The Expressivity of Tree Languages for Syntactic Structures

In this paper, we investigate the expressivity of a series of languages describing syntactic structures, i.e. labeled ordered trees. Such a tree language states a formalism to describe certain sets of trees. We apply them to represent syntactic principles recently used in some theories of syntax. An investigation of the expressivity establishes the relationship to appropriate types of formal grammars, i.e. some versions of the context-free grammars and the mildly contextsensitive grammars. The tree languages considered employ formalisms such as first-order logic, propositional dynamic logic, propositional modal logic, and rational trees. Each of these formalisms commonly describes structures that can be generated by a corresponding context-free grammar. As a basic result we can construct the set of trees specified by a certain principle and our approach can establish the explicit relationship between syntactic principles and the trees. Finally, we discuss some extensions of our approach to capture non-context-free properties of natural languages.