This paper starts from the observation that the standard arguments for compositionality are really arguments for the computability of semantics. Since computability does not entail compositionality, the question of what justifies compositionality recurs. The paper then elaborates on the idea of recursive semantics as corresponding to computable semantics. It is then shown by means of time complexity theory and with the use of term rewriting as systems of semantic computation, that syntactically unrestricted, noncompositional recursive semantics leads to computational explosion (factorial complexity). Hence, with combinatorially unrestricted syntax, semantics with tractable time complexity is compositional.

中文翻译：

---

组合性、可计算性和复杂性

本文从以下观察开始，即组合性的标准论据实际上是语义可计算性的论据。由于可计算性并不需要组合性，因此再次出现了如何证明组合性的问题。然后，本文详细阐述了递归语义与可计算语义相对应的概念。然后通过时间复杂度理论和使用术语重写作为语义计算系统来证明，句法上不受限制的非组合递归语义会导致计算爆炸（阶乘复杂性）。因此，对于组合不受限制的语法，具有可处理时间复杂度的语义是组合的。