Comparing Meseguer's Rewriting Logic with the Logic CRWL

Meseguer’s rewriting logic and the rewriting logic CRWL are two well-known approaches to rewriting as logical deduction that, despite some clear similarities, were designed with different objectives. Here we study the relationships between them, both at a syntactic and at a semantic level. It is not possible to establish an entailment system map between them, but both can be naturally simulated in each other. Semantically, there is no embedding between the corresponding institutions. We also use the syntactic results to prove reflective properties of CRWL and to extend those already known for Meseguer’s rewriting logic.