Approaches to Natural language processing (NLP) may be classified along a double dichotomy open/opaque - strict/adaptive. The former axis relates to the possibility of inspecting the underlying processing rules, the latter to the use of fixed or adaptive rules. We argue that many techniques fall into either the open-strict or opaque-adaptive categories. Our contribution takes steps in the open-adaptive direction, which we suggest is likely to provide key instruments for interdisciplinary research. The central idea of our approach is the Semantic Hypergraph (SH), a novel knowledge representation model that is intrinsically recursive and accommodates the natural hierarchical richness of natural language. The SH model is hybrid in two senses. First, it attempts to combine the strengths of ML and symbolic approaches. Second, it is a formal language representation that reduces but tolerates ambiguity and structural variability. We will see that SH enables simple yet powerful methods of pattern detection, and features a good compromise for intelligibility both for humans and machines. It also provides a semantically deep starting point (in terms of explicit meaning) for further algorithms to operate and collaborate on. We show how modern NLP ML-based building blocks can be used in combination with a random forest classifier and a simple search tree to parse NL to SH, and that this parser can achieve high precision in a diversity of text categories. We define a pattern language representable in SH itself, and a process to discover knowledge inference rules. We then illustrate the efficiency of the SH framework in a variety of tasks, including conjunction decomposition, open information extraction, concept taxonomy inference and co-reference resolution, and an applied example of claim and conflict analysis in a news corpus.