It supplements the account of simple and compound statements offered by formal logic and, reflecting the character of arguments in natural language, widens the scope to include inductive as well as deductive patterns of inference. Assertions have meaning as statements as well as actions and often reveal something about the person who makes them. Not least, they are the main ingredient in patterns of inference.
Assertions also have an epistemic dimension.
Appraising the full meaning of a premiss or conclusion therefore involves gauging whether the statement was asserted merely as a belief or, in addition, as an objective fact or even as an item of knowledge. Finally, assertions have an emotive side. Few arguments of natural language are utterly impersonal. Attitudes and feelings seep from the language of argument and can easily influence what direction a sequence of reasoning may take. Such topics, though important for understanding arguments in natural language, lead it far from the concerns of formal logic.