Temporal and Spatial Analysis in Knowledge-based Physics Problem Solving

Physics problems as stated in textbooks are typically informal and incomplete, and not amenable to the direct application of the general laws of physics. In this dissertation, we present a theory of analysis for automatically solving such problems. In particular, the theory provides a detailed methodology for constructing a formal problem representation, called physical representation, upon which physics laws may be appropriately selected and instantiated. With the equations generated by these laws, the solutions to these problems are obtained through strictly mathematical manipulations. This theory provides a well-structured domain language, in which it is relatively easy to state mechanical knowledge and mechanics problems. In the language we introduce the notion of basic physical phenomenon for representing the knowledge of physical situations and events. This notion serves as both the building block for the physical representation and as a vehicle for accessing the appropriate physical laws. Both basic physical phenomena and more traditional temporal entities, instants and intervals, may be used as time references. This dual-system representation facilitates bi-level abstractions of time necessary to avoid discontinuities introduced by short impulsive phenomena, e.g., collisions, and corresponds well with human-like temporal reasoning. The language also includes an ontology of space, using multiple abstractions to account for its inherent complexity, and representation schemes for physical laws and equations. The other key ingredient of the theory is a repertoire of ordered knowledge sources, formulated to specify the derivation procedures of a physical representation. The domain language, in which these knowledge sources are written, has a structure which is useful as a theoretical basis for determining their ordering and inference step sizes. This practice has proven crucial for building knowledge-based systems that are easy to debug and modify. The theory has been implemented and tested in a computer program which has successfully solved several relatively difficult problems selected from a widely used textbook. Novel methods implemented in the program for intelligently selecting appropriate physics laws and for solving equations are also discussed.