Implementing default and autoepistemic logics via the logic of GK

The logic of knowledge and justified assumptions, also known as the logic of grounded knowledge (GK), was pro-posed by Lin and Shoham as a general logic for nonmono-tonic reasoning. To date, it has been used to embed in it de-fault logic (propositional case), autoepistemic logic, Turner’s logic of universal causation, and general logic programming under stable model semantics. Besides showing the general-ity of GK as a logic for nonmonotonic reasoning, these em-beddings shed light on the relationships among these other logics. In this paper, for the first time, we show how the logic of GK can be embedded into disjunctive logic program-ming in a polynomial but non-modular translation with new variables. The result can then be used to compute the ex-tension/expansion semantics of default logic, autoepistemic logic and Turner’s logic of universal causation by disjunctive ASP solvers such as GNT, cmodels, DLV, and claspD(-2)