It is a standard and generally accepted view that semantics deals with context-independent truth-conditional meaning and pragmatics deals with context-dependent non-truth-conditional meaning. This thesis redefines the dichotomy between semantics and pragmatics on the basis of conventionality of meaning, and provides a theory of semantic meaning where meanings are described as what a speaker expresses by means of conventionalised linguistic devices. In Chapter 1, the standard dichotomy of semantics and pragmatics is introduced from a historical perspective concerning how the field of pragmatics has been established, and problems of the dichotomy are discussed. A redefinition of the dichotomy based on the conventionality of meaning is proposed. In the extended semantic domain, not only does a speaker express an assertion about the world, i.e. truth-conditional meanings, but also indicates the speech situation which the speaker shares with the hearer. In the rest of the thesis, a theory of semantic meanings in this extended domain is developed. Chapters 2 and 3 develop a theory which concerns the meanings a speaker expresses in asserting something about the world by means of linguistic conventions. In Chapter 2, important early theoretical contributions are surveyed and relevant later theories discussed. It is shown that the traditional dyadic approaches to meanings which are based on the concepts of reference and prediction are not incompatible with triadic approaches where meanings are described as speech acts a speaker performs in asserting something about the world using linguistic conventions. In Chapter 3, Austin (1950)'s model of communication is developed into a theory for analysing truth-conditional meaning whereby a speaker refers to an entity or situation by means of demonstrative conventions and describes it by means of descriptive conventions. We discuss the demonstrative conventions which correlate words with a particular entity or situation and the descriptive conventions which correlate words with types of entity or situation. It is also shown that there are four different types of speech act a speaker potentially performs by using the demonstrative and descriptive conventions in different ways.