Title: Categorial Grammar Induction as a Compositionality Measure for Emergent Languages in Signaling Games. Abstract: This paper proposes a method to analyze the compositional structure of emergent languages using Categorial Grammar Induction (CGI). Emergent languages are communication protocols arising among agents in environments such as signaling games. Previous work has studied how similar or dissimilar emergent languages are to natural languages in compositionality. However, most of them focused on trivial compositionality, assuming flat structures in languages. We further focus on non-trivial compositionality, i.e., the relationship between hierarchical syntax and semantics. To this end, we apply CGI to emergent languages, inspired by previous NLP work. Given sentence-meaning pairs of a language, CGI induces 1) a categorial grammar that describes the syntax of the language and 2) a semantic parser that compositionally maps sentences to meanings. We also propose compositionality measures based on the grammar size and semantic parser performance. CGI and the proposed measures enable deeper insights into the non-trivial compositionality of emergent languages, while correlating well with existing measures like TopSim.