Beyond Models: Reimagining the Foundations of Causality

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Author: Denis Avetisyan

A new framework expands the definition of causality, moving beyond traditional model-based approaches to encompass a broader range of systems and clarify the link between cause and explanation.

This paper proposes an abstract definition of causality that generalizes existing methods and extends the concept to formalize explanation through counterfactual reasoning and intervention analysis.

Defining causality typically relies on complex causal models, yet this approach limits application to scenarios beyond those explicitly modeled. The paper ‘Causality Without Causal Models’ introduces an abstracted definition of causality, distilling core principles to transcend the constraints of traditional structural equation models. This generalization not only extends causal inference to diverse systems-including those with backtracking or complex logical formulations-but also provides a foundation for an abstract definition of explanation itself. Could this broadened framework ultimately reveal fundamental connections between causality, explanation, and reasoning across different domains of knowledge?

The Fragility of Correlation: Seeking Genuine Causation

The quest to discern genuine causal links remains a central challenge in science, largely because observed correlations often mask the true direction, or even the existence, of a causal relationship. Simply noting that two events frequently occur together does not establish that one causes the other; a hidden variable, pure chance, or reversed causality could be at play. This distinction is critical; while correlation can be useful for prediction – anticipating future events based on past patterns – it provides no explanatory power. Understanding why something happens requires identifying the specific factors that directly influence an outcome, a process demanding rigorous methodologies to move beyond superficial associations and uncover the underlying mechanisms at work. Establishing causality is not merely an academic exercise; it forms the bedrock of effective intervention and informed decision-making across diverse fields, from medicine and economics to environmental science and public policy.

Conventional statistical approaches frequently falter when applied to intricate systems due to their inherent limitations in discerning true causal links from mere correlations. These methods often assume direct relationships and struggle to account for mediating variables or feedback loops – elements commonplace in real-world phenomena. Interventions within such systems can trigger a cascade of effects, some of which are unexpected or counterintuitive; a change intended to improve one aspect might inadvertently worsen another due to these complex interactions. For instance, attempting to alleviate traffic congestion by adding lanes can, paradoxically, increase traffic volume in the long run – a consequence rarely captured by standard regression models. Consequently, relying solely on observational data and correlational analysis can lead to flawed conclusions and ineffective interventions, highlighting the need for causal inference techniques capable of navigating these complexities.

The pursuit of genuine understanding demands more than simply predicting outcomes; it requires elucidating why those outcomes occur. This work addresses this need by refining the foundations of causal reasoning, building upon the established Halpern-Pearl definition to offer a more generalized framework for identifying and modeling causal relationships. This generalization is not merely a theoretical exercise; it provides the tools necessary to construct explanatory models capable of revealing the underlying mechanisms driving complex systems. Unlike purely predictive models, which may identify correlations without revealing cause, these explanatory models allow for counterfactual reasoning – the ability to ask “what if?” questions and understand the consequences of interventions. By moving beyond correlation to establish causality, researchers can build more reliable and insightful models, ultimately fostering a deeper and more nuanced understanding of the world.

Mapping the Architecture of Influence: Models and Interventions

A causal model formally represents causal relationships between variables using directed acyclic graphs (DAGs). Nodes in the graph represent variables, and directed edges signify a direct causal effect of one variable on another. These models are not simply correlational; they explicitly encode assumptions about the direction of influence. By defining these relationships, a causal model allows for the prediction of how a change in one variable will propagate through the system and affect others. This predictive capability relies on the structure of the graph and the assumed functional relationships between variables, often expressed as conditional probabilities $P(Y|do(X))$, where $do(X)$ represents an intervention setting the value of $X$. The model facilitates analysis by providing a framework to distinguish between causation and correlation, enabling researchers to test hypotheses about underlying mechanisms and predict the outcomes of potential interventions.

Causal models facilitate in silico experimentation through the simulation of interventions, defined as the forced setting of a variable to a specific value. This contrasts with observation, where variables are allowed to fluctuate naturally. By explicitly defining a variable’s value, the model calculates the subsequent distribution of other variables, effectively predicting the consequences of actively manipulating the system. This predictive capability extends beyond simple correlation; interventions allow for the estimation of causal effects – how changes in one variable directly influence others – independent of confounding factors. The results of these simulated interventions are expressed as a revised probability distribution over the affected variables, providing a quantitative assessment of the intervention’s impact.

Intervention in a causal model can induce backtracking, a phenomenon where the manipulated variable’s value is not simply imposed, but propagates effects back through the network to determine consistent values for its causes. This occurs because causal models represent dependencies; changing an effect necessitates recalculating the values of its direct causes to maintain internal consistency. For instance, if a variable $X$ is intervened upon to be set to a specific value, any parent nodes of $X$ will have their values adjusted to be consistent with this intervention, potentially altering their previously determined values. The extent of this upstream propagation depends on the structure of the causal graph and the specific intervention point; complex networks can exhibit extensive backtracking, revealing the interdependencies and feedback loops inherent in the system.

Exploring Alternate Realities: The Logic of Counterfactuals

A counterfactual structure enables the assessment of alternative realities by positing changes to antecedent events and then tracing the resulting consequences. This differs from standard causal modeling which focuses on determining the effects of actual events; instead, counterfactual reasoning explores what would have happened if those events had been different. Formally, a counterfactual statement asks about the value of a variable under a specific intervention – effectively setting that variable to a different value than it actually took. The structure defines the mechanism for computing these alternative outcomes, requiring a precise definition of the causal relationships between variables and a method for propagating the changes through the system. This allows for the evaluation of “what if” scenarios and the identification of the causal impact of specific events.

