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DIRECTIONS FOR QUALITATIVE REASONING
Author(s) -
Kalagnanam Jayant Are.,
Simon Herbert A.
Publication year - 1992
Publication title -
computational intelligence
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.353
H-Index - 52
eISSN - 1467-8640
pISSN - 0824-7935
DOI - 10.1111/j.1467-8640.1992.tb00365.x
Subject(s) - qualitative reasoning , computer science , context (archaeology) , stability (learning theory) , ordinary differential equation , property (philosophy) , theoretical computer science , qualitative analysis , computation , qualitative research , differential equation , mathematics , artificial intelligence , algorithm , machine learning , paleontology , mathematical analysis , philosophy , social science , epistemology , sociology , biology
Sacks & Doyle provide an excellent overview of the fundamental limitations of the SPQR representations for reasoning about the qualitative properties of dynamic systems. We take this opportunity to outline some new directions for qualitative reasoning. In this paper, we provide a rigorous mathematical characterization for the term “qualitative property” in the context of static and dynamic systems. Based on these characterizations, we show that interval representations are well suited for reasoning about the qualitative properties of static systems such as qualitative comparative statics and qualitative stability. Moreover, we also show that symbolic computations help in the derivation of useful global properties of dynamic systems which can be used to guide numerical sampling of differential equations. The integration of symbolic and numeric methods provides a powerful approach for automating the qualitative analysis of differential equations.