Staudacher: Use Theories of Meaning (2010)

By and large, Marc Staudacher endorses the use of evolutionary perspectives on signaling game in his dissertation.

However, in section 7.2.3, he reiterates his concern about a fact that he observed on his blog two years ago: Although there are models of signaling games with infinitely many signals, no model plausibly explains how syntactically structured signals can be aligned with semantically compositional meanings.

"But it seems to be more of a technical problem that will eventually be solved," he adds (pp. 214-15). That seems to be a sound enough intuition. The semantics of a language with finitely many atoms and finitely many relations is learnable in finite time, even if the syntactic span of the language is infinite.

A temporal difference approach could for instance do the trick. Given a signal f(x,y) = b, where b is 0 or 1, an agent could record all of the sentences f(0,0) = b, f(0,1) = b, f(1,0) = b, and f(1,1) = b with fractional observation counts determined by the subjective probability of x = 0, x = 1, y = 0, and y = 1.