8 research outputs found
Implementing Default and Autoepistemic Logics via the Logic of GK
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.Comment: Proceedings of the 15th International Workshop on Non-Monotonic
Reasoning (NMR 2014
Stable Models of Formulas with Generalized Quantifiers (Preliminary Report)
Applications of answer set programming motivated various extensions of the stable model semantics, for instance, to allow aggregates or to facilitate interface with external ontology descriptions. We present a uniform, reductive view on these extensions by viewing them as special cases of formulas with generalized quantifiers. This is done by extending the first-order stable model semantics by Ferraris, Lee and Lifschitz to account for generalized quantifiers and then by reducing the individual extensions to this formalism
From answer set logic programming to circumscription via logic of GK
We first embed Pearce's equilibrium logic and Ferraris's propositional general logic programs in Lin and Shoham's logic of GK, a nonmonotonic modal logic that has been shown to include as special cases both Reiter's default logic in the propositional case and Moore's autoepistemic logic. From this embedding, we obtain a mapping from Ferraris's propositional general logic programs to circumscription, and show that this mapping can be used to check the strong equivalence between two propositional logic programs in classical logic. We also show that Ferraris's propositional general logic programs can be extended to the first-order case, and our mapping from Ferraris's propositional general logic programs to circumscription can be extended to the first-order case as well to provide a semantics for these first-order general logic programs. © 2010 Elsevier B.V. All rights reserved