Qualitative simulation and related approaches for the analysis of dynamic systems

Methods for qualitative simulation allow predictions on the dynamics of a system to be made in the absence of quantitative information, by inferring the range of possible qualitative behaviors compatible with the structure of the system. This article reviews QSIM and other qualitative simulation methods. It discusses two problems that have seriously compromised the application of these methods to realistic problems in science and engineering: the occurrence of spurious behavior predictions and the combinatorial explosion of the number of behavior predictions. In response to these problems, related approaches for the qualitative analysis of dynamic systems have emerged: qualitative phase-space analysis and semi-quantitative simulation. The article argues for a synthesis of these approaches in order to obtain a computational framework for the qualitative analysis of dynamic systems. This should provide a solid basis for further upscaling and for the development of model-based reasoning applications of a wider scope.

[1]  K. Yip KAM: A System for Intelligently Guiding Numerical Experimentation by Computer , 1991 .

[2]  Benjamin Kuipers,et al.  Qualitative and Quantitative Simulation: Bridging the Gap , 1997, Artif. Intell..

[3]  Elisha Sacks,et al.  A Dynamic Systems Perspective on Qualitative Simulation , 1990, Artif. Intell..

[4]  F Guerrin,et al.  Knowledge representation and qualitative simulation of salmon redd functioning. Part II: qualitative model of redds. , 2001, Bio Systems.

[5]  Steffen Schulze-Kremer,et al.  Design and implementation of a qualitative simulation model of lambda phage infection , 1998, Bioinform..

[6]  Benjamin Kuipers,et al.  Non-Intersection of Trajectories in Qualitative Phase Space: A Global Constraint for Qualitative Simulation , 1988, AAAI.

[7]  Toyoaki Nishida Qualitative Reasoning for Automated Exploration for Chaos , 1994, AAAI.

[8]  Pieter J. Mosterman,et al.  Diagnosis of continuous valued systems in transient operating regions , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[9]  Hidde de Jong,et al.  Genetic Network Analyzer: qualitative simulation of genetic regulatory networks , 2003, Bioinform..

[10]  Brian Falkenhainer,et al.  Self-Explanatory Simulations : Scaling up to large models , 2003 .

[11]  Benjamin Kuipers,et al.  Numerical Behavior Envelopes for Qualitative Models , 1993, AAAI.

[12]  Benjamin Kuipers,et al.  Proving Properties of Continuous Systems: Qualitative Simulation and Temporal Logic , 1997, Artif. Intell..

[13]  Wilfried Grossmann,et al.  A Stochastic Approach to Qualitative Simulation using Markov Processes , 1993, IJCAI.

[14]  Brian C. Williams,et al.  Qualitative Reasoning about Physical Systems: A Return to Roots , 1991, Artif. Intell..

[15]  Selahattin Kuru,et al.  Improved Filtering for the QSIM Algorithm , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Olivier Bernard Etude experimentale et theorique de la croissance de dunaliella tertiolecta (chlorophyceae) soumise a une limitation variable de nitrate : utilisation de la dynamique transitoire pour la conception et la validation des modeles , 1995 .

[17]  Kenneth Yip Reasoning about Fluid Motion I: Finding Structures , 1995, IJCAI.

[18]  Benjamin Kuipers,et al.  Automatic Abduction of Qualitative Models , 1992, AAAI.

[19]  Mark A. Kramer,et al.  Qualitative Analysis of Causal Feedback , 1991, AAAI.

[20]  Robert A. Meyers,et al.  Encyclopedia of physical science and technology , 1987 .

[21]  Olivier Bournez,et al.  Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems , 2000, HSCC.

[22]  Ivan Bratko,et al.  Qualitatively Faithful Quantitative Prediction , 2003, IJCAI.

[23]  Elisha Sacks,et al.  Hierarchical Reasoning about Inequalities , 1987, AAAI.

[24]  Benjamin Kuipers,et al.  Process monitoring and diagnosis: a model-based approach , 1991, IEEE Expert.

[25]  Boi Faltings,et al.  Recent advances in qualitative physics , 1993 .

[26]  Radboud Winkels,et al.  Model based reasoning about learner behaviour , 1998 .

[27]  J. Gouzé,et al.  Non-linear qualitative signal processing for biological systems: application to the algal growth in bioreactors. , 1999, Mathematical biosciences.

