Qualitative and quantitative simulation: Bridging the gap

Artificial Intelligence

Volumn 95, Issue 2, 1997, Pages 215-255

  Berleant, Daniel ^a   Kuipers, Benjamin J ^b  

^a 3202 Bell Engineering Center   (United States)

^b University of Texas at Austin   (United States)

Author keywords

Intervals; Q3; QSIM; Qualitative; Semi quantitative; Simulation

Indexed keywords

ARTIFICIAL INTELLIGENCE; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; INTERPOLATION; PROBABILITY;

QUALITATIVE SIMULATION; QUANTITATIVE SIMULATION; SEMI QUANTITATIVE SIMULATION; STEP SIZE REFINEMENT;

COMPUTER SIMULATION;

EID: 0031223975     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0004-3702(97)00050-7     Document Type: Article

References (105)

1. H. Abelson and G.J. Sussman, Structure and Interpretation of Computer Programs (MIT Press, Cambridge, MA, 1985).
2. G. Alefeld and J. Herzberger, Introduction to interval Computations (Academic Press, San Diego, CA, 1983).
3. J.F. Allen, Maintaining knowledge about temporal intervals, Comm. ACM 26 (11) (1983) 832-843.
4. N.S. Asaithambi, S. Zuhe and R.E. Moore, On computing the range of values, Computing 28 (1982) 225-237.
5. D. Berleant, A unified representation for numerical and qualitative simulations, Appl. Computing Review 3 (1) (1995) 23-26.
6. D. Berleant, Automatically verified reasoning with both intervals and probability density functions, Interval Computations 2 (1993) 48-70.
7. D. Berleant, The use of partial quantitative information with qualitative reasoning, Ph.D. Thesis, Tech. Rept. A190-163, Artificial Intelligence Laboratory, University of Texas, Austin, TX (1991).
8. D. Berleant, C. Chandra, K. Bognæs, C. Liaw, L. Sheng and J. Ch'ng, Probabilities of qualitative behaviors for dependability analysis of a fault tolerance model, in: Conference Proceedings 1992 Symposium on Applied Computing, Kansas City, MO (ACM Press, New York, 1992) 883-889; preliminary results in: Workshop Notes AAAI-91 Model Based Reasoning Workshop, Anaheim, CA (1991).
9. D. Berleant, C. Chandra, K. Bognæs, C. Liaw, L. Sheng and J. Ch'ng, Probabilities of qualitative behaviors for dependability analysis of a fault tolerance model, in: Conference Proceedings 1992 Symposium on Applied Computing, Kansas City, MO (ACM Press, New York, 1992) 883-889; preliminary results in: Workshop Notes AAAI-91 Model Based Reasoning Workshop, Anaheim, CA (1991).
10. D. Berleant and B.J. Kuipers, Qualitative-numeric simulation with Q3, in: B. Faltings and P. Struss, Recent Advances in Qualitative Physics (MIT Press, Cambridge, MA, 1992) 3-16.
11. D.G. Bobrow, ed., Qualitative Reasoning about Physical Systems (MIT Press, Cambridge, MA, 1985); reprinted from: Artificial Intelligence 24 (1984).
12. D.G. Bobrow, ed., Qualitative Reasoning about Physical Systems (MIT Press, Cambridge, MA, 1985); reprinted from: Artificial Intelligence 24 (1984).
13. G. Bohlender, C. Ullrich, J. von Gudenberg and L.B. Rall, Pascal-SC: A Computer Language for Scientific Computation (Academic Press, San Diego, CA, 1987).
14. V.C. Boltyanskii, Envelopes (Macmillan, New York, 1964).
15. A. Bonarini and V. Maniezzo, Integrating qualitative and quantitative modeling, Internat. J. Expert Systems 4 (1) (1991) 51-70; preliminary report in: Proceedings 2nd Annual Conference on AI, Simulation and Planning in High Autonomy Systems, Cocoa Beach, FL (IEEE Computer Society Press, Los Alamitos, CA, 1991) 290-297; also in: Internal Working Proceedings 1st European Workshop on Qualitative Reasoning about Physical Systems, Genova, Italy (1991).
16. A. Bonarini and V. Maniezzo, Integrating qualitative and quantitative modeling, Internat. J. Expert Systems 4 (1) (1991) 51-70; preliminary report in: Proceedings 2nd Annual Conference on AI, Simulation and Planning in High Autonomy Systems, Cocoa Beach, FL (IEEE Computer Society Press, Los Alamitos, CA, 1991) 290-297; also in: Internal Working Proceedings 1st European Workshop on Qualitative Reasoning about Physical Systems, Genova, Italy (1991).
