exclusive/inclusive disjunction

The disjunction of two propositions, p or q, is represented in logic by p ∨ q. This is evaluated as true if both p and q are true, and is called inclusive disjunction (‘vel’). A different notion, exclusive disjunction, is defined true only when exactly one of p, q is true, and as false if they are both true. It has been contentious whether in natural language ‘or’ has an exclusive reading, or whether the appearance is the result of implicature.