It is more common that a syntactically unambiguous phrase has a semantic ambiguity; for example, the lexical ambiguity in "Your boss is a funny man" is purely semantic, leading to the response "Funny ha-ha or funny peculiar?"
ɪɾ ɪz mˈoːɹ kˈɑːmən ðˌæɾə sɪntˈæktɪkli ʌnæmbˈɪɡjuːəs fɹˈeɪz hɐz ɐ səmˈæntɪk ˌæmbɪɡjˈuːɪɾi; fɔːɹ ɛɡzˈæmpəl, ðə lˈɛksɪkəl ˌæmbɪɡjˈuːɪɾi ˈɪn "jʊɹ bˈɔs ɪz ɐ fˈʌni mˈæn" ɪz pjˈʊɹli səmˈæntɪk, lˈiːdɪŋ tə ðə ɹᵻspˈɑːns "fˈʌni hˈɑːhˈɑː ɔːɹ fˈʌni pɪkjˈuːlɪɹ?"