Integration of reasoning and algebraic calculus in geometry

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1360, Issue , 1997, Pages 218-234

  Fèvre, Stéhane ^a  

^a INPG IMAG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATION; BIOMINERALIZATION; CALCULATIONS; FORMAL LOGIC; GEOMETRY; SEMANTICS; THEOREM PROVING;

ALGEBRAIC CONSTRAINTS; ALGEBRAIC METHOD; ELEMENTARY GEOMETRY; FIRST ORDER LOGIC; GEOMETRY THEOREM; INFERENCE RULES; PROOF THEORY;

ALGEBRA;

EID: 84956993981     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/bfb0022718     Document Type: Conference Paper

References (22)

1. Bourely, C., Caferra, R. and Peltier, N.: A method for building models automaticatly: Experiments with an extension of OTTER. In: Proceedings of CADE-12, Springer Verlag, LNAI 814, 72-86, 1994.
2. Buchberger, B.: Gröbner bases: An algorithmic method in polynomial ideal theory. In: Multidimensional Systems Theory, Bose, N.K. ed., D. Reidel Publ. Comp., 184-232, 1985.
3. Caferra, R. and Herment, M.: A generic graphic framework for combining inference tools and editing proofs arid formulae. Journal of Symbolic'Computation, 19, 217-243, 1995.
4. Collins, G.E.: Quantifier elimination for the elementary geometry. In: Proceedings of 2nd G.I. Conference on Automata Theory and Formal Languages, Brakhage, H. ed., LNCS 33, 134-183, 1975.
5. Caferra, R. and Zabel, N.: A method for simultaneous search for refutations and models by equational constraint solving. Journal of Symbolic Computation, 13, 613-641, 1992.
6. Chang, C.-L. and Lee, R.C.-T.: Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York-London, 1973.
7. Chou, S-C., Gao, X-S. and Zhang, J-Z.: Automated generation of readable proofs with geometric invariants: I. Multiple and shortest proof generation. Journal of Automated Reasoning. 17, 325-347, 1996.
8. Chou, S-C., Gao, X-S. and Zhang, J-Z.: Automated generation of readable proofs with geometric invariants: II. Theorem proving with full-angles. Journal of Automated Reasoning, 17, 350-370, 1996.
9. Coelho, P. and Pereira, L.M.: Automated reasoning in geometry theorem proving with Prolog. Journal of Automated Reasoning, 2, 329-390, 1996.
10. McCune, W.W.: OTTER 2. 0. In: Proceedings of CADE-10, Springer-Verlag, LNAI 449, 663-664, 1990.
11. Fèvre, S.: A hybrid method for proving theorems in elementary geometry. In: Proceedings of ASCM'95, Scientists Incorporated, 113-123, 1995.
12. Kapur, D., Mundy, J.L. eds.: Geometric Reasoning. MIT Press, Cambridge, 1989.
13. Liu, Z. and Wu, J.: The remainder method for the first-order theorem proving. In: Proceedings of ASCM'95, Scientists Incorporated, 91-97, 1995.
14. Quaife, A.: Automated development of Tarski's geometry. Journal of Automated Reasoning, 5, 97-118, 1989.
15. Robinson, J.A.: A machine-oriented logic based on the resolution principle. Journal of the ACM, 12 23-41, 1965.
16. Stickel, M.E.: Automated deduction by theory resolution. Journal of Automated Reasoning, 1 333-355, 1985.
17. Tarski, A.: A Decision Method for Elementary Algebra and Geometry, 2nd edition. University of California Press, Berkeley and Los Angeles, 1951.
18. Trainen, R.: A new method for undecidability proofs of first-order theories. Journal of Symbolic Computation, 14(5), 437-458, 1990.
19. Wang, D.: Reasoning about geometric problems using an elimination method. In: Automated Practical Reasoning: Algebraic Approaches, Pfalzgraf, J., Wang, D. eds, Springer-Verlag, 147-185, 1996.
20. Wang, D.: An elimination method for polynomial systems. Journal of Symbolic Computation, 16, 83-114, 1993.
21. Wu, W.: Basic principles of mechanical theorem proving in elementary geometries. Journal of Automated Reasoning, 2, 221-252, 1986.
22. Wu, W.: Mechanical Theorem Proving in Geometries: Basic Principles. Springer-Verlag, Wien-New York, 1994.machines: From AI to SMC, in Proc. AISMC-3, LNCS 1138 (1996), 213-239.