Implementing Default and Autoepistemic Logics via the Logic of GK
This work provides a computational method for AI researchers and practitioners dealing with nonmonotonic reasoning, though it is incremental as it builds on existing embeddings of other logics into GK.
The paper tackles the problem of computing nonmonotonic reasoning semantics by embedding the logic of grounded knowledge (GK) into disjunctive logic programming via a polynomial translation, enabling the use of ASP solvers like claspD(-2) to compute extensions/expansions for default logic, autoepistemic logic, and Turner's logic.
The logic of knowledge and justified assumptions, also known as logic of grounded knowledge (GK), was proposed by Lin and Shoham as a general logic for nonmonotonic reasoning. To date, it has been used to embed in it default logic (propositional case), autoepistemic logic, Turner's logic of universal causation, and general logic programming under stable model semantics. Besides showing the generality of GK as a logic for nonmonotonic reasoning, these embeddings 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 programming in a polynomial but non-modular translation with new variables. The result can then be used to compute the extension/expansion semantics of default logic, autoepistemic logic and Turner's logic of universal causation by disjunctive ASP solvers such as claspD(-2), DLV, GNT and cmodels.