What is compositionality?

Primary guiding question for the paper; explores multiple formulations and uses of the term.

Source paper

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claim

concept

Frege Compositionality
gates
Formal linguistic principle: meaning of a whole depends only on meanings of parts and how they are fitted together (bottom-up meaning flow).
Schrödinger Compositional Theory
gates
Process theory variant where composition is non-trivial (whole cannot be decomposed meaningfully) and all ingredients have clear ontological counterparts in reality.
Meaning of a whole (cf. sentence) should only depend on meanings of its parts (cf. words) and how they are fitted together (cf. grammar).
gates
Canonical statement of Frege compositionality principle in formal linguistics; foundational to paper's analysis.
Never ask for word meaning in isolation, but only in the context of a sentence.
gates
Statement of Frege's context principle; shows tension with strict compositional bottom-up approach.

framework

Whitehead Compositionality
gates
Process theory variant requiring all ingredients have clear meaningful ontological counterparts in reality.

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Compositionalityconcept0.930
Central concept: how meaning of wholes depends on meanings of parts and their structural arrangement; multiple formulations explored (Frege, Schrödinger, Whitehead, LEGO).
Complete Compositionalityframework0.867
Strongest form of compositional theory requiring full decomposability and meaningful parts.
compositionconcept0.842
The wiring together of processes to form new processes in process theory
Compositional Semanticsconcept0.823
Denotation function µ decomposes over operations so meaning of compound expressions follows from meanings of parts
Compositional Reasoningconcept0.811
Modular reasoning enabled by monoid and other algebraic laws; central to maintainability and correctness of functional systems.
compositional AIconcept0.807
Artificial intelligence built on compositional principles, including NLP and beyond
Compositional Intelligenceconcept0.802
non-trivial compositionconcept0.775
Composition where a whole cannot be meaningfully decomposed into its original parts, central to Schrödinger compositional theory