This paper introduces a general framework for nonmonotonic reasoning, focusing on properties that characterize nonmonotonic consequence relations. It defines five families of nonmonotonic consequence relations, each characterized by representation theorems that relate proof-theoretic and semantic perspectives. The paper discusses the importance of preferential models, which are stronger than Adams' probabilistic semantics, and explores the expressive power of nonmonotonic systems. It compares nonmonotonic reasoning with conditional logic and highlights the differences between various systems, such as circumscription, default logic, and autoepistemic logic. The paper also presents a cumulative reasoning framework, defining cumulative consequence relations and cumulative models. It shows that these models satisfy certain properties, such as Cautious Monotonicity, and provides a characterization of the relationship between cumulative consequence relations and cumulative models. The paper concludes that preferential models have expressive power that cannot be captured by other nonmonotonic systems, and that the framework of preferential models provides a more accurate understanding of nonmonotonic reasoning than previous approaches.This paper introduces a general framework for nonmonotonic reasoning, focusing on properties that characterize nonmonotonic consequence relations. It defines five families of nonmonotonic consequence relations, each characterized by representation theorems that relate proof-theoretic and semantic perspectives. The paper discusses the importance of preferential models, which are stronger than Adams' probabilistic semantics, and explores the expressive power of nonmonotonic systems. It compares nonmonotonic reasoning with conditional logic and highlights the differences between various systems, such as circumscription, default logic, and autoepistemic logic. The paper also presents a cumulative reasoning framework, defining cumulative consequence relations and cumulative models. It shows that these models satisfy certain properties, such as Cautious Monotonicity, and provides a characterization of the relationship between cumulative consequence relations and cumulative models. The paper concludes that preferential models have expressive power that cannot be captured by other nonmonotonic systems, and that the framework of preferential models provides a more accurate understanding of nonmonotonic reasoning than previous approaches.