Automated deduction looking ahead

AI Magazine

Volumn 20, Issue 1, 1999, Pages 77-98

  Loveland, Donald W ^a  

^a Duke University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MICROPROCESSOR CHIPS; TECHNICAL PRESENTATIONS;

AUTOMATED DEDUCTION;

ARTIFICIAL INTELLIGENCE;

EID: 0032631719     PISSN: 07384602     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (108)

1. Andrews, P. B. 1981. Transforming Matings into Natural Deduction Proofs. In Proceedings of the Fifth Conference on Automated Deduction, eds. W. Bibel and R. Kowalski, 281-292. Lecture Notes in Computer Science 87. Berlin: Springer-Verlag.
2. Andrews, P. B.; Bishop, M.; Issar, S.; Nesmith, D.; Pfenning, F.; and Xi, H. 1996. ITS: A Theorem-Proving System for Classical Type Theory. Journal of Automated Reasoning 16(3): 321-353.
3. Astrachan, O. L. 1994. METEOR: Exploring Model Elimination Theorem Proving. Journal of Automated Reasoning 13(3): 283-296.
4. Bachmair, L.; Ganzinger, H.; Lynch, C.; and Snyder, W. 1992. Basic Paramodulation and Superposition. In Proceedings of the Eleventh Conference on Automated Deduction, ed. D. Kapur, 462-476. Lecture Notes in Artificial Intelligence 607. Berlin: Springer-Verlag.
5. Barker-Plummer, D., andBailin, S. C. 1992. Graphical Theorem Proving: An Approach to Reasoning with the Help of Diagrams. In Proceedings of the European Conference on Artificial Intelligence, 55-59. New York: VViley.
6. Barker-Plummer, D.; Bailin, S. C.; and Ehrlichman, S. M. T. 1996. Diagrams and Mathematics. Paper presented at the Fourth International Symposium on Artificial Intelligence and Mathematics, eds. B. Selman and H. Kautz, 3-5 January, Fort Lauderdale, Florida.
7. Barwise, J., andEtchemendy, J. 1994. Hyperproof. Stanford, Calif.: Center for the Study of Language and Information.
8. Barwise, J., andEtchemendy, J. 1992. The Language of First-Order Logic. 3d ed. Stanford, Calif.: Center for the Study of Language and Information.
9. Beatty, D. L., andBryant, R. E. 1994. Formally Verifying a Microprocessor Using a Simulation Methodology. In Proceedings of the Thirty-First Design Automation Conference, 596-602. New York: Association of Computing Machinery.
10. Bledsoe, VV. W., andFeng, G. 1993. SETVAR. Journal of Automated Reasoning 11(3): 293-314.
11. Bledsoe, W. W., andHines, L. M. 1980. Variable Elimination and Chaining in a Resolution-Based Prover for Inequalities. In Proceedings of the Fifth Conference on Automated Deduction, eds. W. Bibel and R. Kowalski, 70-87. New York: Springer Verlag.
12. Bourbaki, N. 1968. Elements of Mathematics. Reading, Mass.: Addison Wesley.
13. Boyer, R. S., andMoore, J. S. 1988. A Computational Logic Handbook. San Diego, Calif.: Academic.
14. Brand, D. 1975. Proving Theorems with the Modification Method. SIAM Journal on Computing 4:412-430.
15. Bratko, 1.1990. Prolog Programming for Artificial Intelligence. Reading, Mass.: AddisonWesley.
16. Bratko, I., andMuggleton, S. 1995. Applications of Inductive Logic Programming. Communications of the ACM 38(11): 65-70.
17. Bundy, A.; Stevens, A.; van Harmelen, F.; . Ireland, A.; and Smaill, A. 1993. RIPPLING: A Heuristic for Guiding Induction Proofs. Artificial Intelligence 62(2): 185-253.
