The chapter "The Notional Category of Modality" by Angelika Kratzer explores the semantic nature of modality, focusing on its expression in German. Kratzer discusses the variety of ways modality can be expressed in natural languages, including inherent modality, suffixes on adjectives, modal auxiliaries, sentence adverbs, and adjectival phrases. She emphasizes that there is no single syntactic category corresponding to the notional category of modality, and thus, the core question is what modality is. Kratzer introduces the concept of conversational backgrounds, which are functions mapping possible worlds to sets of propositions. These backgrounds contribute premises from which conclusions are drawn, and they determine the force of modal expressions. She distinguishes between realistic and informational conversational backgrounds, where realistic backgrounds track specific bodies of facts, while informational backgrounds represent the intentional content of sources of information. The chapter also discusses the distinction between "root" and "epistemic" modals, noting that root modals depend on circumstantial backgrounds, while epistemic modals depend on epistemic backgrounds. Kratzer argues that these distinctions are not based on formal properties but on the types of event arguments they access in the verbal projection spine. Additionally, Kratzer addresses the graded and comparative notions of possibility, showing how they emerge from ranking worlds according to how close they come to a norm or ideal. She introduces the concept of ordering sources, which are used to induce orderings on the set of accessible worlds and propositions, leading to notions of necessity and possibility. Finally, Kratzer discusses the role of stereotypical conversational backgrounds, which represent what is normal according to a suitable standard. She concludes by emphasizing the importance of separating realistic and normative conversational backgrounds, as they play distinct roles in generating the full range of possible modal meanings in natural languages.The chapter "The Notional Category of Modality" by Angelika Kratzer explores the semantic nature of modality, focusing on its expression in German. Kratzer discusses the variety of ways modality can be expressed in natural languages, including inherent modality, suffixes on adjectives, modal auxiliaries, sentence adverbs, and adjectival phrases. She emphasizes that there is no single syntactic category corresponding to the notional category of modality, and thus, the core question is what modality is. Kratzer introduces the concept of conversational backgrounds, which are functions mapping possible worlds to sets of propositions. These backgrounds contribute premises from which conclusions are drawn, and they determine the force of modal expressions. She distinguishes between realistic and informational conversational backgrounds, where realistic backgrounds track specific bodies of facts, while informational backgrounds represent the intentional content of sources of information. The chapter also discusses the distinction between "root" and "epistemic" modals, noting that root modals depend on circumstantial backgrounds, while epistemic modals depend on epistemic backgrounds. Kratzer argues that these distinctions are not based on formal properties but on the types of event arguments they access in the verbal projection spine. Additionally, Kratzer addresses the graded and comparative notions of possibility, showing how they emerge from ranking worlds according to how close they come to a norm or ideal. She introduces the concept of ordering sources, which are used to induce orderings on the set of accessible worlds and propositions, leading to notions of necessity and possibility. Finally, Kratzer discusses the role of stereotypical conversational backgrounds, which represent what is normal according to a suitable standard. She concludes by emphasizing the importance of separating realistic and normative conversational backgrounds, as they play distinct roles in generating the full range of possible modal meanings in natural languages.