[28]  Adam Finkelstein,et al.  Real-Time Self-Explanatory Simulation , 1993, AAAI.

[29]  Jeroen Keppens,et al.  Centre for Intelligent Systems and Their Applications on Compositional Modelling on Compositional Modelling on Compositional Modelling* , 2022 .

[30]  P. Pandurang Nayak,et al.  Automated Modeling of Physical Systems , 1995, Lecture Notes in Computer Science.

[31]  Benjamin Kuipers,et al.  Causal Reasoning in Medicine: Analysis of a Protocol , 1984 .

[32]  G. Stephanopoulos,et al.  Formal order-of-magnitude reasoning in process engineering , 1989 .

[33]  Wolfgang Nejdl,et al.  Diamon: a model-based troubleshooter based on qualitative reasoning , 1993, IEEE Expert.

[34]  Pascal Van Hentenryck,et al.  A Constraint Satisfaction Approach to Parametric Differential Equations , 2001, IJCAI.

[35]  Nedialko S. Nedialkov,et al.  An Interval Hermite-Obreschkoff Method for Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation , 1998, SCAN.

[36]  Benjamin Kuipers,et al.  Qualitative Simulation as a Temporally-extended Constraint Satisfaction Problem , 1998, AAAI/IAAI.

[37]  Kenneth Man-kam Yip,et al.  Understanding Complex Dynamics by Visual and Symbolic Reasoning , 1991, Artif. Intell..

[38]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering , 1994 .

[39]  O Bernard,et al.  Transient behavior of biological loop models with application to the Droop model. , 1995, Mathematical biosciences.

[40]  Jan-Erik Strömberg,et al.  Combining Qualitative and Quantitative Knowledge to Generate Models of Physical Systems , 1991, IJCAI.

[41]  Bruce W. Porter,et al.  Automated Modeling of Complex Systems to Answer Prediction Questions , 1997, Artif. Intell..

[42]  Benjamin Kuipers,et al.  Qualitative reasoning: Modeling and simulation with incomplete knowledge , 1994, Autom..

[43]  Peter Struss Models of Behavior Deviations in Model-Based Systems , 2004, ECAI.

[44]  Philippe Dague,et al.  Qualitative Reasoning: A Survey of Techniques and Applications , 1995, AI Commun..

[45]  Jean-Pierre Aubin,et al.  Dynamical qualitative analysis of evolutionary systems , 2001, 2001 European Control Conference (ECC).

[46]  Bernhard Rinner,et al.  Monitoring Piecewise Continuous Behaviors by Refining Semi-Quantative Trackers , 1999, IJCAI.

[47]  Brian C. Williams,et al.  The Use of Continuity in a Qualitative Physics , 1984, AAAI.

[48]  Jon Doyle,et al.  Markov analysis of qualitative dynamics 1 , 1991, Comput. Intell..

[49]  Elisha Sacks,et al.  PROLEGOMENA TO ANY FUTURE QUALITATIVE PHYSICS , 1992, Comput. Intell..

[50]  Yoshiteru Ishida,et al.  Using Global Properties for Qualitative Reasoning: A Qualitative System Theory , 1989, IJCAI.

[51]  Benjamin Kuipers,et al.  Qualitative-numeric simulation with Q3 , 1993 .

[52]  Philippe Schnoebelen,et al.  Systems and Software Verification, Model-Checking Techniques and Tools , 2001 .

[53]  Benjamin Kuipers,et al.  Higher Order Derivative Constraints in Qualitative Simulation , 1991, Artif. Intell..

[54]  Dennis DeCoste,et al.  Dynamic Across-Time Measurement Interpretation , 1990, Artif. Intell..

[55]  Elizabeth Bradley,et al.  Automatic construction of accurate models of physical systems , 1996, Annals of Mathematics and Artificial Intelligence.

[56]  Yumi Iwasaki,et al.  Device modelling environment: an interactive environment for modelling device behaviour , 1992 .

[57]  Benjamin Kuipers,et al.  Static and Dynamic Abstraction Solves the Problem of Chatter in Qualitative Simulation , 1997, AAAI/IAAI.

[58]  Ivan Bratko,et al.  Learning Qualitative Models , 2004, AI Mag..

[59]  Daniel S. Weld Comparative Analysis , 1987, IJCAI.

