The theory of syntactic domains

In this essay we develop a mathematical theory of syntactic domains with special attention to the theory of government and binding. Starting from an intrinsic characterization of command relations as defined in [Ba 90] we determine the structure of the distributive lattice of command relations. This allows to introduce implication and negation as constructors, whose logic turns out to be the intuitionistic logic of linear posets. Using what is known about intuitionistic logic we can study how domains can be defined from some basic set of command relations that are naturally supplied by the grammar. Moreover, this can be reversed to see how the requirement that domains can be defined in a particular way constrains the syntax. This general theory will then be applied to GB and we will show that there is great evidence to support our claim that command relations are the basic relations from which all other syntactic domains must be defined in a clear and rigid way.