18. Bundy, A.; van Harmelen, F.; Hesketh, J.; and Smaill, A. 1991. Experiments with Proof Plans for Induction, foumal of Automated Reasoning 7(3): 303-324.
19. Burch, J. R.; Clarke, E. M.; McMillan, K. L.; Dill, D. L.; and Hwang, L. J. 1992. Symbolic Model Checking: 1020 States and Beyond. Information and Computation 98(2): 142-170.
20. Chou, S. C. 1988. Mechanical Geometry Tlieorem Proving. Dordrecht, The Netherlands: D. Reidel.
21. Chou, S. C.; Gao, X. S.; and Zhang, J. Z. 1994. Machine Proofs in Geometry. Singapore: World Scientific.
22. Clarke, E. M., andZhao, X. 1996. Combining Symbolic Computation and Theorem Proving: Some Problems of Ramanujan. In Proceedings of the Thirteenth Conference on Automated Deduction, eds. M. A. McRobbie and J. K. Slaney, 758-763. Lecture Notes in Artificial Intelligence 1104. Berlin: Springer-Verlag.
23. Clarke, E. M., andZhao, X. 1993. ANALVTICA: A Theorem Prover for MATHEMATICA. The Mathematica foumal 3(1): 56-71.
24. Clarke, E. M.; Emerson, E. A.; and Sistla, A. P. 1986. Automatic Verification of FiniteState Concurrent Systems Using Temporal Logic Specifications. ACM Transactions on Programming Languages and Systems 8(2): 244-263.
25. Constable, R., andMurthy, C. 1991. Finding Computational Content from Classical Proofs. In Logical Frameworks, eds. G. Huet and G. Plotkin, 341-362. Oxford, U.K.: Cambridge University Press.
26. Constable, R. L.; Alien, S. E; Bromley, H. M.; Cleaveland, W. R.; Cremer, J. F.; Harper, R. W.; Howe, D. J.; Knoblock, T. B.; Mendier, N. P.; Panangaden, P.; Sasaki, J. T.; and Smith, S. F. 1986. Implementing Mathematics with the NUPRL Proof Development System. New York: Prentice Hall.
27. Coquand, T., andHuet, G. 1988. The Calculus of Constructions. Information and Computation 76(2): 95-120.
28. Craigen, D.; Kromodimoeljo, S.; Meisels, I.; Pase, B.; and Saaltink, M. 1992. EVES System Description. In Proceedings of the Eleventh Conference on Automated Deduction, ed. D. Kapur, 771-775. Lecture Notes in Artificial Intelligence 607. Berlin: Springer-Verlag.
29. Craigen, D.; Kromodimoeljo, S.; Meiseis, I.; Pase, B.; and Saaltink, M. 1991. EVES: An Overview. In Proceedings of VDM'91, Noordwijkerhout, The Netherlands, October.
30. Dann, B. I., andWolf, A. 1996. Natural Language Presentation and Combination of Automatically Generated Proofs. In Proceedings of the First Conference on Frontiers of Combining Systems, 175-192. Norwell, Mass.: Kluwer Academic.
31. Dahn, B. L; Gehne, J.; Honigmann, T.; and Wolf, A. 1997. Integration of Automated and Interactive Theorem Proving in ILF. In Proceedings of the Fourteenth Conference on Automated Deduction, ed. W. W. McCune, 57-60. Lecture Notes in Artificial Intelligence 1249. Berlin: Springer-Verlag.
32. Davis, M., andPutnam, H. 1960. A Computing Procedure for Quantification Theory. Journal of the ACM 7:201-215.
33. Davis, M.; Logemann, G.; and Loveland, D. 1962. A Machine Program for Theorem Proving. Communications of the ACM 5(7): 394-397.
34. Dechter, R., andPearl, J. 1988. NetworkBased Heuristics for Constraint-Satisfaction Problems. Artificial Intelligence 34(1): 1-38.
