Function-variable Elimination and Its Limitations

Kiyoshi Akama, Ekawit Nantajeewarawat

2015

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.

Paper Citation

in Harvard Style

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

in Bibtex Style

@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},
}

in EndNote Style

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