Authors:
Kiyoshi Akama
1
and
Ekawit Nantajeewarawat
2
Affiliations:
1
Hokkaido University, Japan
;
2
Thammasat University, Thailand
Keyword(s):
Query-answering Problem, Equivalent Transformation, Meaning-preserving Skolemization, Problem Solving.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Knowledge Engineering and Ontology Development
;
Knowledge Representation
;
Knowledge-Based Systems
;
Symbolic Systems
Abstract:
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.