A Recursive Counterfactual Structure leverages the framework of Recursive Causal Models to enable the analysis of increasingly complex “what if” scenarios. Recursive Causal Models define relationships between variables allowing for iterative reasoning; applying this to counterfactuals means that interventions or changes to one variable can be propagated through the model to determine effects on others, and then these effects can themselves be treated as new interventions in a recursive process. This allows for the modeling of chains of counterfactual reasoning – assessing not just the immediate consequence of an altered event, but also how that consequence alters subsequent events, and so on. The resulting structure permits a more nuanced understanding of causal relationships by capturing second- and higher-order effects that simpler counterfactual analyses would miss.

The validity of counterfactual inferences hinges on the establishment of an acceptable model representing the causal system under investigation. This model must be consistent with both observed data and pre-existing theoretical assumptions; discrepancies between model predictions and empirical evidence invalidate subsequent counterfactual reasoning. This work addresses model acceptability by extending existing definitions of causal models and inference procedures, specifically ensuring that these extensions do not introduce inconsistencies with established principles. A model failing to meet these criteria will produce counterfactual statements that, while logically derived from the model, do not accurately reflect potential alternative realities and therefore lack practical or scientific value.

The Pursuit of Parsimony: Distilling Essential Causes

The pursuit of truly insightful explanations hinges on identifying a minimal cause – the smallest set of factors sufficient to bring about an effect, excluding any redundant contributors. This principle acknowledges that complex phenomena rarely stem from a single source, but striving for parsimony is essential for interpretability. A minimal cause isn’t simply a cause, but the most efficient causal story; it avoids unnecessary complexity that obscures underlying mechanisms and hinders predictive power. By rigorously eliminating factors that don’t fundamentally alter the outcome – those that offer no additional explanatory value – researchers can build models that are not only accurate but also readily understood, fostering deeper insights and more effective interventions. This focus on essential causes moves beyond simply describing what happened, to illuminating why it happened in the most concise and revealing way possible.

Causal explanation is not a purely objective process; rather, it is fundamentally shaped by the knowledge possessed by the individual – the agent – constructing the explanation. What constitutes a satisfactory explanation shifts depending on the background information available to that agent; a cause considered sufficient for someone with limited knowledge may be deemed incomplete or even irrelevant to someone with a more comprehensive understanding of the underlying mechanisms. This perspective-dependent nature of causality means that the same event can elicit different explanations from different observers, each valid within the context of their individual knowledge states. Consequently, a complete model of causal reasoning must account not only for the relationships between events but also for the cognitive framework of the agent doing the explaining, acknowledging that explanations are interpretations built upon a foundation of pre-existing knowledge and beliefs.

The human capacity to understand why things happen frequently relies on a principle known as but-for causality – a core concept within formalized causal models. This intuitive reasoning process assesses a scenario by asking whether an event would have occurred without a specific prior event; if the answer is no, the prior event is deemed a cause. This isn’t simply philosophical musing; it’s demonstrably how people attribute responsibility, assess blame, and make predictions about future events. Consequently, the ability to represent and compute these but-for relationships is essential for artificial intelligence systems striving to mimic human-level reasoning, enabling them to move beyond mere correlation and toward genuine understanding of cause and effect, even in complex, multifaceted situations.

The pursuit of defining causality, as explored within the article, reveals a fascinating tension. It isn’t merely about establishing connections between events, but understanding what would have occurred under different circumstances – a realm of counterfactuals. This aligns with the observation of Blaise Pascal: “The eloquence of youth is that it knows nothing.” In the context of causal inquiry, this speaks to the initial, often naive, assumptions made when constructing any system of understanding. The article’s extension of causality beyond traditional causal models acknowledges that any framework, no matter how sophisticated, is built upon a foundation of initial approximations. Just as youthful eloquence stems from a lack of experience, early causal models represent a preliminary grasp of complex realities, destined to evolve or, inevitably, decay with the passage of time and the accrual of further observation.

What Lies Ahead?

The pursuit of causality, it seems, inevitably circles back upon itself. This work, by loosening the strictures of traditional causal modeling, doesn’t so much solve the problem of defining cause and effect as it shifts the locus of difficulty. The abstract definition offered is elegant, certainly, but systems learn to age gracefully – and a definition unbound from specific structures may simply reveal the inherent limitations of applying such a rigid concept universally. The question isn’t whether causality exists, but whether the human need to delineate it is itself a productive constraint, or merely a comforting illusion.

Future work will likely grapple with the practical implications of this generalization. Applying this abstract framework to real-world systems-those messy, incomplete, and often stubbornly resistant to formalization-will be a considerable challenge. The emphasis may need to shift from identifying causal relationships to understanding the degree of causal connection, acknowledging that most systems operate on gradients rather than absolutes. Sometimes observing the process is better than trying to speed it up.

Perhaps the most intriguing avenue lies in the extension to explanation. If causality is broadened, so too is the scope of what constitutes a satisfactory explanation. This could lead to a richer, more nuanced understanding of complex phenomena, moving beyond simple cause-and-effect narratives toward a more holistic appreciation of interconnectedness. The decay of systems is inevitable; understanding how they decay may prove more valuable than attempting to prevent it.

Original article: https://arxiv.org/pdf/2511.21260.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-11-28 21:42