This thesis deals with advanced notions of equivalence between nonmonotonic logic programs under the answer-set semantics, a topic of increasing interest because such notions form the basis for program optimisation, debugging, modular programming, and program verification.
In fact, there is extensive research in answer-set programming dealing with different notions of equivalence between programs. Prominent among these notions is uniform equivalence which checks whether two programs have the same semantics when joined with an arbitrary set of facts. In this thesis, we study a family of more fine-grained versions of uniform equivalence, viz. relativised uniform equivalence with projection, which extends standard uniform equivalence in terms of two additional parameters: one for specifying the input alphabet and one for specifying the output alphabet for programs.