ABSTRACT
This chapter discusses the formulation of a first-order semantics for a given L taking a relation of multiple denotation as sole semantical primitive. For purposes of a deductive development of a formalized semantical meta-language, it seems both natural and convenient to take certain semantical relations as primitive. The chapter talks about four kinds of axioms: logical axioms, non-logical or translational axioms, syntactical axioms and some semantical axioms. It also talks about some specification of the primitive vocabulary: primitive logical constants, translational primitives, structural-descriptive primitives, syntactical primitive, expressional variables and semantical primitive. Semantics presupposes syntax and contains it as a part, and a semantical meta-language must therefore contain a syntactical one as a part. The chapter explains four parts: a logical part, a syntactical part, a translational part and a semantical part. In terms of multiple denotation, all other semantical notions that are required are definable.
