This paper explores some of the opportunities for using vector product operations to model compositional phenomena in natural language. These vector operations are all well-known and used in mathematics and physics, particularly in quantum mechanics. Instead of designing new vector composition operators, this paper gathers a list of existing operators, and a list of typical composition operations in natural language, and describes two small experiments that begin to investigate the use of certain vector operators to model certain language phenomena.
Though preliminary, our results are encouraging. It is our hope that these results, and the gathering of other untested semantic and vector compositional challenges into a single paper, will stimulate further research in this area.