A language L is semantic if for every TM $M$ and $N$, If $M$ and $N$ compute the same function, L contains both or none.

• Compute the same function -> Do the same thing
• A language is semantic if it discriminates based on behavior/function/semantic
• If two TM that compute the same function (do the same thing) one is included in L and one is not, then L has made the decision not based on behavior, but syntax!

How to prove a language is semantic?

You can't.

How to prove a language is non-semantic?

Give an example of two TMs (codes) that compute the same function (do the same thing), where one is in the language and one does not.