Trajectory Constraints in Qualitative Simulation

We present a method for specifying temporal constraints on trajectories of dynamical systems and enforcing them during qualitative simulation. This capability can be used to focus a simulation, simulate non-autonomous and piecewise-continuous systems, reason about boundary condition problems and incorporate observations into the simulation. The method has been implemented in TeQSIM, a qualitative simulator that combines the expressive power of qualitative differential equations with temporal logic. It interleaves temporal logic model checking with the simulation to constrain and refine the resulting predicted behaviors and to inject discontinuous changes into the simulation.

[1]  Benjamin Shults,et al.  Qualitative Simulation and Temporal Logic: Proving Properties of Continuous Systems , 1996 .

[2]  Giorgio Brajnik,et al.  Guiding and refining simulation using temporal logic , 1996, Proceedings Third International Workshop on Temporal Representation and Reasoning (TIME '96).

[3]  D. DeCoste.  Goal-directed qualitative reasoning with partial states , 1994 .

[4]  T. Parsons,et al.  Toward a General Theory of Action , 1952 .

[5]  Daniel G. Bobrow,et al.  Modeling Time in Hybrid Systems: How Fast Is "Instantaneous"? , 1995, IJCAI.

[6]  Kenneth D. Forbus.  Introducing Actions into Qualitative Simulation , 1989, IJCAI.

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

[8]  Giorgio Brajnik,et al.  Temporal Constraints on Trajectories in Qualitative Simulation , 1996 .

[9]  Rina Dechter,et al.  Temporal Constraint Networks , 1989, Artif. Intell..

[10]  A. John Mallinckrodt,et al.  Qualitative reasoning: Modeling and simulation with incomplete knowledge , 1994, at - Automatisierungstechnik.

[11]  James F. Allen.  Towards a General Theory of Action and Time , 1984, Artif. Intell..

[12]  Kenneth D. Forbus.  Qualitative Process Theory , 1984, Artificial Intelligence.

[13]  Shuji Doshita,et al.  Reasoning about Discontinuous Change , 1987, AAAI.

[14]  E. Allen Emerson,et al.  Temporal and Modal Logic , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.