From Notes to Coursera/Stanford's Introduction to Philosophy, Chapter 9: Equality:
----------------------------------------------------------------------------------

"Although the semantics of Relational Logic does not, by itself, tell us which 
terms are equal and which are not, the idea of co-referentiality does impose 
some contraints. For example, we cannot believe a=b and b=c and at the same time 
believe that a!=c."

In my system (http://subbot.org/logicagent), I can do the following:

---

C:\logicagent>ruby logicbot.rb
Hello
I have loaded C:/logicagent/logicagent-api.yaml.
C:/logicagent/graph.yaml loaded.

> Socrates = a philosopher
Okay, Socrates = a philosopher.

> a philosopher = Aristotle
Okay, a philosopher = Aristotle.

> is Socrates Aristotle?
Yes, Socrates is Aristotle.

> Socrates is not Aristotle.
Okay, Socrates is not Aristotle.

> is Socrates a philosopher?
Yes, Socrates is a philosopher.

> is Aristotle a philosopher?
Yes, Aristotle is a philosopher.

> is Socrates Aristotle?
No, Socrates is not Aristotle.

>

---

So by default if a=b and b=c, a=c: "=" is an Equivalence Relation.  However, 
I can tell it that, in a specific case, a!=c. Then if I tell it b=d, the program 
still assumes a=d and c=d (unless I tell it different):

---

> a philosopher is a lover of wisdom.
Okay, a philosopher is a lover of wisdom.

> is Socrates a lover of wisdom?
Yes, Socrates is a lover of wisdom.

> is Aristotle a lover of wisdom?
Yes, Aristotle is a lover of wisdom.

>

---

Thus I am adding some context-dependency to the system: I can override the 
default inference procedure in specific cases. In other words, I can add 
exceptions.