[60]  Feng Zhao,et al.  STA: Spatio-Temporal Aggregation with Applications to Analysis of Diffusion-Reaction Phenomena , 2000, AAAI/IAAI.

[61]  Adam Farquhar,et al.  Modeling and Simulation of a Complex Industrial Process , 1997, IEEE Expert.

[62]  Philippe Dague,et al.  Mathematical Foundations of Qualitative Reasoning , 2004, AI Mag..

[63]  Pieter J. Mosterman,et al.  A comprehensive methodology for building hybrid models of physical systems , 2000, Artif. Intell..

[64]  Qiang Shen,et al.  Fuzzy qualitative simulation , 1993, IEEE Trans. Syst. Man Cybern..

[65]  Kumar Sankar Ray,et al.  An Extension of QSIM with Qualitative Curvature , 1997, Artif. Intell..

[66]  H. D. Jong,et al.  Qualitative simulation of the initiation of sporulation in Bacillus subtilis , 2004, Bulletin of mathematical biology.

[67]  Ivan Bratko,et al.  Qualitative Simulation with CLP , 2002 .

[68]  Brian Falkenhainer,et al.  Compositional Modeling: Finding the Right Model for the Job , 1991, Artif. Intell..

[69]  Bernhard Rinner,et al.  Semi-quantitative system identification , 2000, Artif. Intell..

[70]  Chris Bailey-Kellogg,et al.  Qualitative Spatial Reasoning Extracting and Reasoning with Spatial Aggregates , 2004, AI Mag..

[71]  Bernd Neumann,et al.  Comparative Simulation , 1994, AAAI.

[72]  Herbert Kay,et al.  SQsim: a simulator for imprecise ODE models , 1998 .

[73]  Sergio Yovine,et al.  Towards Computing Phase Portraits of Polygonal Differential Inclusions , 2002, HSCC.

[74]  P. Johnson-Laird Mental models , 1989 .

[75]  Louise Travé-Massuyès,et al.  Fuzzy Causal Simulation in Process Engineering , 1993, IJCAI.

[76]  中園 薫 A Qualitative Physics Based on Confluences , 1986 .

[77]  J. A. Kamps,et al.  Qualitative Reasoning beyond the Physics Domain: The Density Dependence Model of Organizational Ecology , 1995 .

[78]  Shuji Doshita,et al.  Qualitative Analysis of Behavior of Systems of Piecewise Linear Differential Equations with two State Variables , 1995, Artif. Intell..

[79]  Brian C. Williams,et al.  Qualitative Analysis of MOS Circuits , 1984, Artif. Intell..

[80]  Qiang Shen,et al.  Prioritising Behaviours in Qualitative Simulation , 1993, IJCAI.

[81]  Paul A. Luker,et al.  Qualitative Simulation Modeling and Analysis , 1991, Advances in Simulation.

[82]  Philippe Dague Numeric Reasoning with Relative Orders of Magnitude , 1993, AAAI.

[83]  Feng Zhao,et al.  Spatial Aggregation: Theory and Applications , 1996, J. Artif. Intell. Res..

[84]  Adam Farquhar,et al.  Numerical Interval Simulation: Combined Qualitative and Quantitative Simulation to Bound Behaviors of Non-Monotonic Systems , 1995, IJCAI.

[85]  Giordano Lanzola,et al.  Qualitative models in medical diagnosis , 1990, Artif. Intell. Medicine.

[86]  Hidde de Jong,et al.  Qualitative Simulation of Genetic Regulatory Networks: Method and Application , 2001, IJCAI.

[87]  Qiang Shen,et al.  Exhibiting the behavior of time-delayed systems via an extension to qualitative simulation , 2005, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[88]  A. Makarovic,et al.  Parsimony in Model-Based Reasoning , 1991 .

[89]  Bert Bredeweg,et al.  An overview of approaches to qualitative model construction , 1996, The Knowledge Engineering Review.

[90]  Lyle H. Ungar,et al.  Model‐based approach to automated hazard identification of chemical plants , 1995 .

[91]  Jeroen Keppens,et al.  Disaggregation in Compositional Modelling of Ecological Systems via Dynamic Constraint Satisfaction , 2001 .

[92]  Riccardo Bellazzi,et al.  A Qualitative-Fuzzy Framework for Nonlinear Black-Box System Identification , 1999, IJCAI.

