Going a bit further down the grid cell encoding rabbit hole: If the highest level of representation is at the autobiographical memory level and cognitively there is some sort of representation and relationships between objects there should be some sorts of basic operations.
This is exactly one of the issues I have been thinking about for many years. (my oldest notes on this run back over a decade)
One of the possibilities that keeps bubbling up as a strong candidate for internal representation is the tuple. That uses our internal spatial representation and system arranges our objects as (object)(relation)(object)
BTW: It’s nice that the rest of the world is starting to converge on the internal spatial representation that seemed most likely to me over the years!
With this long, self-congratulatory introduction - tonight I bumped into a very interesting paper that explores some of these same concepts:
https://www.ncbi.nlm.nih.gov/m/pubmed/30146305/
If you are the sort of person that uses a certain SH web page to view your papers you will be needing to use this DOI address:
doi: 10.1016/j.neuron.2018.07.047