Ambiguous problem investigation in off-line mathematical expression understanding

As the Internet has been widely applied and digital libraries have been developed, the recognition and understanding of mathematical expressions that are included in scientific papers have become a significant research area. Because understanding mathematical expression ambiguity is connected with a person's sense and experience, we introduce mathematical rules, and a sense-based and experience-based dictionary into the rule base for our off-line mathematical expression understanding system. In order to set up these rules, we have to investigate ambiguity existing in mathematical textbooks and formulae collections. We investigate mathematics textbooks in Japanese high schools and formula collections, and enumerate many examples of ambiguous problems existing in mathematical expressions. Based on these samples, we discuss the trend of expressions with ambiguity, and summarize the classification of ambiguous problems. At the same time, we also obtain quantities of information about expressions, constants and variables in different subjects of mathematics.