35. Dechter, R., andRish, I. 1994. Directional Resolution: The Davis-Putnam Procedure Revisited. In Proceedings of the Third International Conference on Knowledge Representation and Reasoning (KR'94), 134-145. San Francisco, Calif.: Morgan Kaufmann.
36. Denzinger, J., andSchulz, S. 1996. Learning Domain Knowledge to Improve Theorem Proving. In Proceedings of the Thirteenth Conference on Automated Deduction, eds. M. A. McRobbie and J. K. Slaney, 62-76. Lecture Notes in Artificial Intelligence 1104. Berlin: Springer-Verlag.
37. Detlefs, D. 1996. An Overview of the Extended Static Checking System. In Proceedings of the First Workshop on Formal Methods in Software Practice (FMSP '96), 1-9. New York: Association for Computing Machinery.
38. Deville, Y. 1990. Logic Programming: Systematic Program Development. Reading, Mass.: Addison-Wesley.
39. Fujita, M.; Slaney, J.; and Bennett, F. 1993. Automatic Generation of Some Results in Finite Algebra. In Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, 52-57. Menlo Park, Calif.: International Joint Conferences on Artificial Intelligence.
40. Ganzinger, H., ed. 1996. Proceedings of the Seventh International Conference on Rewriting Techniques and Applications, RTA-96. Lecture Notes in Computer Science 1103. Berlin: Springer-Verlag.
41. Gelernter, H. 1963. Realization of a Geometry Theorem-Proving Machine. In Computers and Tliought, eds. E. Feigenbaum and J. Feldman, 134-152. New York: McGraw-Hill.
42. Gelernter, H.; Hanson, J. R.; and Loveland, D. W. 1963. Empirical Explorations of the Geometry-Theorem Proving Machine. In Computing and Tliought, eds. E. Feigenbaum and J. Feldman, 153-163. New York: McGraw-Hill.
43. Goldson, D.; Reeves, S.; and Bornet, R. 1993. A Review of Several Programs for the Teaching of Logic. The Computer Journal 36(4): 373-386.
44. Gordon, M. J., andMelham, T. F., eds. 1993. Introduction to HOL: A Theorem-Proving Environment for Higher-Order Logic. Oxford, U.K.: Cambridge University Press.
45. Green, C. 1969. Theorem Proving by Resolution as a Basis for Question-Answering Systems. In Machine Intelligence 4, eds. B. Meltzer and D. Michie, 183-20S. Edinburgh, U.K.: Edinburgh University Press.
46. Henzinger, T. A., andHo, P.-H. 1995. HYTECH: The Cornell Hybrid Technology Tool. In Hybrid Systems II, 265-294. Lecture Notes in Computer Science 999. Berlin: Springer-Verlag.
47. Hines, L. 1994. SIR +VE and Integers. In Proceedings of the Twelfth Conference on Automated Deduction, ed. A. Bundy, 416-430. New York: Springer Verlag.
48. Ho, P. H. 1995. The Algorithmic Analysis of Hybrid Systems. Ph.D. thesis, Computer Science Department, Cornell University.
49. Howe, D. J. 1996. Importing Mathematics from HOL into NUPRL. In Tlieorem Proving in Higher-Order Logics, eds. J. von Wright, J. Grundy, and J. Harrison, 267-282. Lecture Notes in Computer Science 1125. Berlin: Springer-Verlag.
50. Howe, D. J. 1987. The Computational Behavior of Girard's Paradox. In Proceedings of the IEEE Symposium on Logic in Computer Science, 205-214. Washington, D.C.: IEEE Computer Society.
51. Huang, X., andFiedler, A. 1996. Presenting Machine-Found Proofs. In Proceedings of the Thirteenth Conference on Automated Deduction, eds. M. A. McRobbie and J. K. Slaney, 221-225. Lecture Notes in Artificial Intelligence 1104. Berlin: Springer-Verlag.
