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Function-variable Elimination and Its Limitations
Description
The famous proof method by the conventional Skolemization and resolution has a serious limitation. It does not guarantee the correctness of proving theorems in the presence of built-in constraints. In order to understand this difficulty, we use meaning-preserving Skolemization (MPS) and equivalent transformation (ET), which together provide a general framework for solving query-answering (QA) problems on first-order logic. We introduce a rule for function variable elimination (FVE), by which we regard the conventional Skolemization as a kind of the composition of MPS and FVE. We prove that the FVE rule preserves the answers to a class of QA problems consisting of only user-defined atoms, while we cannot prove it in the presence of built-in constraints. By avoiding the application of the FVE rule in MPS & ET computation, we obtain a more general solution for proof problems, which guarantees the correctness of computation even in the presence of built-in constraints.
Journal
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- Proceedings of the 7th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management
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Proceedings of the 7th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management 212-222, 2015-01-01
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