Well-defined is a property of _functions_ ; well-formed is a property of _logical propositions_. A well-defined function is any function that is single-valued (see Tim Gowers's site for a good explanation) and a well-formed proposition is any proposition that makes sense syntactically. This function is not well defined: $$ f(a/b)=a+b. $$ This proposition is not well-formed: $$ PQ\land. $$ (EDIT: It actually is well-formed if you use reverse Polish notation. But the string $(P\implies(QQ))$ is definitely not well-formed) Does that clear up the matter?