17. A. Bonarini and V. Maniezzo, Integrating qualitative and quantitative modeling, Internat. J. Expert Systems 4 (1) (1991) 51-70; preliminary report in: Proceedings 2nd Annual Conference on AI, Simulation and Planning in High Autonomy Systems, Cocoa Beach, FL (IEEE Computer Society Press, Los Alamitos, CA, 1991) 290-297; also in: Internal Working Proceedings 1st European Workshop on Qualitative Reasoning about Physical Systems, Genova, Italy (1991).
18. P.P. Bonissone, A fuzzy sets based linguistic approach: theory and applications, in: Proceedings 1980 Winter Simulation Conference, Orlando, FL (IEEE, New York, 1980) 99-111 ; also in: M.M. Gupta and E. Sanchez, eds., Approximate Reasoning in Decision Analysis (North-Holland, Amsterdam, 1982).
19. P.P. Bonissone, A fuzzy sets based linguistic approach: theory and applications, in: Proceedings 1980 Winter Simulation Conference, Orlando, FL (IEEE, New York, 1980) 99-111 ; also in: M.M. Gupta and E. Sanchez, eds., Approximate Reasoning in Decision Analysis (North-Holland, Amsterdam, 1982).
20. P.P. Bonissone and K.S. Decker, Selecting uncertainty calculi and granularity: an experiment in trading off precision and complexity, in: L.N. Kanal and J.F. Lemmer, eds., Uncertainty in Artificial Intelligence (Elsevier, Amsterdam, 1986) 217-247.
21. A. Brandt, Multi-level adaptive solutions to boundary-value problems, Math. Comput. 31 (138) (1977) 333-390.
22. W.L. Briggs, A Multigrid Tutorial (SIAM, Philadelphia, PA, 1987).
23. R.A. Brooks, Symbolic reasoning among 3-D models and 2-D images, Artificial Intelligence 17 (1981) 285-348.
24. R.E. Bryant, MOSSIM: a switch-level simulator for MOS LSI, in: Proceedings 18th Design Automation Conference (1981) 786-790.
25. B.R. Chawla, H.K. Gummel and P. Kozak, MOTIS - an MOS timing simulator, IEEE Trans. Circuits and Systems 22 (12) (1975) 901-910.
26. P.R. Cohen and E.A. Feigenbaum, eds., Handbook of Artificial Intelligence 3 (William Kaufmann Inc., Los Altos, CA, 1982) 313-321.
27. E.W. Coiera, Qualitative superposition. Artificial Intelligence 56 (2-3) (1992) 171-196.
28. H. Cornelius and R. Lohner, Computing the range of values of real functions with accuracy higher than second order, Computing 33 (1984) 331-347.
29. D.T. Dalle Molle, Qualitative simulation of dynamic chemical processes, Ph.D. Thesis, Chemical Engineering Department, University of Texas, Austin, TX (1989) ; reprinted as: Tech. Rept. AI89-107, Artificial Intelligence Laboratory, University of Texas, Austin, TX (1989).
30. D.T. Dalle Molle, Qualitative simulation of dynamic chemical processes, Ph.D. Thesis, Chemical Engineering Department, University of Texas, Austin, TX (1989) ; reprinted as: Tech. Rept. AI89-107, Artificial Intelligence Laboratory, University of Texas, Austin, TX (1989).
31. D.T. Dalle Molle and T.F. Edgar, Qualitative modeling of chemical reaction systems, in: M.L. Mavrovouniotis, ed., Artificial Intelligence in Process Engineering (Academic Press, San Diego, CA, 1991).
32. B. D'Ambrosio, Extending the mathematics in qualitative process theory, in: Proceedings AAAI-87, Seattle, WA (MIT Press, Cambridge, MA, 1987) 595-599.
33. E. Davis, Constraint propagation with interval labels, Artificial Intelligence 32 (3) (1987) 281-331.
34. T.L. Dean and M. Boddy, Reasoning about partially ordered events, Artificial Intelligence 36 (3) (1988) 375-399.
35. D. DeCoste, Dynamic across-time measurement interpretation, Artificial Intelligence 51 (1-3) (1991) 273-341 ; also in: Proceedings AAAI-90, Boston, MA (MIT Press, Cambridge, MA, 1990) 373-379.
