Abstract
Improvements in formal reasoning systems enable these systems to produce large sets of solutions that may grow rather complex. However, automatically generated presentations of these data lack a sufficient degree of conciseness. In order to improve the presentation of problem solutions that can be casted in terms of sets of ground atoms, we adapt linguistic aggregation techniques to specificities of formal problems. We define novel constructs that can express sets of propositions with highly regular alternations on predicate argument values concisely, including special forms of disjunctions and versions for formulas. We demonstrate applications to model generation and to categorization proofs. The presentations obtained highlight commonalities among and differences across solution parts in a much better way than previous approaches do, thereby supporting the inspection of properties holding across several solutions, and the discovery of flaws in problem specifications.
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
Busemann, S.: Best-First Generation. In: Proc. of the 8th International Workshop on Natural Language Generation, Hearstmonceaux, UK, pp. 101–110 (1996)
Colton, S., Bundy, A., Walsh, T.: Automatic Concept Formation in Pure Mathematics. In: Proc. of IJCAI 1999, Stockholm, pp. 786–793 (1999)
Coscoy, Y., Kahn, G., Théry, L.: Extracting Text from Proof. Typed Lambda Calculus and its Application (1995)
Dahn, I.: Using ILF as a User Interface for Many Theorem Provers. In: Proc. of User Interfaces for Theorem Provers, Eindhoven (1998)
Dalianis, H.: Aggregation in Natural Language Generation. Computational Intelligence 15(4) (1999)
Freihat, H.: Realisierung aggregierter Ausdrücke in mehreren Sprachen und mit Formeln. Master thesis, University of the Saarland (forthcoming)
Giunchiglia, F., Villafiorita, A., Walsh, T.: Theories of Abstrction. AI Communications 10(3-4), 167–176 (1997)
Horacek, H., Konrad, K.: Presenting Herbrand Models with Linguistically Motivated Techniques. In: Proc. of CIMCA 1999, Vienna (1999)
Huang, X., Fiedler, A.: Proof Verbalization as an Application of NLG. In: 15th International Conference on Artificial Intelligence, Nagoya, Japan, pp. 965–970 (1997)
Konrad, K., Wolfram, D.: System Description: Kimba, A Model Generator for Many-Valued First-Order Logics. In: 16th Proc. of CADE, Trento, Italy, pp. 282–286 (1999)
Mann, B., Moore, J.: Computer as Author – Results and Prospects. Research Report ISI/RR-79-82, Univ. of Southern California, Information Sciences Institute (1980)
Mann, B., Moore, J.: Computer Generation of Multiparagraph English Text. American Journal of Computational Linguistics 8(2), 17–29 (1981)
Meier, A., Pollet, M., Sorge, V.: Comparing Approaches to Explore the Domain of Residue Classes. Journal of Symbolic Computation 34(4), 287–306 (2002)
Reape, M., Mellish, C.: What is Aggregation Anyhow? In: Proc. of 7th European Workshop on Natural Language Generation, Toulouse, France (1999)
Shaw, J.: Segregatory Coordination and Ellipsis in Text Generation. In: Proc. of the 36th ACL and the 17th COLING, pp. 1220–1226 (1998)
Shaw, J.: Clause Aggregation Using Linguistic Knowledge. In: Proc. of the 9th International Workshop on Natural Language Generation, pp. 138–147 (1998)
Siekmann, J., Benzmüller, C., Brezhnev, V., Cheikhrouhou, L., Fiedler, A., Franke, A., Horacek, H., Kohlhase, M., Meier, A., Melis, E., Moschner, M., Normann, I., Pollet, M., Sorge, V., Ullrich, C., Wirth, C.-P., Zimmer, J.: Proof Development with 0MEGA. In: Proc. of the 18th CADE-02, Kopenhagen, pp. 144–149 (2002)
Stickel, M.: Schubert’s Steamroller Problem: Formalisation and Solutions. Journal of Automated Reasoning 2(1), 89–101 (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Horacek, H. (2003). Presenting Sets of Problem Solutions Concisely. In: Günter, A., Kruse, R., Neumann, B. (eds) KI 2003: Advances in Artificial Intelligence. KI 2003. Lecture Notes in Computer Science(), vol 2821. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39451-8_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-39451-8_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20059-8
Online ISBN: 978-3-540-39451-8
eBook Packages: Springer Book Archive