depõ

depþ is a theoretical measure in linguistics used to quantify the depth of dependency structures in sentences. The term appears in discussions of dependency grammar and computational parsing as a lightweight index of sentence complexity. The inclusion of the thorn letter þ in depþ is a stylistic choice intended to distinguish the concept from ordinary depth measures and to evoke historical orthography.

Formally, depþ(S) is defined as the maximum number of dependency links on any path from the root of the sentence's dependency tree to a leaf. In practical terms, it is the length of the longest chain of head-dependent relations in the sentence. Higher values indicate more nested or layered dependencies.

Calculation examples: The simple sentence The cat slept has depþ equal to 1. A sentence like The cat that the dog chased slept has a higher depþ, reflecting a nesting of a relative clause; typical estimates place this around 3 for the example, depending on the annotation scheme. In passages with multiple center-embeddings, depþ can reach higher values and is often used as a proxy for parsing difficulty.

Applications of depþ include benchmarking, cross-language typology, and the evaluation of parsing algorithms. It is not a universal measure; values can vary with annotation conventions and treebank design. Critics argue that depþ abstracts away important discourse and semantic factors, so it should be used in conjunction with other measures of complexity.

See also dependency grammar, parse trees, syntactic depth.