Relative Expressiveness of Defeasible Logics II

TL;DR

This paper compares different defeasible logics, showing that most are equally expressive except for differences in ambiguity handling, completing a prior study on their relative expressiveness.

Contribution

It demonstrates that all defeasible logics in the DL framework are equally expressive under the first notion, and clarifies the impact of defeat and ambiguity handling on expressiveness.

Findings

All DL logics are equally expressive under the first definition.

Logics with individual defeat are as expressive as those with team defeat.

Differences in expressiveness mainly stem from ambiguity handling.

Abstract

(Maher 2012) introduced an approach for relative expressiveness of defeasible logics, and two notions of relative expressiveness were investigated. Using the first of these definitions of relative expressiveness, we show that all the defeasible logics in the DL framework are equally expressive under this formulation of relative expressiveness. The second formulation of relative expressiveness is stronger than the first. However, we show that logics incorporating individual defeat are equally expressive as the corresponding logics with team defeat. Thus the only differences in expressiveness of logics in DL arise from differences in how ambiguity is handled. This completes the study of relative expressiveness in DL begun in \cite{Maher12}.