36. D. DeCoste, Dynamic across-time measurement interpretation, Artificial Intelligence 51 (1-3) (1991) 273-341 ; also in: Proceedings AAAI-90, Boston, MA (MIT Press, Cambridge, MA, 1990) 373-379.
37. J. de Kleer, Qualitative and quantitative knowledge in classical mechanics, Tech. Rept. AI-TR-352, MIT, Artificial Intelligence Laboratory, Cambridge, MA (1975).
38. W. Derrick and S. Grossman, Elementary Differential Equations with Applications (Addison-Wesley, Reading, MA, 1976).
39. F. DiCesare, Z. Sahnoun and P.P. Bonissone, Linguistic summarization of fuzzy data, Inform. Sci. 52 (1990) 141-152.
40. D. Dubois and H. Prade, Fuzzy arithmetic in qualitative reasoning, in: Ensembles Flous 87: Algèbre, Intégrations, Calcul d'Intervalles et Approximations, Rapport L.S.I. No. 302, Langages et Systèmes Informatiques, ENSEEIHT, Toulouse, France (1988).
41. D. Dubois and H. Prade, Operations on fuzzy numbers, Internat. J. Systems Sci. 9 (6) (1978).
42. D. Dvorak, Model-based monitoring of dynamic systems, in: Proceedings IJCAI-89, Detroit, MI (1989) 1238-1243.
43. D. Dvorak, Monitoring and diagnosis of continuous dynamic systems using semiquantitative simulation, Ph.D. Thesis, Tech. Rept. AI92-170. Artificial Intelligence Laboratory, University of Texas, Austin, TX (1992).
44. P. Eijgenraam, The Solution of Initial Value Problems Using Interval Arithmetic: Formulation and Analysis of an Algorithm (Mathematisch Centrum, Amsterdam, 1981).
45. B. Faltings and P. Struss, Recent Advances in Qualitative Physics (MIT Press, Cambridge, MA, 1992).
46. A. Farquhar and G. Brajnik, A Semi-Quantitative Physics Compiler, in: Proceedings 8th International Workshop on Qualitative Reasoning, 1994.
47. P.A. Fishwick, Fuzzy simulation: specifying and identifying qualitative models, Internat. J. General Systems 19 (1991) 295-316.
48. K.D. Forbus, Qualitative process theory, Artificial Intelligence 24 (1984) ; reprinted in: D.G. Bobrow, ed., Qualitative Reasoning about Physical Systems (MIT Press, Cambridge, MA, 1985).
49. K.D. Forbus, Qualitative process theory, Artificial Intelligence 24 (1984) ; reprinted in: D.G. Bobrow, ed., Qualitative Reasoning about Physical Systems (MIT Press, Cambridge, MA, 1985).
50. K.D. Forbus, Interpreting measurements of physical systems, in: Proceedings AAAI-86, Philadelphia, PA (MIT Press, Cambridge, MA, 1986) 113-117.
51. K.D. Forbus and B. Falkenhainer, Self-explanatory simulations: an integration of qualitative and quantitative knowledge, in: B. Faltings and P. Struss, Recent Advances in Qualitative Physics (MIT Press, Cambridge, MA, 1992) 49-66 ; also in: Proceedings AAAI-90, Boston, MA (MIT Press, Cambridge, MA, 1990) 380-387.
52. K.D. Forbus and B. Falkenhainer, Self-explanatory simulations: an integration of qualitative and quantitative knowledge, in: B. Faltings and P. Struss, Recent Advances in Qualitative Physics (MIT Press, Cambridge, MA, 1992) 49-66 ; also in: Proceedings AAAI-90, Boston, MA (MIT Press, Cambridge, MA, 1990) 380-387.
53. K.D. Forbus and B. Falkenhainer, Self-explanatory simulations: scaling up to large models, in: Proceedings AAAI-92, San Jose, CA (MIT Press, Cambridge, MA, 1992).
54. J.W. Forrester, Industrial Dynamics (MIT Press, Cambridge, MA, 1961).
55. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations (Prentice-Hall, Englewood Cliffs, NJ, 1971).
56. W. Hamscher, Modelling digital circuits for troubleshooting, Artificial Intelligence 51 (1-3) (1991) 223-271.
57. P. Henrici, Discrete Variable Methods for Ordinary Differential Equations (John Wiley and Sons, New York, 1962).
58. E. Hyvönen, Constraint reasoning based on interval arithmetic: the tolerance propagation approach, Artificial Intelligence 58 (1-3) (1992) 71-112.
59. A. Kaufmann and M. Gupta, Introduction to Fuzzy Arithmetic (Van Nostrand Reinhold Co., New York, 1985).
