Model Theory is the field of mathematics that studies the relationships between algebraic structures and the syntactic expressions that they make valid. As such, this field emphasizes the embedding of knowledge into models.
In this talk we will introduce a meta-mathematical approach to Machine Intelligence using Model Theory. In particular, we will show how we can introduce knowledge and data into semilattices and how we can later manipulate it, by adding to these structures special elements called atoms that both encode the structure of the semilattice and can be operated on to enforce syntactic expressions. We will see how, using such ideas, we are guaranteed to find a simple rule in our data, if it exists. By doing so, we are able to find generalising models.
We will also discuss some relevant properties of our approach, like its mathematical transparency, the fact that we are only using set-theoretical operations that do not rely on optimisation, the possibility of combining data with formal knowledge and the reduced dependency on statistics and hyperparameters.