Compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent parts. This means that the meaning of a sentence can be understood by breaking it down into its individual words and phrases and then combining their meanings.

Semantic interpretation is the process of assigning a meaning to a linguistic expression. This can be done in a variety of ways, including using a dictionary, looking at the context in which the expression is used, or using one's own knowledge of the world.

Compositionality is a powerful tool for understanding the meaning of language, but it also presents some challenges. One challenge is that the meaning of a word can change depending on its context. For example, the word "bank" can refer to a financial institution, a riverbank, or a seat in a stadium. Another challenge is that the meaning of a sentence can be ambiguous. For example, the sentence "The man hit the ball" could mean that the man hit the ball with his hand or that the man hit the ball with a bat. Finally, there are multiple ways to interpret a linguistic expression. For example, the sentence "The cat is on the mat" could be interpreted as meaning that the cat is sitting on the mat or that the cat is lying on the mat.

Compositionality is a fundamental principle of language that has a wide range of applications. Some of the most common applications of compositionality include natural language processing, machine translation, and speech recognition. In natural language processing, compositionality is used to develop computer programs that can understand and generate human language. In machine translation, compositionality is used to develop computer programs that can translate text from one language to another. In speech recognition, compositionality is used to develop computer programs that can recognize spoken words.

The study of compositionality is a relatively new field, and there are still many open questions. Some of the most important open questions include: How can we develop a compositional theory of meaning that can account for the full range of linguistic phenomena? How can we develop compositional algorithms for natural language processing, machine translation, and speech recognition? How can we use compositionality to develop new ways of understanding language and communication?