I wouldn't know how to write something that "summarizes how I (as the computer) should move Pacman in relation to the presence or absence of other thing." I can't figure out what that's supposed to mean. Given the image shown, I would have said "if PacMan reaches a wall, the computer should not continue moving PacMan in that direction."

Also, why anthropomorphize the computer? And why are we "summarizing" instead of instructing the computer? The question asked for a declarative solution and then is surprised that the children gave declarative answers. [edit: I misread what was being said in that portion of the paper and that portion of has been replaced by this bit in square brackets]

The experiment seems extremely sloppy. It can't possibly show what it purports to show, there's way too much in the design of the study that could have biased the results, the sample sizes tiny, the task unclear, and the quantitative analysis subjective.