Theta Theory: operads and coloring
This work addresses a foundational issue in computational linguistics by providing a mathematical model for syntactic theory, though it appears incremental as it builds on existing operad and Minimalism frameworks.
The paper tackles the problem of implementing theta theory in generative linguistics by constructing a colored operad that generates syntactic objects through a coloring algorithm, showing that this approach equivalently filters structures formed by Merge and implies a semantic dichotomy between External and Internal Merge.
We give an explicit construction of the generating set of a colored operad that implements theta theory in the mathematical model of Minimalism in generative linguistics, in the form of a coloring algorithm for syntactic objects. We show that the coproduct operation on workspaces allows for a recursive implementation of the theta criterion. We also show that this filtering by coloring rules on structures freely formed by Merge is equivalent to a process of structure formation by a colored version of Merge: the form of the generators of the colored operad then implies the dichotomy is semantics between External and Internal Merge, where Internal Merge only moves to non-theta positions.