[93]  Qiang Shen,et al.  Diagnosing continuous systems with qualitative dynamic models , 1995, Artif. Intell. Eng..

[94]  F. E. Finch,et al.  Qualitative modeling and fault diagnosis of dynamic processes by MIDAS , 1992 .

[95]  Peter Struss,et al.  Global Filters for Qualitative Behaviors , 1988, AAAI.

[96]  Kenneth D. Forbus,et al.  Building problem solvers: listings , 1993 .

[97]  Nedialko S. Nedialkov,et al.  Some recent advances in validated methods for IVPs for ODEs , 2002 .

[98]  Lyle H. Ungar,et al.  Dynamic process monitoring and fault diagnosis with qualitative models , 1995, IEEE Trans. Syst. Man Cybern..

[99]  Daniel G. Bobrow,et al.  Qualitative Reasoning With Higher-Order Derivatives , 1989, AAAI.

[100]  Enrico W. Coiera,et al.  Learning Qualitative Models of Dynamic Systems , 2004, Machine Learning.

[101]  Kenneth D. Forbus Qualitative Process Theory , 1984, Artif. Intell..

[102]  Peter Struss,et al.  Mathematical aspects of qualitative reasoning , 1988, Artif. Intell. Eng..

[103]  Ulrich Junker,et al.  History-based Interpretation of Finite Element Simulations of Seismic Wave Fields , 1995, IJCAI.

[104]  T. Csendes Developments in Reliable Computing , 2000 .

[105]  Jan Lunze Qualitative modelling of dynamical systems motivation, methods, and prospective applications , 1998 .

[106]  Benjamin J. Kaipers,et al.  Qualitative Simulation , 1989, Artif. Intell..

[107]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and Linear Algebra , 1974 .

[108]  Mario Stefanelli,et al.  Generating Explanations of Pathophysiological Systems Behaviors from Qualitative Simulation of Compartmental Models , 1995, AIME.

[109]  Kenneth D. Forbus Interpreting Observations of Physical Systems , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[110]  Karsten R. Heidtke,et al.  Design and implementation of a qualitative simulation model of λ phage infection , 1997 .

[111]  Feng Zhao,et al.  Extracting and Representing Qualitative Behaviors of Complex Systems in Phase Spaces , 1991, IJCAI.

[112]  Kenneth D. Forbus,et al.  Qualitative Modeling in Education , 2004, AI Mag..

[113]  Bert Bredeweg,et al.  Qualitative models of interactions between two populations , 2002, AI Commun..

[114]  A. C. Cem Say L'Hôpital's Filter for QSIM , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[115]  Radu Mateescu,et al.  Model Checking Genetic Regulatory Networks Using GNA and CADP , 2004, SPIN.

[116]  Herbert A. Simon,et al.  Causality and Model Abstraction , 1994, Artif. Intell..

[117]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[118]  Benjamin Kuipers,et al.  Taming Intractible Branching in Qualitative Simulation , 1987, IJCAI.

[119]  Hidde de Jong,et al.  Semi-Quantitative Comparative Analysis , 1999, IJCAI.

[120]  Benjamin Kuipers,et al.  QSIM: The Program and Its Use , 1990 .

[121]  Olivier Bernard,et al.  Discrimination of Semi-Quantitative Models by Experiment Selection: Method and Application in Population Biology , 2001, IJCAI.

[122]  Peter Struss,et al.  Automated Qualitative Domain Abstraction , 2003, IJCAI.

[123]  Peter Struss,et al.  Current Topics in Qualitative Reasoning , 2004, AI Mag..

[124]  Pascal Van Hentenryck,et al.  A Constraint Satisfaction Approach for Enclosing Solutions to Parametric Ordinary Differential Equations , 2002, SIAM J. Numer. Anal..

[125]  Peter Struss Modellbasierte Systeme und qualitative Modellierung , 2003, Handbuch der Künstlichen Intelligenz.

[126]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[127]  Elizabeth Bradley,et al.  Global solutions for nonlinear systems using qualitative reasoning , 1998, Annals of Mathematics and Artificial Intelligence.

[128]  Jan L. Top,et al.  Engineering ontologies , 1997, Int. J. Hum. Comput. Stud..

