用代数结构统一描述语法与形态的接口机制。
The Algebraic Structure of Morphosyntax
- 将形态树建模为一个代数结构，通过操作符范畴实现组合。
- 揭示了语法与形态间可变边界的数学对应关系。
- 适合形式语言学与认知科学交叉研究者阅读。
在合并（Merge）的数学框架和强最小主义论题背景下，本文提出一种形态-语法接口的数学模型。形态具有组合性，由形态树构成一个代半群（magma）。不同于句法，形态内部无移动现象。存在余积分解，但需将形态树集合扩展至更广的可能输入，以参与句法树的构建。这些元素构成一个操作符范畴上的代数，通过该代数与操作符范畴代数之间的对应关系，描述句法形态树的形成过程。在此设定下，分布式形态学中的某些操作被重新解释为允许语法与形态边界灵活调整的变换。
原文摘要 · Abstract (English)
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.
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