In a previous post, I described a paper that wrote questions as a LISP expression. The authors of that paper take their input from today’s paper by Goodman et. al. I think it’s clear to everyone that concepts, as humans use them, is highly compositional. We can use them abstractly, concretely, suppositionally, and in every way imaginable. It’s interesting to ponder whether this is the reason why our languages are so flexible or whether languague’s flexibility has made our thought so flexible.

So, the first claim of this paper is that “concepts have a language-like compositionality and encode probabilistic knowledge. These features allow them to be extended productively to new situations and support flexible reasoning and learning by probabilistic inference.” This is fairly uncontroversial.

What the authors consider then is a formal system capable of expressing the same. Their suggestion is a probabilistic programming language called Church. The develop various helper constructs in this language that help with capturing ‘randomness’, ‘conditionality’, and ‘queries’. There isn’t must to show about these programs, as they are just regular programs. Compositionality is obvious in that functions can be used and extended. Uncertainty is encoded by impure functions which return sampled values. But these functions are memoized so that when called by the same input the same answer is returned.

The paper doesn’t introduce anything computational but I’ll bring this back when I find papers that develop this concept computationally.