Here are three first order axioms that represents a part of a mereology theory.
Reflexivity $\forall x : part(x,x)$
Antisymmetry $\forall x \forall y : ((part(x,y) \land part(y,x)) \implies (x = y))$
Transitivity $\forall x \forall y \forall z :((part(x,y) \land part(y,z)) \implies part(x,z))$
Here is my attempt to present these axioms as a set of conceptual graphs (CG). CGs can be represented in Common Logic (ISO zipped PDF).
My understanding of the above CG is as follows:
The variables are universally quantified.
The arrow on graph representing reflexivity is bi-directional.
Both antisymmetry and transitivity are represented by an IF-THEN contexts.
The three graphs are all related by conjunction.
Dotted lines are co-references.
Equality (=) is actually commutative, but is represented as a directed relation .
Question:
Is my attempt at representing the FOL sentence as CG's reasonable? How could my representation be improved?
This questions spans logic and knowledge representation so it may not be a good fit for a mathematics forum. Perhaps someone could suggest a more appropriate forum for questions such as this.
I don't really know about the technical details of Conceptual Graphs, but I do know that it is based off Existential Graphs, and here are the respective representations in Existential Graphs:
$\forall x \ part(x,x)$:
$\forall x \forall y \ ((part(x,y) \land part(y,x)) \to x = y)$:
$\forall x \forall y \forall z \ ((part(x,y) \land part(y,z)) \to part(x,z))$:
The last two certainly look like what you have!