Is there any definition of such functions in lattice theory?

Question

Let $\mathfrak L$ be a lattice and $f:\mathfrak L\to \mathbb R$ be a function. We say that $f$ obeys $\mathfrak L$ if for any $A,B\in \mathfrak L$ we have

$$f(A\vee B)=f(A)+f(B)-f(A\wedge B)$$

I expect that such definition already exists. Any reference or comment is welcome.

Answer 1

This is called a valuation on $\mathfrak L$, see Birkhoff's book for more on that.