We revisit the framework of Computational Logic by Kowalski and recast some of its ideas within the formal setting of Answer Set Programming. This shift allows us to abstract away from procedural concerns and instead rely on the semantic properties of programs and the computational capabilities of answer set solvers. In addition, shadowing the narrative by Kowalski allows us to shed the light on logic programs with and without strong negation as well as these that allow users to write not not preceding an atom in the rule. We discuss formal and informal properties of these connectives and the possibilities for their elimination.