Semantic analysis of matrix structures

The automatic interpretation of mathematical text structures has received only limited attention so far. While there has been work on the particularities of the character recognition of two dimensional formulas such as matrices in texts, very little has been done on exploiting their additional semantics in order to make them available for further processing. We present an algorithm that provides the interface between the recognition of matrix expressions and their concrete interpretation as mathematical objects. Given an underspecified matrix representation as they commonly appear in textbooks, containing ellipses and fill symbols, our algorithm extracts the semantic information contained. Matrices are interpreted as a collection of regions that can be interpolated with a particular term structure. The effectiveness of our algorithm can be demonstrated by its ability to derive concrete instances for the processed matrix representations in a symbolic computation system.