Building machines that can understand text like humans is an AI-complete problem. A great deal of research has already gone into this, with astounding results, allowing everyday people to discuss with their telephones, or have their reading materials analysed and classified by computers. A prerequisite for processing text semantics, common to the above examples, is having some computational representation of text as an abstract object. Operations on this representation practically correspond to making semantic inferences, and by extension simulating understanding text. The complexity and granularity of semantic processing that can be realised is constrained by the mathematical and computational robustness, expressiveness, and rigour of the tools used. This dissertation contributes a series of such tools, diverse in their mathematical formulation, but common in their application to model semantic inferences when machines process text. These tools are principally expressed in nine distinct models that capture aspects of semantic dependence in highly interpretable and non-complex ways. This dissertation further reflects on present and future problems with the current research paradigm in this area, and makes recommendations on how to overcome them. The amalgamation of the body of work presented in this dissertation advances the complexity and granularity of semantic inferences that can be made automatically by machines.