52. Kapur, D., andSubramaniam, M. 1996. Mechanically Verifying a Family of Multiplier Circuits. In Proceedings of the Conference on Computer-Aided Verification, eds. R. Alur and T. Henzinger, 135-146. Lecture Notes in Computer Science 1102. Berlin: Springer-Verlag.
53. Kapur, D., andZhang, H. 1996. An Overview of Rewrite Rule Laboratory. Com-puters and Mathematics with Applications 29(2): 91-114.
54. Kaufmann, M., andMoore, J. S. 1996. ACL2: An Industrial Strength Version of NQTHM. In Proceedings of the Eleventh Annual Conference on Computer Assurance, 23-34. Washington, D.C.: IEEE Computer Society.
55. Kautz, H., andSelman, B. 1996. Pushing the Envelope: Planning, Propositional Logic, and Stochastic Search. In Proceedings of the Thirteenth National Conference on Artificial Intelligence (AAAI-96), 11941201. Menlo Park, Calif.: American Association for Artificial Intelligence.
56. Kautz, H.; McAIlester, D.; and Selman, B. 1996. Encoding Plans in Propositional Logic. In Proceedings of the Fourth International Conference on Principles of Knowledge Representation and Reasoning, 374-384. San Francisco, Calif.: Morgan Kaufmann.
57. King, D., andArthan, R. 1996. Development of Practical Verification Tools. ICL Systems Journal 11(1): 106-122.
58. Knuth, D. E., andBendix, P. B. 1970. Simple Word Problems in Universal Algebra. In Combinatorial Problems in Abstract Algebras, ed. J. Leech, 263-270. New York: Pergamon.
59. Kolata, G. 1996. With Major Math Proof Brute Computers Show Flash of Reasoning Power. New York Times, Sunday, 10 December, Cl, C8-C10.
60. Kowalski, R. 1984. Robert Kowalski on Logic Programming: An Interview. Future Generations Computer Systems, 1(1): 79-83.
61. Kunen, K. 1996a. Moufang Quasigroups. Journal of Algebra 183(1): 231-234.
62. Kunen, K. 1996b. Quasigroups, Loops, and Associative Laws. Journal of Algebra 185(1): 194-204.
63. Levesque, H. J.; Reiter, R.; Lespérance, Y.; Lin, F.; and Scherl, R. B. 1997. GOLOG: A Logic Programming Language for Dynamic Domains. Journal of Logic Programming 31(1-3): 59-83.
64. Löveland, D. W. 1984. Automated Theorem Proving: A Quarter-Century Review. In Automated Theorem Proving: after 25 Years, eds. D. Bledsoe and D. Löveland, 1-45. Contemporary Mathematics 29. Providence, R.I.: American Mathematical Society.
65. Löveland, D. W. 1969. A Simplified Format for the Model Elimination Procedure. Journal of the ACM 16(3): 349-363.
66. McCarthy, J. 1968. Programs with Common Sense. In Semantic Information Procession, ed. M. Minsky, 403-418. Cambridge, Mass.: The MIT Press.
67. McCarthy, J., andHayes, P. 1969. Some Philosophical Problems from the Standpoint of Artificial Intelligence. In Machine Intelligence 4, eds. B. Meltzer and D. Michie, 463-502. Edinburgh, U.K.: Edinburgh University Press.
68. McCune, VV. 1996. 33 Basic Test Problems: A Practical Evaluation of Some Paramodulation Strategies. Technical Report ANL/MCS-P618-1096, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois.
69. McCune, W. 1994. OTTER 3.0 Reference Manual and Guide. Technical Report ANL-94/6, Argonne National Laboratory, Argonne, Illinois.
70. McCune, W. 1993. Single Axioms for Groups and Abelian Groups with Various Operations. Journal of Automated Reasoning 10(1): 1-13.
71. McCune, M., andWos, L. 1997. OTTER. The CADE-13 Competition Incarnations. Journal of Automated Reasoning 18(2): 211-220.
