compositionality: one construct, many systems

The principle of compositionality holds that the meaning of a complex expression is determined by the meanings of its parts together with the way they are syntactically combined, and nothing more. Montague's Universal grammar built a formal semantics of natural language on exactly this discipline, pairing each syntactic rule with a semantic rule so that interpretation tracks structure step for step. The referent is a constraint linking syntax to meaning in human language, and it is the identical principle that reappears in the semantics of programming languages and in the general theory of meaning.[1]

Unit

The rule-by-rule mapping from syntactic structure to meaning

Recovery means

Not applicable

Measured by

Checked by whether each syntactic rule has a corresponding semantic rule, so meaning is a function of parts and their combination

In programming-language theory the same principle is the backbone of denotational semantics: the meaning, or denotation, of a compound program is defined as a function of the meanings of its sub-expressions, so a program's behavior can be understood by composing the meanings of its parts. Stoy's Denotational Semantics sets out this Scott–Strachey approach, in which each syntactic construct is assigned a denotation built from those of its constituents. It is the same compositionality construct as in natural-language semantics, here guaranteeing that formal languages mean what their structure says they mean.[2]

Unit

The denotation of a program as a function of its sub-expressions' denotations

Recovery means

Not applicable

Measured by

Verified by assigning each syntactic construct a denotation defined from the denotations of its constituents

As a general principle in the theory of meaning, compositionality states that the meaning of a whole is a function of the meanings of its parts and their mode of combination, a thesis often traced to Frege and used to explain how finite speakers understand indefinitely many novel sentences. Pelletier's The principle of semantic compositionality examines what the principle actually claims, how it can be made precise, and what would count for or against it. It is the same construct abstracted away from any one language, the shared backbone of the linguistic and computational cases.[3]

Unit

The claim that a whole's meaning is fixed by its parts and their combination

Recovery means

Not applicable

Measured by

Examined by making the parts, the mode of combination, and the meaning function precise, then testing the claim against hard cases