First-Order Models:

Here if we proposed first-order logic as a good knowledge representation language than propositional logic is just because there is more expressive than we can write more of our sentences in logic. Hence the sentences we are going to want to concern rewrites and inference rules will include quantification. However all of the rewrite rules we've seen so much far can be used in propositional logic hence first-order logic use. Now there we consider rules that rely on information about the quantifiers, which are not available to an agent working with a propositional logic representation scheme. 

Just before we considered at first-order inference rules we have to pause to consider what it means to an inference rule to be sound. Hence earlier we defined this as a meaning the top entails the bottom: that there any model of the former was a model of the latter. In fact first-order logic introduces new syntactic elements like constants, functions, variables, predicates and quantifiers alongside the propositional connectives. Because we need to completely revise our definition of model and a notion of a 'possible world' that defines where a sentence is true or false in that world.