The paper shows that syntactic heads, phases, and constraints like EPP and PIC can be expressed as a colored operad bud generating system, equivalent to a colored Merge filtering process.
Theta Theory: operads and coloring
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abstract
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.
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Hypermagmas and Colored Operads: Heads, Phases, and Theta Roles
The paper shows that syntactic heads, phases, and constraints like EPP and PIC can be expressed as a colored operad bud generating system, equivalent to a colored Merge filtering process.