[129]  Benjamin Kuipers,et al.  Comprehending Complex Behavior Graphs through Abstraction , 1996 .

[130]  Brian C. Williams,et al.  Decompositional Modeling through Caricatural Reasoning , 1994, AAAI.

[131]  Benjamin Kuipers,et al.  Qualitative Simulation: Then and Now , 1993, Artif. Intell..

[132]  Feng Zhao,et al.  Computational dynamics: Modeling and visualizing trajectory flows in phase space , 1993, Annals of Mathematics and Artificial Intelligence.

[133]  Kenneth D. Forbus QPE: Using assumption-based truth maintenance for qualitative simulation , 1988, Artif. Intell. Eng..

[134]  H. Levent Akin,et al.  Sound and complete qualitative simulation is impossible , 2003, Artif. Intell..

[135]  Klaus Eisenack,et al.  Graph Theoretical Analysis of Qualitative Models in Sustainability Science , .

[136]  Hidde de Jong,et al.  Comparative envisionment construction : A general method for the comparative analysis of dynamical systems , 1997 .

[137]  Jean-Pierre Aubin,et al.  Qualitative simulation of differential equations , 1989, Differential and Integral Equations.

[138]  Johan de Kleer Multiple Representations of Knowledge in a Mechanics Problem-Solver , 1977, IJCAI.

[139]  Alen Varsek,et al.  Qualitative Model Evolution , 1991, IJCAI.

[140]  Benjamin Kuipers,et al.  A Qualitative Method to Construct Phase Portraits , 1993, AAAI.

[141]  Giorgio Brajnik,et al.  Focusing qualitative simulation using temporal logic: theoretical foundations , 1998, Annals of Mathematics and Artificial Intelligence.

[142]  Kenneth D. Forbus Using Qualitative Physics to Create Articulate Educational Software , 1997, IEEE Expert.

[143]  Alon Y. Halevy,et al.  Automated Model Selection for Simulation Based on Relevance Reasoning , 1997, Artif. Intell..

[144]  Bruce W. Porter,et al.  Automated Modeling for Answering Prediction Questions: Selecting the Time Scale and System Boundary , 1994, AAAI.

[145]  Elisha Sacks,et al.  Automatic Analysis of One-Parameter Planar Ordinary Differential Equations by Intelligent Numeric Simulation , 1991, Artif. Intell..

[146]  Benjamin Kuipers,et al.  Reasoning with Qualitative Models , 1993, Artif. Intell..

[147]  Herbert A. Simon,et al.  The mathematical bases for qualitative reasoning , 1991, IEEE Expert.

[148]  Elizabeth Bradley,et al.  Reasoning about nonlinear system identification , 2001, Artif. Intell..

[149]  Kenneth D. Forbus,et al.  Building Problem Solvers , 1993 .

[150]  F Guerrin,et al.  Knowledge representation and qualitative simulation of salmon redd functioning. Part I: qualitative modeling and simulation. , 2001, Bio Systems.

[151]  Ivayla Nedeltcheva Vatcheva,et al.  Computer-Supported Experiment Selection for Model Discrimination , 2001 .

[152]  Selahattin Kuru,et al.  Qualitative System Identification: Deriving Structure from Behavior , 1996, Artif. Intell..

[153]  Harold Abelson The Bifurcation Interpreter: A Step Towards the Automatic Analysis of Dynamical Systems , 1989 .

[154]  J. J. Stoker Nonlinear Vibrations in Mechanical and Electrical Systems , 1950 .

[155]  Yumi Iwasaki,et al.  Reasoning with multiple abstraction models , 1993 .

[156]  Hidde de Jong,et al.  Qualitative Simulation of Large and Complex Genetic Regulation Systems , 2000, ECAI.

[157]  Brian Falkenhainer,et al.  Scaling up Self-Explanatory Simulators: Polynomial-time Compilation , 1995, IJCAI.

[158]  Olivier Bernard,et al.  Global qualitative description of a class of nonlinear dynamical systems , 2002, Artif. Intell..

[159]  D. Bobrow Qualitative Reasoning about Physical Systems , 1985 .

[160]  Nicolaas Mars,et al.  Computer-Supported Resolution of Measurement Conflicts: A Case-Study in Materials Science , 1999 .

[161]  Michael W. Hofbaur,et al.  Lyapunov based reasoning methods , 2001, IEEE Trans. Syst. Man Cybern. Part A.

