This book is a research monograph reporting the attempts of the authors to provide a framework for relating the linguistic form of utterances and their semantic interpretation based on the idea of constraint propagation. Unlike other approaches, it does not impose a hierarchy among linguistic and contextual constraints. Instead, the authors rely on situation schemata which allow an absence of hierarchy and the possibility for a series of situations to further determine the meaning of an utterance. Three aspects of this approach receive detailed treatment: algorithmic production of situation schemata via constraint equations, the interpretation of situation schemata, and the logical properties (persistence, completeness, etc.) of the resulting system. Appendices expand the treatment to propositional phrases, a new proof of a Lyndon-type interpolation theory for many-sorted first order logic, and a proof of a relative saturation lemma. A useful bibliography lists the relevant literature.