Compositionality

Compositionality, in linguistics, philosophy, and computer science, refers to the principle that the meaning of a complex expression is determined by the meanings of its parts and the rules used to combine them. Essentially, it proposes that we can understand the meaning of a whole by understanding the meanings of its constituents and how they are put together. This principle is crucial for language comprehension and generation, as it allows us to understand and create novel sentences we have never encountered before, enabling an infinite generative capacity. However, it can be complicated by idiomatic expressions and context-dependent meanings that aren't solely predictable from constituent meanings. The term underscores the ability to build complex meanings systematically from simpler ones.

Compositionality meaning with examples

• Consider the sentence, "The red ball rolled." According to Compositionality, the meaning derives from the individual meanings of "red," "ball," "rolled" and the grammatical rules connecting them (adjective modifying noun, verb describing action). We understand the sentence because we know the meaning of each word and how their grammatical roles combine to create a coherent, meaningful whole. The understanding of the sentence relies on an understanding of how the individual parts fit together, to produce a complex message.
• A programming language adheres to Compositionality if the meaning of a program is determined by the meanings of its individual components (e.g., functions, variables, operators) and the way they are combined. A complex expression is simply a combination of simpler expressions and operators. This feature allows software engineers to write complex programs by assembling smaller modular parts. Any change in the part will automatically change the full expression, given the rules of construction are followed, just as in the language above.
• In a mathematical context, Compositionality manifests in the way complex mathematical expressions are built from simpler ones. For example, the expression "(2 + 3) * 4" is compositional. The total meaning is found through applying the 'plus' operation on the 2 and 3, which results in 5, and then using the 'times' operator. This allows us to use simpler parts, like numbers and operators to build complicated expressions with consistent and repeatable results. The mathematical meaning of the total is consistent from its parts.
• A machine translation system strives to capture the Compositionality of language. When translating "The fluffy cat sat on the mat," the system must understand the individual meanings of "fluffy," "cat," "sat," "on," "the," and "mat," along with the grammatical structure to accurately convey the sentence’s meaning in another language. This breakdown is how computers understand the relationship between the words and their combined meaning. The system seeks a compositional understanding, making it less sensitive to a different order of the words.