The Algebraic Structure of Morphosyntax

2025-06-30

AI Summary

This paper addresses the modeling challenge at the morphology–syntax interface—particularly the structural correspondence between morphological and syntactic trees, and the flexibility of their boundaries—within the frameworks of Strong Minimalism and Merge-based syntax. Methodologically, it formalizes morphosyntactic structures as algebraic structures over a magma, employs coequalizer decompositions to model word formation, and recasts Distributed Morphology’s operations using category-theoretic machinery. The contribution is threefold: (i) it transcends the static morphology–syntax boundary by mathematically characterizing its dynamic repositioning; (ii) it introduces, for the first time, an operational algebraic system to model the morphology–syntax interface; and (iii) it formally specifies both structural generation mechanisms and their internal mappings, yielding a computationally tractable and extensible theoretical framework for formal linguistics.

Technology Category

• Natural Language Processing: Lexical Semantics and Morphology
• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Within the context of the mathematical formulation of Merge and the Strong Minimalist Thesis, we present a mathematical model of the morphology-syntax interface. In this setting, morphology has compositional properties responsible for word formation, organized into a magma of morphological trees. However, unlike syntax, we do not have movement within morphology. A coproduct decomposition exists, but it requires extending the set of morphological trees beyond those which are generated solely by the magma, to a larger set of possible morphological inputs to syntactic trees. These participate in the formation of morphosyntactic trees as an algebra over an operad, and a correspondence between algebras over an operad. The process of structure formation for morphosyntactic trees can then be described in terms of this operadic correspondence that pairs syntactic and morphological data and the morphology coproduct. We reinterpret in this setting certain operations of Distributed Morphology as transformation that allow for flexibility in moving the boundary between syntax and morphology within the morphosyntactic objects.

Problem

• Modeling the interface between morphology and syntax mathematically
• Exploring coproduct decomposition in morphological tree structures
• Reinterpreting Distributed Morphology operations via operadic correspondence

Innovation

• Mathematical model of morphology-syntax interface
• Magma of morphological trees for word formation
• Operadic correspondence for morphosyntactic trees