Inference with System W Satisfies Syntax Splitting

TL;DR

This paper demonstrates that system W, a nonmonotonic reasoning inference system, satisfies the syntax splitting postulates, extending rational closure and aligning with the principles of relevance and independence in inductive inference.

Contribution

It proves that system W fulfills syntax splitting postulates, making it a new inference operator that extends rational closure and complies with relevance and independence.

Findings

System W satisfies syntax splitting postulates.

System W extends rational closure.

System W aligns with relevance and independence principles.

Abstract

In this paper, we investigate inductive inference with system W from conditional belief bases with respect to syntax splitting. The concept of syntax splitting for inductive inference states that inferences about independent parts of the signature should not affect each other. This was captured in work by Kern-Isberner, Beierle, and Brewka in the form of postulates for inductive inference operators expressing syntax splitting as a combination of relevance and independence; it was also shown that c-inference fulfils syntax splitting, while system P inference and system Z both fail to satisfy it. System W is a recently introduced inference system for nonmonotonic reasoning that captures and properly extends system Z as well as c-inference. We show that system W fulfils the syntax splitting postulates for inductive inference operators by showing that it satisfies the required properties of relevance and independence. This makes system W another inference operator besides c-inference that fully complies with syntax splitting, while in contrast to c-inference, also extending rational closure.