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Published in:
2014 | OriginalPaper | Chapter
A Generalization of Approximation Fixpoint Theory and Application
Authors : Yi Bi, Jia-Huai You, Zhiyong Feng
Published in: Web Reasoning and Rule Systems
Publisher: Springer International Publishing
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The approximation fixpoint theory (AFT) provides an algebraic framework for the study of fixpoints of operators on bilattices, and has been useful in dealing with semantics issues for various types of logic programs. The theory in the current form, however, only deals with consistent pairs on a bilattice, and it thus does not apply to situations where inconsistency may be part of a fixpoint construction. This is the case for FOL-programs, where a rule set and a first-order theory are tightly integrated. In this paper, we develop an extended theory of AFT that treats consistent as well as inconsistent pairs on a bilattice. We then apply the extended theory to FOL-programs and explore various possibilities on semantics. This leads to novel formulations of approximating operators, and new well-founded semantics and characterizations of answer sets for FOL-programs. The work reported here shows how consistent approximations may be extended to capture wider classes of logic programs whose semantics can be treated uniformly.