Reasoning in Logic about Continuous Systems

An intelligent agent, reasoning symbolically ill a continuous world, needs to infer properties of the behaviors of continuous systems. A qualitative simulator, such as QSI NI , con— structs a set. of possible behaviors corisis— tent with a qualitative differential equation (QDE) and initial state. This set of behaviors is expressed as a flinte tree of qualitative state descriptions. li-i the case of QS1 lvi, this set is guaranteed to contain the “actual” behavior under certain circumstances. We call this property the “soundness” of QSI lvi. Tile behavior tree call then be interpreted as a model for statenients in a branching— time telilporal logic such as Expressive Behavior Tree Logic ( EBTL) , which we intro— duce. Because QSl M is sound, validity of an EF3TL proposition (necessarily p) implies the corresponding theorem about the dynani— ical system described by the QDE. Therefore, at least for universals, statements in temporal logic about conti iuous systems can he proved by qualitative simulation. This allows a liy-~ brid reasoning system to prove such comlnon~sense stat emnelits as “what, goes up (in a con— stallt gravitational field) must conic down or to do such expert reasoning about dymiani— ical systems as proving the stability of a 11011— 1 inear, heterogeneous controller.