Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning. Essays Dedicated to Michael Gelfond on the Occasion of His 65th Birthday pages:12 -32
Much research in logic programming and non-monotonic reasoning originates from dissatisfaction with classical logic as a knowledge representation language, and with classical deduction as a mode for automated reasoning. Discarding these classical roots has generated many interesting and fruitful ideas. However, to ensure the lasting impact of the results that have been achieved, it is important that they should not remain disconnected from their classical roots. Ultimately, a clear picture
should emerge of what the achievements of answer set programming mean in the context of classical logic, so that they may be given their proper place in the canon of science. In this paper, a look at different aspects of ASP, in an effort to identify precisely the limitations of classical logic that they exposed and investigate how the ASP approaches can be transferred back to the classical setting. Among the issues we thus address are the closed world assumption, "classical" and default negation, default reasoning with exceptions, definitions, lp-functions and the
interpolation technique and the strong introspection operator. We investigate the ASP-methodology to encode knowledge using these language constructs and come across a dichotomy in the ASP-methodology.