[162]  Lance Tokuda Managing Occurrence Branching in Qualitative Simulation , 1996, AAAI/IAAI, Vol. 2.

[163]  Jean-Luc Gouzé,et al.  Dealing with Discontinuities in the Qualitative Simulation of Genetic Regulatory Networks , 2002, ECAI.

[164]  Brian C. Williams,et al.  Doing Time: Putting Qualitative Reasoning on Firmer Ground , 1986, AAAI.

[165]  Benjamin Kuipers,et al.  Qualitative Simulation , 1986, Artificial Intelligence.

[166]  Patrick J. Hayes,et al.  The second naive physics manifesto , 1995 .

[167]  Ramon E. Moore Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[168]  Hidde de Jong,et al.  Selection of Perturbation Experiments for Model Discrimination , 2000, ECAI.

[169]  Kenneth D. Forbus Qualitative physics: past present and future , 1988 .

[170]  P. Dague,et al.  Order of magnitude reasoning in qualitative differential equations , 1989 .

[171]  Gautam Biswas,et al.  Multi-level qualitative reasoning applied to CMOS digital circuits , 1992, Artif. Intell. Eng..

[172]  Oskar Dressler On-Line Diagnosis and Monitoring of Dynamic Systems based on Qualitative Models and Dependency-recording Diagnosis Engines , 1996, ECAI.

[173]  Ashish Tiwari,et al.  Series of Abstractions for Hybrid Automata , 2002, HSCC.

[174]  Hidde de Jong,et al.  Comparative envisionment construction: A technique for the comparative analysis of dynamical systems , 1999, Artif. Intell..

[175]  Gautam Biswas,et al.  A Formal Modeling Scheme for Continuous Systems: Focus on Diagnosis , 1993, IJCAI.

[176]  Kenneth Man-kam Yip,et al.  Model Simplification by Asymptotic Order of Magnitude Reasoning , 1993, Artif. Intell..

[177]  Benjamin Kuipers,et al.  Model Decomposition and Simulation: A Component Based Qualitative Simulation Algorithm , 1997, AAAI/IAAI.

[178]  E. Bradley AUTONOMOUS EXPLORATION AND CONTROL OF CHAOTIC SYSTEMS , 1995 .

[179]  N. Nedialkov,et al.  ODE Software that Computes Guaranteed Bounds on the Solution , 2000 .

[180]  P. Pandurang Nayak,et al.  Causal Approximations , 1992, Artif. Intell..

[181]  Elisha Sacks,et al.  Automatic Qualitative Analysis of Dynamic Systems Using Piecewise Linear Approximations , 1990, Artif. Intell..

[182]  Philippe Dague Symbolic Reasoning with Relative Orders of Magnitude , 1993, IJCAI.

[183]  Enrico W. Coiera,et al.  Qualitative Superposition , 1992, Artif. Intell..

[184]  Daniele Theseider Dupré,et al.  State-based vs Simulation-based Diagnosis of Dynamic Systems , 2000, ECAI.

[185]  Jean-Luc Gouzé,et al.  TRANSIENT BEHAVIOR OF BIOLOGICAL MODELS AS A TOOL OF QUALITATIVE VALIDATION—APPLICATION TO THE DROOP MODEL AND TO A N-P-Z MODEL , 1996 .

[186]  Daniel S. Weld Reasoning about Model Accuracy , 1992, Artif. Intell..

[187]  Brian Falkenhainer,et al.  Self-Explanatory Simulations: An Integration of Qualitative and Quantitative Knowledge , 1990, AAAI.

[188]  H. D. Jong,et al.  Qualitative simulation of genetic regulatory networks using piecewise-linear models , 2004, Bulletin of mathematical biology.

[189]  Johan de Kleer,et al.  Readings in qualitative reasoning about physical systems , 1990 .

[190]  Alan S. Perelson,et al.  System Dynamics: A Unified Approach , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[191]  Hwee Tou Ng,et al.  Model-Based, Multiple-Fault Diagnosis of Dynamic, Continuous Physical Devices , 1991, IEEE Expert.

[192]  Ross D. King,et al.  Learning Qualitative Metabolic Models , 2004, ECAI.

[193]  E. Bradley,et al.  Phase-space control system design , 1993, IEEE Control Systems.

