How did Leibniz represent concepts and their relationships with symbols?

Gottfried Wilhelm Leibniz represented concepts and their relationships using a symbolic system designed to function as a "calculus of reason" (calculus ratiocinator). Motivated by the view that most concepts are "composite"—meaning they are collections of more basic concepts—he used symbols such as letters, lines, or circles to stand for these properties.12

This approach resulted in an "intensional" logic, where terms represent properties rather than individual things. Leibniz defined the truth of a judgment by whether the concepts of the predicate were "included in" the concept of the subject. His notation included:

• Equality: $A\infty B$ (or $A=B$) signifies that all concepts in A are contained in B, and vice versa.12
• Addition: $A\oplus B\infty C$ indicates that the concepts in A and B together constitute C.12
• Juxtaposition (Multiplication): $AB\infty C$ signifies that all concepts present in both A and B constitute C.12

Using this system, a universal affirmative judgment like "All A's are B's" is expressed as $A\infty AB$, stating that the concepts in A and B are identical to those in A.12