# What is a good example to illustrate the difference between isomorphic and homomorphic representations?

I am learning about "knowledge representation" in my intro to AI course and one of the key ideas has to do with isomorphic vs homomorphic representations. The examples I find when I google around are mainly on the topic of mathematical graphs, which are over my head.

Can someone give me a simple, non-mathematical example of homomorphic vs isomorphic knowledge representation to help me wrap my head around the idea?

• "which are over my head" -- this is something you need to change, asap. "non-mathematical example of homomorphic vs isomorphic" -- I'm not an expert, but you seem to be asking for a non-mathematical explanation of an inherently mathematical concept. "Can you explain football without using football terms or rules?"
– Raphael
Feb 17, 2016 at 13:04
• I don't think knowledge representation is an "inherently mathematical concept". According to my class notes, In isomorphism, every element of the representing world is in the representation; whereas in homomorphism, multiple elements of the representing world are combined in the representation. Feb 17, 2016 at 13:15
• For example, I think an old-fashioned thermometer is more isomorphic than a digital read-out -- at least so far as I understand it. Feb 17, 2016 at 13:15
• @Raphael I don't think football's a good example. :-) There are two sets of eleven people who kick a ball around a field. There are two rectangular targets, at opposite ends of the field. Each set of people has its own target and scores a point for kicking the ball into it. After 90 minutes, the set of people with the most points wins. Feb 17, 2016 at 18:56
• @Teusz Homo- and isomorphism are mathematical concepts. Their definition is, literally, one line each. I have no idea what your instructor is getting at using the terms like this.
– Raphael
Feb 18, 2016 at 7:20