Abstract
We describe a method to build an environment for processing mathematical domains of computation. Basically, the environment may aid the user in: (i) specifying correct abstract computational structures and their models, (ii) completing the sets of properties of operators by means of a learning method and (iii) determining the correct domain in which a mathematical computation must be performed. The system is built upon a hybrid knowledge representation system.
Preview
Unable to display preview. Download preview PDF.
References
Bachmaier, L., Dershowitz, N., Hsiang, J.: Proof Orderings for Equational Proof; Proc. LISC 86, 346–357.
Bibel, W.: Automated Theorem Proving; Vieweg; 1982.
Belnap N.D.: A Useful Four-Valued Logic; in “Modern Uses of Multiple-Valued Logic”, ed. G. Epstein and J.M. Dunn, on: Reidel, 1977, pp. 8–37.
Bittencourt G.: An Architecture for Hybrid Knowledge Representation; Ph D Thesis; Universität Karlsruhe; 1990.
Brachman R.J., Fikes R.E., Levesque H.J.: KRYPTON: A Functional Approach to Knowledge Representation; IEEE Computer, 16 (10), pp. 67–73, 1983.
Horty J.F., Thomason R.H., Touretzky D.S.: A Skeptical Theory of Inheritance in Nonmonotonic Semantic Nets; Report CMU-CS-87-175, Carnegie-Mellon Univ., 1987.
Knuth D.E., Bendix P.B.: Simple Word Problems in Universal Algebras; OXFORD, 263–298; 1967.
Martelli A., Montanari U.: An Efficient Unification Algorithm; ACM-TOPLAS, 4(2), pp. 258–282, 1982.
Mitchell T.M., Keller R.M., Kedar-Ceballi S.T.: Explanation-Based Generalization: A Unifying View; Machine Learning 1 47–80; Kluwer Academic Publishers; 1986.
Patel-Schneider P.F.: A Decidable First-Order Logic for Knowledge Representation; Proceedings of IJCAI 9, pp. 455–458, 1985.
Waldinger, R.: Achieving Several Goals Simultaneously; in Machine Intelligence 6 (eds. E. Elcock and D. Michie), 94–136, Ellis Horwood; 1977.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Calmet, J., Tjandra, I.A. (1991). Representation of mathematical knowledge. In: Ras, Z.W., Zemankova, M. (eds) Methodologies for Intelligent Systems. ISMIS 1991. Lecture Notes in Computer Science, vol 542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54563-8_110
Download citation
DOI: https://doi.org/10.1007/3-540-54563-8_110
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54563-7
Online ISBN: 978-3-540-38466-3
eBook Packages: Springer Book Archive