This additional chapter explores the semantics of classical logic and conditional logic. In classical logic, the semantics of a set of sentences S is determined by the set of all the interpretations (or semantic structures), called models, that make all the sentences in S true. The main concern of classical logic is with the notion of a sentence C being a logical consequence of S, which holds when C is true in all models of S.

Semantic structures in classical logic are arbitrary sets of individuals and relationships, which constitute the denotations of the symbols of the language in which sentences are expressed. In this chapter, I argue the case for restricting the specification of semantic structures to sets of atomic sentences, called Herbrand interpretations.