''Baba is You'' is a recent puzzle game in which the player builds a set of rules by pushing squares with words written on them. If we leave aside the combinatorial difficulty of how to move the blocks around without getting stuck, the game seems to be unique insofar as it is determined entirely by rules which the player builds. The total set of rules can be enlarged or made smaller (for example, if we have Key Is Defeat and push Key away from the rest of the rule, the number of rules is reduced by one).


A rule is made from at least three words (where the second connecting word is usually ‘is’) and a word can be a noun, an adjective, a conjunction, or a verb. For example, in Key is Open, the word ‘Open’ is a verb, implying that the key will remove a door if it is manipulated onto the same square as the door. In order for a level to have a winning strategy, each level must have a Win condition and a You condition.


I am trying to think if there is something mathematically interesting about the way that one changes the logical rules to solve a puzzle. For me, the game is a bit paradoxical because it definitely *appeals* to mathematicians but I do not think there is anything actually mathematical to be said about it in terms of set theory and formal logic (besides the trivial combinatorics of most effectively finding a solution).


The mathematical aspect seems to be that often one needs to make creative changes to the underlying rules in order to arrive at a scenario which can be solved (perhaps something like writing a proof by finding the correct language with the logical truths which you need). This seems more philosophical than mathematical to me though.



Set theory / Formal logic of Baba is You
The developer has [this GDC talk](https://www.youtube.com/watch?v=Jf5O8S5GiOo) where he talks about the mechanics which you might find interesting. My impression is it's a lot of random hacks, which may fit with your description.


