Consider two relations: traveler[Trip*Person]
and dest[Trip*Destination]
. The first relation tells which persons have traveled on which trip. The diagram shows this as red dashed lines. The second relation links trips to destinations. It is depicted by dotted blue lines in the diagram.
From this diagram, we can tell which statements are true (i.e. facts). The statements are given both formally and in natural language. The elaborate version is a literate translation of the semantics in logic. The ordinary version tells the same in a more human sounding manner.
The following statements do NOT follow from the population shown in the diagram:
Would you like a different explanation of the residual operators? This page explains them in natural language. Click here for the explanation of residual operators in logic.
Formal statement
Elaborate natural language
Ordinary natural language
"Peter" (traveler~/dest~) "Rome"
For each trip, if it has destination Rome, then it has been made by Peter.
Every trip to Rome has been made by Peter.
Formal statement
Elaborate natural language
Ordinary natural language
"Peter" (traveler\dest) "Rome"
For each trip, if Peter has made the trip then its destination is Rome.
Every trip that Peter made has Rome as destination.
"Peter" (traveler\dest) "Paris"
For each trip, if Peter has made the trip then its destination is Paris.
Every trip that Peter made has
Paris as destination.
"Peter" (traveler~/dest~) "Paris"
For each trip, if Paris is the destination then Peter has made that trip.
Every trip to Paris has been made by Peter.