Function-variable Elimination and Its Limitations

Kiyoshi Akama, Ekawit Nantajeewarawat

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.

References

  1. Akama, K. and Nantajeewarawat, E. (2011a). MeaningPreserving Skolemization. In Proceedings of the 3rd International Conference on Knowledge Engineering and Ontology Development, pages 322-327, Paris, France.
  2. Akama, K. and Nantajeewarawat, E. (2011b). MeaningPreserving Skolemization. Technical report, Hokkaido University, Sapporo, Japan.
  3. Akama, K. and Nantajeewarawat, E. (2012). Proving Theorems Based on Equivalent Transformation Using Resolution and Factoring. In Proceedings of the Second World Congress on Information and Communication Technologies, WICT 2012, pages 7-12, Trivandrum, India.
  4. Akama, K. and Nantajeewarawat, E. (2013). Embedding Proof Problems into Query-Answering Problems and Problem Solving by Equivalent Transformation. In Proceedings of the 5th International Conference on Knowledge Engineering and Ontology Development, pages 253-260, Vilamoura, Portugal.
  5. Akama, K. and Nantajeewarawat, E. (2014). Equivalent Transformation in an Extended Space for Solving Query-Answering Problems. In Proceedings of the 6th Asian Conference on Intelligent Information and Database Systems, LNAI 8397, pages 232-241, Bangkok, Thailand.
  6. Akama, K. and Nantajeewarawat, E. (2015). FunctionVariable Elimination and Its Limitations. Technical report, Hokkaido University, Sapporo, Japan.
  7. Chang, C.-L. and Lee, R. C.-T. (1973). Symbolic Logic and Mechanical Theorem Proving. Academic Press.
  8. Motik, B., Sattler, U., and Studer, R. (2005). Query Answering for OWL-DL with Rules. Journal of Web Semantics, 3(1):41-60.
  9. Robinson, J. A. (1965). A Machine-Oriented Logic Based on the Resolution Principle. Journal of the ACM, 12:23-41.
Download


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