Relative Expressiveness of Defeasible Logics

TL;DR

This paper investigates the relative expressiveness of different defeasible logics within the DL framework, focusing on their ability to simulate each other's reasoning capabilities and how features like team defeat and ambiguity handling affect this.

Contribution

It establishes conditions for simulation-based relative expressiveness and compares the expressiveness of logics with different features like team defeat and ambiguity handling.

Findings

Logics with and without team defeat are equally expressive.

Ambiguity blocking and propagating logics are not mutually simulatable.

Simulation must be modular to be meaningful.

Abstract

We address the relative expressiveness of defeasible logics in the framework DL. Relative expressiveness is formulated as the ability to simulate the reasoning of one logic within another logic. We show that such simulations must be modular, in the sense that they also work if applied only to part of a theory, in order to achieve a useful notion of relative expressiveness. We present simulations showing that logics in DL with and without the capability of team defeat are equally expressive. We also show that logics that handle ambiguity differently -- ambiguity blocking versus ambiguity propagating -- have distinct expressiveness, with neither able to simulate the other under a different formulation of expressiveness.