Today I read a paper titled “Representation Theory for Default Logic”
The abstract is:
Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent.
As such, it is inherently second-order.
In this paper, we study the problem of representability of a family of theories as the set of extensions of a default theory.
We give a complete solution to the representability by means of normal default theories.
We obtain partial results on representability by arbitrary default theories.
We construct examples of denumerable families of non-including theories that are not representable.
We also study the concept of equivalence between default theories.