From the documentation:

Classes inherit this setting from a parent class when one class extends or implements another.

Theres additional information in the documentation for sharing keywords.

From the documentation:

• The sharing setting of the class where the method is defined is applied, not of the class where the method is called. For example, if a method is defined in a class declared with with sharing is called by a class declared with without sharing, the method will execute with sharing rules enforced.

• If a class isn’t declared as either with or without sharing, the current sharing rules remain in effect. This means that the class doesn’t enforce sharing rules except if it acquires sharing rules from another class. For example, if the class is called by another class that has sharing enforced, then sharing is enforced for the called class.
• Both inner classes and outer classes can be declared as with sharing. The sharing setting applies to all code contained in the class, including initialization code, constructors, and methods.
• Inner classes do not inherit the sharing setting from their container class.
• Classes inherit this setting from a parent class when one class extends or implements another.

Sharing settings are inherited by default (specifying a sharing setting overrides this), but sharing settings are also applied as defined in source, if there is one.

So, if you have a child who is with sharing, and a parent who is without sharing, when you call a parent method from a child object, the current sharing context would be without sharing, since the parents sharing setting is set that way.

Theres additional information in the documentation for sharing keywords.