstrate efficacy in linear regression, probabilistic programming, and noisy circuit modeling.

This study addresses the identifiability of interventional effects under complex causal structures. It proposes a unified identification framework by directly interpreting single-world intervention graphs (SWIGs) as joint representations of observational and interventional distributions, thereby transcending their conventional role as mere bridges to potential outcomes. Integrating SWIGs with do-calculus and structured probabilistic modeling, the approach not only recovers classical results such as backdoor adjustment but also substantially extends the applicability of front-door criteria to more intricate scenarios. This advancement provides a more scalable theoretical foundation for identifying causal effects under general intervention structures.

该研究通过图手术和do-算子在确定性无环结构因果模型中建立了精确对应，解决了两者操作等价性的数学表述问题。

This work addresses critical challenges in safety-critical rule-based systems—namely poor scalability, fragility, and goal mis-specification—which often lead to reward hacking and failures in formal verification. To overcome these limitations, the authors propose a neuro-symbolic causal framework that integrates first-order logic abductive trees, structural causal models, and deep reinforcement learning within a MAPE-K control loop. A novel meta-layer architecture enables the automatic synthesis and formal verification of rules from natural language objectives. This meta-layer comprises a goal/rule synthesizer and a rule verification engine, which iteratively generate necessary and sufficient causal rule sets grounded in legal and safety principles provided by human experts. Evaluated in an autonomous driving scenario, the approach successfully derives a minimal yet complete rule set, formally encoded as logical constraints, demonstrating its modularity, traceability, and practical applicability.

本文针对现有因果推理框架无法处理循环因果依赖的问题，提出了一种新的二部图因果模型(BGCMs)，通过明确指定干预方程、目标变量及其值来解决标准干预的模糊性。

This work addresses the challenge of preserving trajectory properties during simplification and transformation of hybrid systems involving differential-algebraic equations (DAEs). To this end, the paper introduces differential-algebraic refinement logic (dARL), a formal framework that builds upon trajectory semantics to support stepwise verification and simplification of DAE-based programs while guaranteeing semantic preservation at each transformation step. The core contribution lies in the first complete and provably correct refinement calculus for index reduction of DAEs, thereby establishing a formal foundation and syntactic assurance for incremental verification of complex DAE systems.