60. H.A. Kautz and P.B. Ladkin, Integrating metric and qualitative temporal reasoning, in: Proceedings AAAI-91, Anaheim, CA (MIT Press, Cambridge, MA, 1991) 241-246.
61. H. Kay, Refining imprecise models and their behaviors, Ph.D. Thesis, Department of Computer Science, University of Texas, Austin, TX (1996).
62. H. Kay and B.J. Kuipers, Numerical behavior envelopes for qualitative models, in: Proceedings AAAI-93, Washington, DC (MIT Press, Cambridge, MA, 1993) 606-613.
63. G.T. Kelley, J.I. Glasgow and R.E. Ellis, Extracting qualitative descriptions from quantitative models, in: Proceedings 2nd Annual Conference on AI, Simulation and Planning in High Autonomy Systems, Cocoa Beach, FL (IEEE Computer Society Press, Los Alamitos, CA, 1991) 298-305.
64. Y. Kiang, Exploration of qualitative reasoning and its applications to management, Ph.D. Thesis, University of Texas at Austin, Austin, TX (1991).
65. L.V. Kolev, V.M. Mladenov and S.S. Vladov, Interval mathematics algorithms for tolerance analysis, IEEE Trans. Circuits and Systems 35 (8) (1988) 967-975.
66. B.J. Kuipers, Qualitative Reasoning (MIT Press, Cambridge, MA, 1994).
67. B.J. Kuipers, Qualitative simulation. Artificial Intelligence 32 (1986) 57-95.
68. B.J. Kuipers and D. Berleant, Using incomplete quantitative knowledge in qualitative reasoning, in: Proceedings AAAI-88, St. Paul, MN (MIT Press, Cambridge, MA, 1988) 324-329.
69. R.J. Lohner, Enclosing the solutions of ordinary initial and boundary value problems, in: E. Kaucher, U. Kulisch and C. Ullrich, eds., Computerarithmetic: Scientific Computation and Programming Languages (Teubner, Stuttgart, 1987) 255-286.
70. A.K. Mackworth and E.C. Freuder, The complexity of some polynomial network consistency algorithms for constraint satisfaction problems, Artificial Intelligence 25 (1985) 65-74.
71. D. McDermott and E. Davis, Planning routes through uncertain territory, Artificial Intelligence 22 (1984) 107-156.
72. I. Meiri, Combining qualitative and quantitative constraints in temporal reasoning, in: Proceedings AAAI-91, Anaheim, CA (MIT Press, Cambridge, MA, 1991) 260-267.
73. A. Missier and L. Travé-Massuyès, Temporal information in qualitative simulation, in: Proceedings 2nd Annual Conference on AI, Simulation and Planning in High Autonomy Systems, Cocoa Beach, FL (IEEE Computer Society Press, Los Alamitos, CA, 1991) 298-305.
74. J. Mohammed and R. Simmons, Qualitative simulation of semiconductor fabrication, in: Proceedings AAAI-86, Philadelphia, PA (MIT Press, Cambridge, MA, 1986) 794-799.
75. R.E. Moore, Methods and Applications of Interval Arithmetic (SIAM, Philadelphia, PA, 1979).
76. T. Nishida and S. Doshita, Reasoning about global behavior of ordinary differential equations by combining qualitative and quantitative analysis, in: Proceedings 2nd Annual Conference on AI, Simulation and Planning in High Autonomy Systems, Cocoa Beach, FL (IEEE Computer Society Press, Los Alamitos, CA, 1991) 98-107.
77. J.-P. Nordvik, P. Smets and P. Magrez, Fuzzy qualitative modeling, in: B. Bouchon, L. Saitta and R.R. Yager, eds., Uncertainty and Intelligent Systems (Springer, New York, 1988).
78. W. Older and A. Vellino, Constraint arithmetic on real intervals, in: F. Benhamou and A. Colmerauer, eds., Constraint Logic Programming, Collected Papers (MIT Press, Cambridge, MA).
79. W. Press, B. Flannery, S. Teukolsky and W. Vetterling, Numerical Recipes (Cambridge University Press, Cambridge, MA, 1986).
80. E. Sacks, Hierarchical reasoning about inequalities, in: Proceedings AAAI-87, Seattle, WA (MIT Press, Cambridge, MA, 1987) 649-654.
81. E. Sacks, Automatic analysis of one-parameter planar ordinary differential equations by intelligent numerical simulation, Artificial Intelligence 48 (1991) 27-56.
82. E. Sacks, Review of K. Yip, KAM: A System for Intelligently Guided Numerical Experimentation by Computer (MIT Press, Cambridge, MA, 1991), SIGART Bull. 3 (3) (1992) 18-19.
