Logic, Reasoning under Uncertainty and Causality

TL;DR

This paper introduces a unified framework that combines logic, uncertainty reasoning, and causality using set-theoretic approaches, enabling comprehensive modeling of knowledge and causal relationships.

Contribution

It extends traditional logic to incorporate uncertainty and causal reasoning through a novel set-theoretic framework and causal spaces.

Findings

Logic is reformulated in set-theoretic terms for certainty.

The framework is extended to handle uncertainty.

Causal spaces effectively model causal knowledge.

Abstract

A simple framework for reasoning under uncertainty and intervention is introduced. This is achieved in three steps. First, logic is restated in set-theoretic terms to obtain a framework for reasoning under certainty. Second, this framework is extended to model reasoning under uncertainty. Finally, causal spaces are introduced and shown how they provide enough information to model knowledge containing causal information about the world.