Modeling Indeterministic Causal Laws and Interventionist Counterfactuals

Core Concepts

Indeterministic causal laws, where the effect does not uniquely determine the cause, require a more general modeling approach than deterministic causal models. The paper proposes a framework of relational causal teams to represent and reason about interventionist counterfactuals in the presence of indeterministic causal laws, and provides complete axiomatizations for this setting.

Abstract

The paper investigates the generalization of causal models to the case of indeterministic causal laws, where the effect does not uniquely determine the cause. It provides an overview of the differences in modeling that this more general perspective enforces, and proposes an implementation of generalized models in the style of causal team semantics.
In indeterministic causal models, the laws are not represented by functions (as in the deterministic case), but more generally by relations. This leads to significant differences in the axiomatization of interventionist counterfactuals compared to the deterministic case. The paper provides strongly complete axiomatizations over the full class of indeterministic models and over its recursive subclass, where cyclic causal relationships are forbidden.
The key insights are:

Uncertainty: Indeterministic laws require a shift from causal models to the more general causal teams, which allow a multiplicity of variable assignments compatible with the causal laws.

Specifying causal laws: In the indeterministic case, the causal laws cannot be simply represented as functions, but need to be specified as relations. This raises challenges in identifying the direct causes of a variable.

Interventions: Interventions on indeterministic models can produce multiple possible scenarios, even in the acyclic (recursive) case. This leads to important differences compared to the deterministic case, such as the failure of composition principles.

Axiomatization: The paper provides a strongly complete axiomatization for the logic of interventionist counterfactuals over the full class of indeterministic models, as well as over the recursive subclass. The axiomatization highlights key differences from the deterministic case, such as the importance of might-counterfactuals and the failure of principles like Composition.

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Key Insights Distilled From

On the logic of interventionist counterfactuals under indeterministic causal laws

by Fausto Barbe... at arxiv.org 04-16-2024

https://arxiv.org/pdf/2312.07223.pdf

Deeper Inquiries

What are the potential applications of the proposed framework of relational causal teams in fields like machine learning, epidemiology, or social sciences, where indeterministic causal relationships are common

The framework of relational causal teams proposed in the context above has various potential applications in fields where indeterministic causal relationships are prevalent. In machine learning, these models can be used to capture complex causal dependencies that are not fully deterministic. By allowing for relations instead of functions to represent causal laws, the framework can handle situations where multiple outcomes are possible given certain inputs, which is common in real-world data. This can lead to more accurate and robust machine learning models that can account for uncertainty and variability in data.
In epidemiology, the framework can be applied to model the spread of diseases or the effectiveness of interventions in situations where causality is not deterministic. For example, in studying the impact of public health policies on disease transmission, the indeterministic nature of causal relationships can be better captured using relational causal teams. This can help public health officials make more informed decisions and predictions based on the complex and uncertain causal mechanisms at play.
In social sciences, especially in areas like economics or sociology, where human behavior is influenced by a multitude of factors and is often unpredictable, the framework can provide a more nuanced understanding of causal relationships. By allowing for indeterministic causal laws, researchers can model the intricate interactions between various social, economic, and environmental factors that shape human behavior and societal outcomes. This can lead to more accurate predictive models and better policy recommendations in areas such as poverty alleviation, education, or urban planning.

How could the current framework be extended to also handle probabilistic causal laws, in addition to the purely indeterministic ones considered here

To extend the current framework to handle probabilistic causal laws in addition to purely indeterministic ones, modifications and enhancements would be required. One approach could be to introduce a probabilistic component to the relational causal teams, where the relations between variables represent probabilistic dependencies instead of deterministic ones. This would involve incorporating probability distributions into the causal laws to capture the likelihood of different outcomes based on the input variables.
Another extension could involve integrating Bayesian networks into the framework, where probabilistic graphical models are used to represent causal relationships between variables. By combining the relational causal teams with Bayesian networks, researchers can model both deterministic and probabilistic causal mechanisms in a unified framework. This hybrid approach would allow for a more comprehensive representation of causal relationships, accommodating both indeterministic and probabilistic aspects of causality.
Furthermore, the framework could be extended to include causal inference techniques that are specifically designed for handling probabilistic causal relationships, such as causal Bayesian networks or causal graphical models. These methods can provide a formalism for estimating causal effects in the presence of uncertainty and variability, allowing researchers to make more accurate and reliable causal inferences from observational data.

Are there any connections or analogies between the logical principles governing interventionist counterfactuals in indeterministic causal models and the philosophical debates around free will and determinism

There are indeed connections and analogies between the logical principles governing interventionist counterfactuals in indeterministic causal models and the philosophical debates around free will and determinism. The concept of interventionist counterfactuals, which involves reasoning about the effects of interventions on causal systems, can be related to the philosophical question of free will and determinism.
In the context of indeterministic causal models, interventionist counterfactuals allow us to explore the potential outcomes of different interventions on a system with indeterministic causal laws. This mirrors the philosophical debate between free will and determinism, where the idea of interventions can be seen as analogous to human agency and the ability to make choices that influence outcomes in a world where causality is not strictly deterministic.
Furthermore, the notion of counterfactuals in indeterministic causal models raises questions about the nature of causation, agency, and responsibility in a world where outcomes are not predetermined. This parallels the philosophical discussions about free will, moral responsibility, and the implications of determinism on human actions and choices.
By studying interventionist counterfactuals in the context of indeterministic causal models, we can gain insights into how causal relationships operate in complex and uncertain systems, shedding light on the interplay between causality, agency, and unpredictability. This can contribute to both the philosophical discourse on free will and determinism and the practical applications of causal reasoning in various fields.