Definition:Exclusive Or/Semantics of Exclusive Or

Semantics of Exclusive Or
Let $p \oplus q$ denote the exclusive disjunction of two statements $p$ and $q$. The exclusive disjunction is used to represent any statement in natural language such that exactly one of two substatements are held to be true.

Thus $p \oplus q$ can be interpreted as:
 * $p$ or $q$, but not both
 * Either $p$ or $q$.