Could someone somewhat plainly explain what is unification, when it is

[EvLer]

Could someone somewhat plainly explain what is unification, when it is used and what does it "buy"? I just have heard of it and searched online a bit but it is a bit hazy for me.
A small example would be appreciated as well .

 

[HallsofIvy]

What field are you talking about? "Unification", in general, means "unifying" or combining two concepts. The most famous "unification" is not in mathematics but in physics: unifying Gravity and Electromagnatism, the "unified field theory".

 

[EvLer]

sorry, yeah, I am talking about mathematical logic (computer science related) more so than physics.

 

[verty]

From wikipedia:

In mathematical logic, in particular as applied to computer science, a unification of two terms is a join (in the lattice sense) with respect to a specialisation order. That is, we suppose a preorder on a set of terms, for which t* ≤ t means that t* is obtained from t by substituting some term(s) for one or more free variables in t. The unification u of s and t, if it exists, is a term that is a substitution instance of both s and t. If any common substitution instance of s and t is also an instance of u, u is called minimal unification.

I think one can think of it as a token that is of both types. There is no possible unification of 'square' and 'circle' because one can't get a square circle, but 'red' and 'ball' are unified in 'red ball'. Anyway, that's my intuition of it. 'Red ball' is a minimal unification because all other unifications (like 'red beach ball') do qualify as red balls.

Or perhaps I'm totally wrong.

 

[verty]

Oh, I didn't quite read it properly. A unification is a join between a general term and a more specific term, like a chain of inclusion. A labrador is a dog and a dog is an animal, so I guess the unification of labrador and animal is that chain (labrador <= dog <= animal). A minimal unification is the shortest chain of inclusion between the two terms.

Er, no, that's not right either. One of the mathematical folks will surely explain it shortly.

 

[HallsofIvy]

Your first example was correct. The unification of "labrador" and "animal" is "animal". In a slightly more useful example, the unification of "labrador" and "persion", in terms of biology, would be "mammal", the smallest class that includes both.