Dog owner owns one to many dogs. Dog is owned by zero or one dog owner.
Relationships in xtUML are a first-class part of the language. Also called associations, these constructs are more than documentation. They are part of the language and constrain the population of instances of the various classes. Associations also allow for quick traversal from an instance of one class to the instances of related classes.
For example, if you know a particular dog owner, you can traverse across R1 to get the set of dogs owned by that dog owner.