Causality and Decision-making: A Logical Framework for Systems and Security Modelling

TL;DR

This paper develops a logical framework for understanding causality and decision-making in complex systems, integrating modal logic, causal models, and counterfactual reasoning to analyze system behavior and security.

Contribution

It introduces a minimalistic logical theory combining transition systems, modal logic, and causal reasoning, with novel operators for intervention and separation, applicable to distributed microservices.

Findings

Framework unifies causal reasoning with system modeling.

Validated through equivalence theorems and examples.

Applicable to decision-making in distributed systems.

Abstract

Causal reasoning is essential for understanding decision-making about the behaviour of complex `ecosystems' of systems that underpin modern society, with security -- including issues around correctness, safety, resilience, etc. -- typically providing critical examples. We present a theory of strategic reasoning about system modelling based on minimal structural assumptions and employing the methods of transition systems, supported by a modal logic of system states in the tradition of van Benthem, Hennessy, and Milner, and validated through equivalence theorems. Our framework introduces an intervention operator and a separating conjunction to capture actual causal relationships between component systems of the ecosystem, aligning naturally with Halpern and Pearl's counterfactual approach based on Structural Causal Models. We illustrate the applicability through examples of of decision-making about microservices in distributed systems. We discuss localized decision-making through a separating conjunction. This work unifies a formal, minimalistic notion of system behaviour with a Halpern--Pearl-compatible theory of counterfactual reasoning, providing a logical foundation for studying decision making about causality in complex interacting systems.