Relative Expressiveness of Defeasible Logics
This work addresses foundational issues in non-monotonic reasoning for AI and logic communities, providing incremental insights into the expressiveness of defeasible logics.
The paper tackles the problem of comparing the expressiveness of defeasible logics by defining relative expressiveness through modular simulations, showing that logics with and without team defeat are equally expressive, while ambiguity blocking and ambiguity propagating logics have distinct expressiveness and cannot simulate each other.
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.