Abstract: This chapter gives a small informal theory for a language fragment including quantifiers in illustration. The discussion in subsequent chapters takes place, then, in this new framework in which the axioms of the theory are either reference axioms or satisfaction axioms. The chapter discusses also some issues having to do with how to apply these devices to natural languages, particularly with regard to the use of regimented versions of natural language sentences which aid in the presentation of a formal theory for the language.

Keywords: reference axioms, satisfaction axioms, language fragment, natural languages,