Semantics is concerned with meaning: what meanings are, how meanings are assigned to words, phrases and sentences of natural and formal languages, and how meanings can be combined and used for inference and reasoning. The goal of this chapter is to introduce computational linguists and computer scientists to the tools, methods, and concepts required to work on natural language semantics. Semantics, while often paired with pragmatics, is nominally distinct. On a traditional view, semantics concerns itself with the compositional buildup of meaning from the lexicon to the sentence level whereas pragmatics concerns the way in which contextual factors and speaker intentions affect meaning and inference (see, e.g., Potts to appear in this volume). Although the semantics-pragmatics distinction is historically important, and continues to be widely adopted, in practice it is not clearcut. Work in semantics inevitably involves pragmatics and vice versa. Furthermore, it is not a distinction which is of much relevance for applications in computational linguistics. This chapter is organized as follows. In sections 2 and 3 we introduce foundational concepts and discuss ways of representing the meaning of sentences, and of combining the meaning of smaller expressions to produce those sentential meanings. In section 4 we discuss the representation of meaning for larger units, especially with respect to anaphora, and introduce two formal theories that go beyond sentence meaning: Discourse Representation Theory and Dynamic Semantics. Then, in section 5 we discuss temporality, introducing event semantics, and describing standard approaches to the semantics of tense and aspect. Section 6 concerns the tension between the surface-oriented statistical methods characteristic of much of computational linguistics and the more abstract methods typical of formal semantics and includes discussion of a range of phenomena for which it seems particularly important to utilize insights from formal semantics..
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