83. E. Sacks, Review of K. Yip, KAM: A System for Intelligently Guided Numerical Experimentation by Computer (MIT Press, Cambridge, MA, 1991), SIGART Bull. 3 (3) (1992) 18-19.
84. R.A. Saleh and A.R. Newton, Mixed-Mode Simulation (Kluwer, Boston, MA, 1990).
85. Q. Shen and R. Leitch, Fuzzy qualitative simulation, IEEE Trans. Systems Man Cybernet. 23 (1993) 1038-1061.
86. Q. Shen and R. Leitch, Integrating common-sense and qualitative simulation by the use of fuzzy sets, in: B. Faltings and P. Struss, Recent Advances in Qualitative Physics (MIT Press, Cambridge, MA, 1992) 83-100.
87. R. Simmons, The use of qualitative and quantitative simulations, in: Proceedings AAAI-83, Washington, DC (MIT Press, Cambridge, MA, 1983) 364-368.
88. R. Simmons, "Commonsense" arithmetic reasoning, in: Proceedings AAAI-86, Philadelphia, PA (MIT Press, Cambridge, MA, 1986) 118-124.
89. R. Simmons, A theory of debugging plans and interpretations, in: Proceedings AAAI-88, St. Paul, MN (MIT Press, Cambridge, MA, 1988) 94-99.
90. R. Simmons, The roles of associational and causal reasoning in problem solving, Artificial Intelligence 53 (1-2) (1992) 159-207.
91. R. Simmons and R. Davis, Generate, test and debug: combining associational rules and causal models, in: Proceedings IJCAI-87, Milan, Italy (1987) 1071-1078.
92. J.M. Siskind and D.A. McAllester, Nondeterministic Lisp as a substrate for constraint logic programming, in: Proceedings AAAI-93, Washington, DC (MIT Press, Cambridge, MA, 1993).
93. C.J. Terman, RSIM - a logic-level timing simulator, in: Proceedings IEEE International Conference on Computer Design (1983) 437-440.
94. R.M. Tong and P.P. Bonissone, Linguistic decision analysis using fuzzy sets. Memorandum No. UCB/ERL M79/72, Electronics Research Laboratory, University of California, Berkeley, CA (1979).
95. E.R. Tufte, The Visual Display of Quantitative Information (Graphics Press, Cheshire, CT, 1983).
96. M. Vescovi, A. Farquhar and Y. Iwasaki, Numerical interval simulation: bounding behaviors of non-monotonic systems, in: Proceedings IJCAI-95, Montreal, Que. (1995).
97. B.C. Williams, Doing time: putting qualitative reasoning on firmer ground, in: Proceedings AAAI-86, Philadelphia, PA (MIT Press, Cambridge, MA, 1986) 105-112.
98. B.C. Williams, MINIMA: a symbolic approach to qualitative algebraic reasoning, in: Proceedings AAAI-88, St. Paul, MN (MIT Press, Cambridge, MA, 1988) 264-269.
99. B.C. Williams, A theory of interactions: unifying qualitative and quantitative algebraic reasoning, Artificial Intelligence 51 (1-3) (1991) 39-94.
100. K. Yip, KAM: A System for Intelligently Guided Numerical Experimentation by Computer (MIT Press, Cambridge, MA, 1991).
101. D.M. Young, Stability (h → 0 and h > 0) for systems, Course Notes Supplement 78.6, revises: D.M. Young and R.T. Gregory, A Survey of Numerical Mathematics II (Addison-Wesley, Reading, MA, 1972) 566-573, Center for Numerical Analysis, University of Texas at Austin (1978).
102. D.M. Young, Stability (h → 0 and h > 0) for systems, Course Notes Supplement 78.6, revises: D.M. Young and R.T. Gregory, A Survey of Numerical Mathematics II (Addison-Wesley, Reading, MA, 1972) 566-573, Center for Numerical Analysis, University of Texas at Austin (1978).
103. D.M. Young and R.T. Gregory, A Survey of Numerical Mathematics II (Addison-Wesley, Reading, MA, 1972).
104. F. Zhao, Extracting and representing qualitative behaviors of complex systems in phase spaces, Artificial Intelligence 69 (1994) 51-92; also in: Proceedings IJCAI-91, Sidney, Australia (Morgan Kaufmann, Los Altos, CA, 1991).
105. F. Zhao, Extracting and representing qualitative behaviors of complex systems in phase spaces, Artificial Intelligence 69 (1994) 51-92; also in: Proceedings IJCAI-91, Sidney, Australia (Morgan Kaufmann, Los Altos, CA, 1991).