- M maps blank nodes to blank nodes.
- M(lit)=lit for all RDF literals lit which are nodes of G.
- M(uri)=uri for all RDF URI references uri which are nodes of G.
- The triple ( s, p, o ) is in G if and only if the triple ( M(s), p, M(o) ) is in G’
Now for time being think that you are looking into a mirror. What do you see is a reflection of yourself. It means that if you map any feature of your body you find an equivalent feature in your mirror image as well (real eye to image eye, real nose to image nose etc). So looking into mirror is a bijective function and we call it as isomorphism i.e. having equal in shape.
This isomorphism is an interesting phenomenon which helps to move from one domain to another domain based on the equivalence properties. For example, if we have a problem domain x and we have a solution domain y but lets say we don’t know how to approach from y to x. So what we can do here is that we try to find an isomorphic image of x lets say z for which we know how to approach from y to z. Once we find such z we apply same set of property rules on y and reach to x. It is possible because the isomorphism preserve the property between two different objects.
With this concept, can you now imagine how can we go in and out with quantitatively between Mathematics and Philosophy.
This previous line takes me many years back, my undergraduate days, when I tried (unknowingly) to bring our social structure in equivalence to the Mathematical terms (variables, constants) and theorems and then tried to find the solutions for our social problems by solving the mathematical equations. Well, I happily accept that I could not progress on that exercise more then few days because may be my knowledge and understanding of the society and required Maths were limited. But today I find that what I tried years back without any guidance and willingness (just in wildness of my own world) has deep routes and possibility Mathematical science. Yes, Mathematicians and great social thinkers can sit together to again work on such attempts (may be they are already doing somewhere ).