Abstract
This paper presents a new partial logic that generalises the traditional proposition and first order predicate logics for incompletely specified domains. Three values are considered in the partial logic (false, true, and don’t care) instead of two values considered in the traditional logic. The operations, formulas, laws, and inference rules constitute a basis for knowledge representation and deductive reasoning when the world is not completely specified. The Robinson’s resolution principle is generalised for situation when a clause can take the don’t care value. Methods for the transition from partial deductive reasoning to inference in the first order predicate logic are proposed. The presented theoretical results are illustrated with examples. The proposed models and methods speed up the deductive reasoning process and decrease the number of clauses needed for knowledge representation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Damiani, M. and de Micheli, G. Don’t care set specifications in combinational and synchronous logic circuits. IEEE Trans. On CAD, 12, 1993, pp. 365–388.
Filman, R. Reasoning with worlds and truth maintenance in a knowledge-based programming environment. Communications of the ACM, 31 (4), 1988, pp. 382–401.
Pliuskevicius, R. The saturated tableaux for linear miniscoped hom-like temporal logic. Journal of Automated Reasoning, 13, 1994, pp. 391–407.
Prihozhy, A. A. Methods of partial logic. Proc. Int. Conf. on Neuro Computers and Artificial Intelligence, Brest, 1999.
Prihozhy, A. A. Logic inference in partial logic. Intelligent Systems, Minsk, Belarus, 1998, pp. 123–140.
Prihozhy, A. A. Algebra of partial logic. New Technologies for Computers and Mechanics, Brest, Belarus, 1998, pp. 168–174.
Prihozhy, A. A. If-diagrams: theory and application. PATMOS’97: Proc. European Workshop, Belgium, 1997, pp. 369–378.
Robinson, J. A. A machine-oriented logic based on the resolution principle. Journal of the Association for Computing Machinary, 12 (1), 1965, pp. 23–41.
Sakalauskaite, J. Ordered Resolution for Finitely-Valued First-Order Logics. Preprintas Nr. 95–3, Vilnius, Lietuva, 1995, 10 p.
Zadeh, L. A. The Role of Fuzzy Logic in the Management of Uncertainty in Expert Systems. Approximate Reasoning in Expert Systems. Elsevier Science Publishers, North Holland, 1985, pp. 3–41.
Zavadskas, E., Peldschus, F., Kaklauskas, A. Multiple Criteria Evaluation of Projects in Construction. Vilnius, Technika, 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Prihozhy, A., Prihozhaya, L. (2001). Methods of Partial Logic for Knowledge Representation and Deductive Reasoning in Incompletely Specified Domains. In: Barzdins, J., Caplinskas, A. (eds) Databases and Information Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9636-7_22
Download citation
DOI: https://doi.org/10.1007/978-94-015-9636-7_22
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5657-3
Online ISBN: 978-94-015-9636-7
eBook Packages: Springer Book Archive