Abstract
We illustrate TeQsim, a qualitative simulator for continuous dynamical systems that combines the expressive power of qualitative differential equations with temporal logic to constrain and refine the resulting predicted behaviors. Temporal logic is used to specify constraints that restrict the simulation to a region of the state space and to specify trajectories for input variables. A propositional linear‐time temporal logic is adopted, which is extended to a three valued logic that allows a formula to be conditionally entailed when quantitative information specified in the formula can be applied to a behavior to refine it. We present a formalization of the logic with correctness and completeness results for the adopted model checking algorithm. We show an example of the simulation of a non‐autonomous dynamical system and illustrate possible application tasks, ranging from simulation to monitoring and control of continuous dynamical systems, where TeQsim can be applied.
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References
J.F. Allen, Towards a general theory of action and time, Artificial Intelligence 23 (1984) 123–;154.
R. Alur and T. Henzinger, Real-time logics: complexity and expressiveness, Information and Computation 104(1) (1993) 35–;77.
F. Bacchus and F. Kabanza, Using temporal logic to control search in a forward chaining planner, in: Proc. of the 3rd European Workshop on Planning (EWSP), Assisi, Italy (AAAI Press, August 1995).
F. Bacchus and F. Kabanza, Planning for temporally extended goals, in: Proc. of the Thirteenth National Conference on Artificial Intelligence, eds. B. Clancey and D. Weld (AAAI Press, August 1996).
M. Barbeau, F. Kabanza and R. St-Denis, Synthesizing plant controllers using real-time goals, in: Proc. IJCAI ’95(Morgan Kaufmann, August 1995) pp. 791–;798.
D. Berleant and B.J. Kuipers, Using incomplete quantitative knowledge in qualitative reasoning, in: Proc. of the Sixth National Conference on Artificial Intelligence(1988) pp. 324–;329.
G. Bhat, R. Cleaveland and O. Grumberg, Efficient on-the-fly model checking for CTL*, in: Proc. Conf. Logic in Computer Science (LICS ’95)(1995).
G. Brajnik, Statistical properties of qualitative behaviors, in: Proc. Eleventh International Workshop for Qualitative Reasoning, Cortona, Italy (June 1997) pp. 233–;240.
G. Brajnik and D.J. Clancy, Temporal constraints on trajectories in qualitative simulation, in: Proc. of the Thirteenth National Conference on Artificial Intelligence, eds. B. Clancey and D. Weld (AAAI Press, August 1996) pp. 979–;984.
G. Brajnik and D.J. Clancy, Temporal constraints on trajectories in qualitative simulation, Technical Report UDMI-RT-01-96, Dip. di Matematica e Informatica, University of Udine, Udine, Italy (January 1996).
R. Dechter, I. Meiri and J. Pearl, Temporal constraint networks, Artificial Intelligence 49 (1991) 61–;95.
D. DeCoste, Goal-directed qualitative reasoning with partial states, Technical Report 57, The Institute for the Learning Sciences, University of Illinois at Urbana-Champaign (August 1994).
E.A. Emerson, Temporal and modal logic, in: Handbook of Theoretical Computer Science, ed. J. van Leeuwen (Elsevier/MIT Press, 1990) Chapter 16, pp. 995–;1072.
T.A. Henzinger, Half-order modal logic: how to prove real-time properties, in: Proc. of the Ninth Annual Symposium on Principles of Distributed Computing(ACM Press, 1990) pp. 281–;296.
D. Jonescu and J.Y. Lin, Optimal supervision of discrete event systems in a temporal logic framework, IEEE Transactions on Systems, Man and Cybernetics 25(12) (December 1995) 1595–;1605.
H. Kay and B.J. Kuipers, Numerical behavior envelopes for qualitative models, in: Proc. of the Eleventh National Conference on Artificial Intelligence(AAAI Press/MIT Press, 1993).
B.J. Kuipers, Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge(MIT Press, Cambridge, MA, 1994).
B.J. Kuipers and B. Shults, Reasoning in logic about continuous change, in: Principles of Knowledge Representation and Reasoning (KR ’94)(Morgan Kaufmann, 1994).
B. Shults and B. Kuipers, Proving properties of continuous systems: qualitative simulation and temporal logic, Artificial Intelligence 92 (1997) 91–;129.
J.G. Thistle and W.M. Wonham, Control problems in a temporal logic framework, International Journal on Control 44(4) (1986) 943–;976.
T. Washio and M. Kitamura, A fast history-oriented envisioning method introducing temporal logic, in: Ninth International Workshop on Qualitative Reasoning (QR ’95), Amsterdam (May 1995) pp. 279–;288.
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Brajnik, G., Clancy, D.J. Focusing qualitative simulation using temporal logic: theoretical foundations. Annals of Mathematics and Artificial Intelligence 22, 59–86 (1998). https://doi.org/10.1023/A:1018990024350
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DOI: https://doi.org/10.1023/A:1018990024350