Mathematics is the language of God and so is the language of our mind. A man may speak many languages but there is only one way of storing everything he speaks.
Below is probably how information from the external world coming inside is stored.
As proposed by Noam Chomsky in Universal Grammar, the L.A.D, Language Acquisition Device is a default installation we are born with. A child at a very young age can easily speak properly structured sentences using the rules inside the LAD.
Most of predicate logic, first order and higher order logic representations solve an extremely small part of the problem but are definitely a good start. Consider the below statement for example.
Sentence 1: All purple mushrooms are poisonous
Logic Representation:
∀x[(Mushroom(x) ∧ Purple(x)) → Poisonous(x)]
What we understand from the above represented logic is that If a mushroom is not purple then the mushroom is not Poisonous. Various inferences for the same statement can be.
∀x[(Mushroom(x) ∧ ¬Purple(x)) → ¬Poisonous(x)]
Mushroom but not purple --> Not Poisonous
∀x[(¬Mushroom(x) ∧Purple(x)) → ¬Poisonous(x)]
Not a mushroom but purple --> Not Poisonous
Sentence 2: Everest is the highest mountain on Earth.
Logical Representation:
Mountain(everest) ∧ ¬∃x[Mountain(x) ∧ Higher(x, everest) ∧ On(x, earth)]
Most of this logic assumes the availability of functions like Mushroom, Purple, Higher, On etc. A computer program capable of being able to automatically create these functions must know how to derive those functions but based on what and how many of them?
Inference: I ll need to run more experiments with longer sentences and try to find a way to build these functions. A man with little knowledge of a language can express ideas in that language to another human being without the use of proper grammar. Building a computer program capable of forming grammatically correct sentences is an easy problem to solve and can be done with a readily available Text Corpus but a program capable of storing thoughts in a mathematically solvable format is the hard part. Thoughts are mathematical models.