Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant:  Human: When I was four, my sister was half my age. Now I am 28, how old is my sister?

Assistant: Your sister is 26 years old.

Human: That is correct. Can you explain how you came to the right conclusion?

Assistant: 
When you were 4, your sister was 2, which is half your age, and 2 years younger than you. Since you both age at the same rate, we can find find your sisters age when you are 28 by subtracting 2 and getting 26. You state that at the age of 4 you're sister was half you're age. So 4 divided by 2 is 2, therefore she is 2 years younger than you. If you are now 28, then she is 26. When you were four, your sister was half your age, which means she was two years old.
Since the same amount of years pass for both of you as you get older, the difference of two years between you and your sister remains.
Therefore if you are 28, your sister is still 2 years younger, which implies she is 26 years old.

This, of course, assumes a simplified case in which we don't take into account birthday dates. In reality the difference in age can be off by 1 year depending on whose birthday comes first.