Logical Approach to Theorem Proving with Term Rewriting on KR-logic

Tadayuki Yoshida, Ekawit Nantajeewarawat, Masaharu Munetomo, Kiyoshi Akama

2019

Abstract

Term rewriting is often used for proving theorems. To mechanizing such a proof method with computation correctness guaranteed strictly, we follow LPSF, which is a general framework for generating logical problem solution methods. In place of the first-order logic, we use KR-logic, which has function variables, for correct formalization. By repeating (1) specialization by a substitution for usual variables, and (2) application of an already derived rewriting rule, we can generate a term rewriting rule from the resulting equational clause. The obtained term rewriting rules are proved to be equivalent transformation rules. The correctness of the computation results is guaranteed. This theory shows that LPSF integrates logical inference and functional rewriting under the broader concept of equivalent transformation.

Paper Citation

in Harvard Style

Yoshida T., Nantajeewarawat E., Munetomo M. and Akama K. (2019). Logical Approach to Theorem Proving with Term Rewriting on KR-logic. In Proceedings of the 11th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2019) - Volume 2: KEOD; ISBN 978-989-758-382-7, SciTePress, pages 282-289. DOI: 10.5220/0008165902820289

in Bibtex Style

@conference{keod19,
author={Tadayuki Yoshida and Ekawit Nantajeewarawat and Masaharu Munetomo and Kiyoshi Akama},
title={Logical Approach to Theorem Proving with Term Rewriting on KR-logic},
booktitle={Proceedings of the 11th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2019) - Volume 2: KEOD},
year={2019},
pages={282-289},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0008165902820289},
isbn={978-989-758-382-7},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 11th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2019) - Volume 2: KEOD
TI - Logical Approach to Theorem Proving with Term Rewriting on KR-logic
SN - 978-989-758-382-7
AU - Yoshida T.
AU - Nantajeewarawat E.
AU - Munetomo M.
AU - Akama K.
PY - 2019
SP - 282
EP - 289
DO - 10.5220/0008165902820289
PB - SciTePress