In a definition
Definition. Proposition P(x) holds if
- A(x) is true;
- B(x) is true.
Usually I'd expect to see "and" or "or" to connect the two statements. What does the semicolon ";" mean? Is there a convention about this?
In particular, I saw a semicolon used this way in the following definition from page 71 of Probabilistic Graphical Models:
Using a semicolon like this is not really proper mathematical grammar, and so it is not something you can expect to see often and there are not clear conventions for what it means. I would expect, though, that a semicolon like this almost always means "and". In particular, it seems quite clear that the semicolon means "and" in the example you are interested in (the second part of the definition seems to not even make sense without assuming the first part, since "no other node" seems to mean "no node other than the one referred to in the previous statement).