[194]  Andrea Bonarini,et al.  A qualitative simulation approach for fuzzy dynamical models , 1994, TOMC.

[195]  Sami Souissi,et al.  Qualitative behavior of stage-structured populations: application to structural validation , 1998 .

[196]  Daniel S. Weld Theories of comparative analysis , 1990 .

[197]  Benjamin Kuipers,et al.  Qualitative simulation using time-scale abstraction , 1988, Artif. Intell. Eng..

[198]  W. M. Kim Roddis,et al.  CRACK: qualitative reasoning about fatigue and fracture in steel bridges , 1992, IEEE Expert.

[199]  Jan Lunze,et al.  Qualitative modelling of linear dynamical systems with quantized state measurements , 1994, Autom..

[200]  Josep Vehí,et al.  A Survey on Interval Model Simulators and their Properties Related to Fault Detection , 2000 .

[201]  Kenneth Yip Structural Inferences from Massive Datasets , 1997, IJCAI.

[202]  Toyoaki Nishida Grammatical Description of Behaviors of Ordinary Differential Equations in Two-Dimensional Phase Space , 1997, Artif. Intell..

[203]  Benjamin Kuipers,et al.  Reasoning about energy in qualitative simulation , 1992, IEEE Trans. Syst. Man Cybern..

[204]  Kenneth D. Forbus Qualitative Process Theory: Twelve Years After , 1993, Artif. Intell..

[205]  Daniel S. Weld,et al.  Query-directed approximation , 1993 .

[206]  Peter Struss,et al.  A Prototype for Model-based On-board Diagnosis of Automotive Systems , 2000, AI Commun..

[207]  Liliana Ironi,et al.  Automated mathematical modeling from experimental data: an application to material science , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[208]  Arie Rip,et al.  The Computer Revolution in Science: Steps Towards the Realization of Computer-Supported Discovery Environments , 1997, Artif. Intell..

[209]  Chris Bailey-Kellogg,et al.  Influence-based model decomposition for reasoning about spatially distributed physical systems , 2001, Artif. Intell..

[210]  Olivier Raiman,et al.  Order of Magnitude Reasoning , 1986, Artif. Intell..

[211]  Brian C. Williams,et al.  A Theory of Interactions: Unifying Qualitative and Quantitative Algebraic Reasoning , 1991, Artif. Intell..

[212]  Toyoaki Nishida,et al.  Generating Quasi-symbolic Representation of Three-Dimensional Flow , 1993, AAAI.

[213]  Giorgio Brajnik,et al.  Trajectory Constraints in Qualitative Simulation , 1996, AAAI/IAAI, Vol. 2.

[214]  Robert Milne,et al.  Gas-Turbine Condition Monitoring Using Qualitative Model-Based Diagnosis , 1997, IEEE Expert.

[215]  N. Smith,et al.  Automated modelling: a discussion and review , 1996, The Knowledge Engineering Review.

[216]  Philip Schaefer,et al.  Analytic Solution of Qualitative Differential Equations , 1991, AAAI.

[217]  Olivier Dordan,et al.  Mathematical Problems Arising in Qualitative Simulation of a Differential Equation , 1992, Artif. Intell..

[218]  Kenneth D. Forbus Qualitative Reasoning About Space and Motion , 1983 .

[219]  Brian C. Williams,et al.  MINIMA: A Symbolic Approach to Qualitative Algebraic Reasoning , 1988, AAAI.

[220]  Thomas F. Edgar,et al.  Qualitative Modeling of Chemical Reaction Systems , 1990 .

[221]  Benjamin Kuipers,et al.  The composition and validation of heterogeneous control laws , 1994, Autom..

[222]  George J. Pappas,et al.  Discrete abstractions of hybrid systems , 2000, Proceedings of the IEEE.

[223]  Adam Farquhar,et al.  A Qualitative Physics Compiler , 1994, AAAI.

[224]  Peter Struss,et al.  Fundamentals of Model-Based Diagnosis of Dynamic Systems , 1997, IJCAI.

[225]  Daniel S. Weld The Use of Aggregation in Causal Simulation , 1986, Artif. Intell..

[226]  Gerald J. Sussman,et al.  Intelligence in scientific computing , 1989, CACM.

[227]  P. Pandurang Nayak Automated Modelling of Physical Systems , 1995 .