On the Conditional Logic of Simulation Models

TL;DR

This paper introduces a formal framework for analyzing conditional reasoning in simulation models through interventions, providing axiomatizations, complexity analysis, and highlighting differences from existing approaches.

Contribution

It formalizes conditional reasoning via interventions in simulation models, compares it with existing frameworks, and establishes NP-completeness of satisfiability.

Findings

Axiomatizations of the proposed framework

Comparison with normality-ordering and causal models

NP-completeness of satisfiability problem

Abstract

We propose analyzing conditional reasoning by appeal to a notion of intervention on a simulation program, formalizing and subsuming a number of approaches to conditional thinking in the recent AI literature. Our main results include a series of axiomatizations, allowing comparison between this framework and existing frameworks (normality-ordering models, causal structural equation models), and a complexity result establishing NP-completeness of the satisfiability problem. Perhaps surprisingly, some of the basic logical principles common to all existing approaches are invalidated in our causal simulation approach. We suggest that this additional flexibility is important in modeling some intuitive examples.