72. MacKenzie, D. 1996. The Automation of Proof, A Historical and Sociological Exploration. IEEE Annals of the History of Computing 17(3): 7-29.
73. Manna, Z., andWaldinger, R. 1980. A Deductive Approach to Program Synthesis. ACM Transactions on Programming Languages 2(1): 90-121.
74. Melis, E., andWhittle, J. 1996. Internal Analogy in Theorem Proving. In Proceedings of the Thirteenth Conference on Automated Deduction, eds. M. A. McRobbie and J. K. Slaney, 92-105. Lecture Notes in Artificial Intelligence 1104. Berlin: Springer-Verlag.
75. Miller, D. A. 1984. Expansion Tree Proofs and Their Conversion to Natural Deduction Proofs. In Proceedings of the Seventh Conference on Automated Deduction, ed. R. Shostak, 347-370. Lecture Notes in Computer Science 170. Berlin: Springer-Verlag.
76. Milner, R.; Tofte, M.; and Harper, R. 1990. Tlie Definition of Standard ML. Cambridge, Mass.: MIT Press.
77. Moore, J. S. 1994. Introduction to the OBDD Algorithm for the ATP Community. Journal of Automated Reasoning 12(1): 33-45.
78. Moser, M.; Ibens, O.; Letz, R.; Steinbach, J.; Goller, C.; Schumann, J.; and Mayr, K. 1997. SETHEO and E-SETHEO: The CADE-13 Systems. Journal of Automated Reasoning 18(2): 237-246.
79. Murthy, C. 1991. An Evaluation Semantics for Classical Proofs. In Proceedings of the IEEE Symposium on Logic in Computer Science, 96-109. Washington, D.C.: IEEE Computer Society.
80. Nadathur, G., andMiller, D. 1988. An Overview of LAMBDA-PROLOG. In Proceedings oftheFiftli International Conference and Symposium on Logic Programming, 810-827. Cambridge, Mass.: MIT Press.
81. Newell, A.; Shaw, J. C.; and Simon, H. A. 1963. Empirical Explorations of the Logic Theory Machine: A Case Study in Heuris-tics. In Computers and Tliought, eds. E. Feigenbaum and J. Feldman, 134-152. New York: McGraw-Hill.
82. Owen, S. 1990. Analogy for Automated Reasoning. San Diego, Calif.: Academic.
83. Owre, S.; Rushby, J. M.; and Shankar, N. 1992. pvs: A Prototype Verification System. In Proceedings of the Eleventh Conference on Automated Deduction, ed. D. Kapur, 748-752. Lecture Notes in Artificial Intelligence 607. Berlin: Springer-Verlag.
84. Paulson, L. C. 1994. ISABELLE: A Generic Theorem Prover. Lectures Notes in Computer Science 828. Berlin: Springer-Verlag.
85. Paulson, L. C. 1993. Set Theory for Verification: I. From Foundations to Functions. Journal ofAiitomatedReasoning 11(3): 353-389.
86. Paulson, L. C., andGrabczewski, K. 1996. Mechanizing Set Theory. Journal of Automated Reasoning 17(3): 291-323.
87. Péli, G., andMasuch, M. 1997. The Logic of Propagation Strategies: Axiomatizing a Fragment of Organizational Ecology in First-Order Logic. Organization Science 8(3): 310-331.
88. Péli, G.; Bruggeman, J.; Masuch, M.; and O Nuallâin, B. 1994. A Logical Approach to Formalizing Organizational Ecology. American Sociological .Review 59(4): 571-593.
89. Plaisted, D. A., andZhu, Y. 1997. Ordered Semantic Hyper Linking. In Proceedings of the Fourteenth National Conference on Artificial Intelligence, 472-477. Menlo Park, Calif.: American Association for Artificial Intelligence.
