According to SPARQL Property Paths, negation is expressed with the operator !, i.e., !(a|b|c|d) means any relations that do not fall into {a, b, c, d}.

Based one this definition, I find the following example very counterintuitive.

PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
PREFIX : <http://rdf.freebase.com/ns/> 

ASK {
:m.0262dl9 
!(:type.object.type|<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>) 
:common.topic
}

The above query returns false because the only relations from :m.0262dl9 to :common.topic are :type.object.type and <http://www.w3.org/1999/02/22-rdf-syntax-ns#type>, which are negated. However, if we add ^:type.object.type, which means the inverse of :type.object.type to the negated set, the answer becomes true. In other words, we modify

!(:type.object.type|<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>)

to

!(:type.object.type|^:type.object.type|<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>)

This is quite weird, since the first query is false entails that the second query must also be false. I am really not sure why the second query returns true. Am I misunderstanding the definition of ! or ^?