Abstract
Reasoning about uncertainty is one of the main cornerstones of Knowledge Representation. Formal representations of uncertainty are numerous and highly varied due to different types of uncertainty intended to be modeled such as vagueness, imprecision and incompleteness. There is a rich body of theoretical results that has been generated for many of these approaches. It is often the case though, that pragmatic tools for reasoning with uncertainty lag behind this rich body of theoretical results. Rough set theory is one such approach for modeling incompleteness and imprecision based on indiscernibility and its generalizations. In this paper, we provide a pragmatic tool for constructively reasoning with generalized rough set approximations that is based on the use of Answer Set Programming (Asp). We provide an interpretation of answer sets as (generalized) approximations of crisp sets (when possible) and show how to use Asp solvers as a tool for reasoning about (generalized) rough set approximations situated in realistic knowledge bases. The paper includes generic Asp templates for doing this and also provides a case study showing how these techniques can be used to generate reducts for incomplete information systems. Complete, ready to run clingoAsp code is provided in the Appendix, for all programs considered. These can be executed for validation purposes in the clingoAsp solver.
Highlights
We provide an interpretation of answer sets as approximations of crisp sets and show how to use Answer Set Programming (Asp) solvers as a tool for reasoning about rough set approximations situated in realistic knowledge bases
Show how to use Asp solvers as a tool for reasoning about rough set approximations situated in realistic knowledge bases
We have shown how Asps, an established tool for reasoning about incomplete relations and nonmonotonic reasoning, can be leveraged to serve as a basis for reasoning about generalized rough set approximations
Summary
Formal representations of uncertainty are numerous and highly varied due to different types of uncertainty intended to be modeled such as vagueness, imprecision and incompleteness. By combining rough relations as components in Asp rules, and using the heuristic techniques associated with Asp such as CWA or LCWA, the status of elements in the boundary region can be changed by default using commonsense or expert knowledge associated with an application at hand. This in turn can result in a substantial improvement of the informational quality of rough knowledge bases used in such applications.
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