90. QED. 1994. The QED Manifesto. In Proceedings of the Twelfth International Conference on Automated Deduction, ed. A. Bundy, 238-251. Berlin: Springer-Verlag. A comprehensive view of QED can be obtained on the web site at www.mcs.anl.gov/qed.
91. Robinson, J. A. 1992. Logic and Logic Programming. Communications of the ACM 35(3): 40-65.
92. Robinson, J. A. 1965. A Machine-Oriented Logic Based on the Resolution Principle. Journal of the ACM 12(1): 23-41.
93. Slanet, J.; Fujita, M.; and Stickel, M. 1995. Automated Reasoning and Exhaustive Search: Quasigroup Existence Problems. Computers and Mathematics with Applications 29(2): 115-132.
94. Siekmann, J. H., andWrightson, G., eds. 1983. The Automation of Reasoning, Volumes 1 and 2. Berlin: Springer-Verlag.
95. Smith, D. R. 1990. KIDS: A Semi-Automated Program Development System. IEEE Transactions on Sofhvare Engineering (Special Issue on Formal Methods) 16(9): 1024-1043.
96. Stickel, M. E. 1975. A Complete Unification Algorithm for Associative-Commutative Functions. In Proceedings of the Fourth International Joint Conference on Artificial Intelligence, 423-434. Menlo Park, Calif.: International Joint Conferences on Artificial Intelligence.
97. Stickel, M.; Waldinger, R.; Lowry, M.; Pressburger, T.; and Underwood, 1.1994. Deductive Composition of Astronomical Software from Subroutine Libraries. In Proceedings of the Twelfth Conference on Automated Deduction, ed. A. Bundy, 341-355. Lecture Notes in Artificial Intelligence 814. Berlin: Springer-Verlag.
98. Suppes, P., andMcDonald, J. 1984. Student Use of an Interactive Theorem Prover. In Automated Theorem Proving: After 25 Years, eds. W. Bledsoe and D. Loveland, 315-360. Contemporary Mathematics 29. Providence, R.I.: American Mathematical Society.
99. Sutcliffe, G., andSuttner, C. B. 1997. The Results of the CADE-13 ATP System Competition. Journal of Automated Reasoning 18(2): 271-286.
100. Suttner, C. B., andSutcliffe, G. 1998. The CADE-14 ATP System Competition. Journal of Automated Reasoning 21(1): 99-134.
101. Suttner, C. B., andSutcliffe, G. 1997. The Design of the CADE-13 ATP System Competition. Journal of Automated Reasoning 18(2): 139-162.
102. Thayer, F. J.; Farmer, W. M.; and Guttman, J. D. 1993. IMPS: An Interactive Mathematical Proof System. Journal of Automated Reasoning 11(2): 213-248.
103. Walsh, T.; Nunes, A.; and Bundy, A. 1992. The Use of Proof Plans to Sum Series. In Proceedings of the Eleventh Conference on Automated Deduction, ed. D. Kapur, 325-339. Lecture Notes in Artificial Intelligence 607. Berlin: Springer-Verlag.
104. Weidenbach, C. 1997. SPASS: Version 0.49. Journal of Automated Reasoning (Special Issue on the CADE-13 ATP System Competition) 18(2): 247-252.
105. Winker, S., andWos, L. 1978. Automated Generation of Models and Counter Examples and Its Application to Open Questions in Ternary Boolean Algebra. In Proceedings of the Eighth International Symposium on Multiple-Valued Logic, 251-256. Washington, D.C.: IEEE Computer Society.
106. Wos, L. 1996. OTTER and the Moufang Identity Problem. Journal of Automated Reasoning 17(2): 215-257.
107. Wos, L.; Robinson, G.; and Carson, D. 1965. Efficiency and Completeness of the Set of Support Strategy in Theorem Proving. Journal of the ACM 12(4): 536-541.
108. Wos, L.; Robinson, G.; Carson, D.; and Shalla, L. 1967. The Concept of Demodulation in Theorem Proving. Journal of the ACM 14(4): 698-709.