Generating readable proofs: A heuristic approach to theorem proving with spider diagrams

Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)

Volumn 2980, Issue , 2004, Pages 166-181

  Flower, Jean ^a   Masthoff, Judith ^a   Stapleton, Gem ^a  

^a UNIVERSITY OF BRIGHTON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; FUNCTIONS; PROBLEM SOLVING; THEOREM PROVING; HEURISTIC ALGORITHMS; HEURISTIC METHODS;

CONSTRAINT DIAGRAMS; PROOF WRITING; REASONING SYSTEMS; SPIDER DIAGRAMS; AUTOMATIC PROOFS; AUTOMATICALLY GENERATED; DIAGRAMMATIC REASONING; HEURISTIC APPROACH; HEURISTIC FUNCTIONS; LOGICAL STATEMENTS; READABLE PROOFS;

HEURISTIC METHODS; GRAPHIC METHODS;

EID: 9444275418     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-25931-2_17     Document Type: Conference Paper

References (22)

1. B. I. Bahn and A. Wolf. Natural language presentation and combination of automatically generated proofs. Proc. Frontiers of Combining Systems, Muenchen, Germany, p175-192, 1996.
2. R. Dechter, and J. Pearl. Generalized best-first search strategies and the optimality of A*. Journal of the Association for Computing Machinery, 32, 3, p505-536. 1985.
3. A. Fish, J. Flower, and J. Howse. A Reading algorithm for constraint diagrams. Proc. IEEE Symposium on Visual Languages and Formal Methods, New Zealand, 2003.
4. J. Flower, and G. Stapleton. Automated Theorem Proving with Spider Diagrams. Proc. Computing: The Australasian Theory Symposium, Elsevier science, 2004.
5. C. Goller. Learning search-control heuristics for automated deduction systems with folding architecture networks. Proc. European Symposium on Artificial Neural Networks. D-Facto publications, Apr 1999.
6. P.E. Hart, N.J. Nilsson, and B. Raphael. A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on System Science and Cybernetics, 4, 2, p100-107, 1968.
7. J. Flower, and J. Howse. Generating Euler Diagrams, Proc. Diagrams p.61-75, Springer-Verlag, 2002.
8. J. Howse, F. Molina, and J. Taylor. SD2: A sound and complete diagrammatic reasoning system. Proc. IEEE Symposium on Visual Languages (VL2000), IEEE Computer Society Press p.402-408, 2000.
9. M. Jamnik, Mathematical Reasoning with Diagrams, CSLI Publications, 2001.
10. G. F. Luger. Artificial intelligence: Structures and strategies for complex problem solving. Fourth Edition. Addison Wesley: 2002.
11. D. MacKenzie. Computers and the sociology of mathematical proof. Proc. 3rd Northern Formal Methods Workshop, 1998. http://wwwl.bcs.org.uk/ DocsRepository/02700/2713/mackenzi.pdf.
12. S. Oppacher and S. Suen. HARP: A tableau-based theorem prover. Journal of Automated Reasoning, 4, p69-100, 1988.
13. F. Piroi and B. Buchberger. Focus windows: A new technique for proof presentation. In J. Calmet, B. Benhamou, O. Caprotti, L. Henocque, and V. Sorge, editors, Artificial Intelligence, Automated Reasoning and Symbolic Computation. Proceedings of Joint AICS'2002 - Calculemus'2002 Conference, Marseille, France, July 2002. Springer Verlag, http://www.risc.unilinz.ac.at/people/buchberg/ papers/2002-02-25-A.pdf [Accessed August 2003].
14. S.-J. Shin. The Logical Status of Diagrams. Camb. Uni. Press, 1994.
15. J. Schumann and P. Robinson. □ or SUCCESS is not enough: Current technology and future directions in proof presentation. Proc. IJCAR workshop: Future directions in automated reasoning, 2001.
16. G. Stapleton, J. Howse, and J. Taylor. A constraint diagram reasoning system. Proc. International conference on Visual Languages and Computing, Knowledge systems institute, pp 263-270, 2003.
17. G. Stapleton, J. Howse, J. Taylor and S. Thompson. What can spider diagrams say? Proc. Diagrams 2004.
18. N. Swoboda. Implementing Euler/Venn reasoning systems, In Diagrammatic Representation and Reasoning, Anderson, M., Meyer, B., and Oliver, P., eds, p.371-386 Springer-Verlag, 2001.
19. N. Swoboda and G. Allwein. Using DAG Transformations to Verify Euler/Venn Homogeneous and Euler/Venn FOL Heterogeneous Rules of Inference. Electronic Notes in Theoretical Computer Science, 72, No. 3 (2003).
20. The Visual Modelling Group website. www.cmis.brighton.ac.uk/research/vmg.
21. The Visual Modelling Group technical report on spider diagram reasoning systems at www.cmis.brighton.ac.uk/research/vmg/SDRules.html.
22. W. Windsteiger. An automated prover for Zermelo-FVaenkel set theory in Theorema. LMCS, 2002.