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Authors: Kiyoshi Akama 1 and Ekawit Nantajeewarawat 2

Affiliations: 1 Hokkaido University, Japan ; 2 Thammasat University, Thailand

ISBN: 978-989-758-158-8

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.

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Paper citation in several formats:
Akama, K. and Nantajeewarawat, E. (2015). Function-variable Elimination and Its Limitations.In Proceedings of the 7th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 2: KEOD, (IC3K 2015) ISBN 978-989-758-158-8, pages 212-222. DOI: 10.5220/0005597202120222

@conference{keod15,
author={Kiyoshi Akama. and Ekawit Nantajeewarawat.},
title={Function-variable Elimination and Its Limitations},
booktitle={Proceedings of the 7th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 2: KEOD, (IC3K 2015)},
year={2015},
pages={212-222},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005597202120222},
isbn={978-989-758-158-8},
}

TY - CONF

JO - Proceedings of the 7th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 2: KEOD, (IC3K 2015)
TI - Function-variable Elimination and Its Limitations
SN - 978-989-758-158-8
AU - Akama, K.
AU - Nantajeewarawat, E.
PY - 2015
SP - 212
EP - 222
DO - 10.5220/0005597202120222

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