Herbrand interpretation

Okay kiddo, let's dive into Herbrand interpretation! Imagine that you have a magic wand that can create different things. You can create flowers, toys, or even animals! Now, let’s use this wand to create a language, a special kind of language called “First-Order Logic”.

This language helps us communicate and express different ideas, such as whether a statement is true or false. But how do we know if something is true or false? That’s where Herbrand interpretation comes in!

Herbrand interpretation helps us understand the different possible meanings or interpretations of the language we created. It does this by creating a list of all the possible objects or things we can “point to” in our language. We call these objects the “domain”.

So let’s say we have a simple sentence like “All dogs bark”. In our language, we need to have an object that represents “dogs”. We can create a domain of all the possible things we can point to, like animals and plants. But since our sentence specifically mentions dogs, we can only choose from the objects in our domain that are dogs.

Now, let’s say we have another sentence “Some dogs love bones”. This sentence tells us that there exists something that is a dog and loves bones. We can create another domain that includes all the things that are dogs and some other things that might love bones, like cats or birds.

By creating different domains like this, we can understand the different possible meanings of the language we created. This helps us determine whether a sentence is true or false, and helps us communicate our ideas clearly.

So that’s Herbrand interpretation, using our magic wand to create different domains of objects that helps us understand the different possible meanings of our language!