Strong compositionality refers to compound expressions that are determined by the meaning of its immediate parts and a top-level syntactic function that describes their combination.
Weak compositionality refers to compound expressions that are determined by the meaning of its parts as well as their complete syntactic combination.
As a guideline for constructing semantic theories, this is generally taken, as in the influential work on the philosophy of language by Donald Davidson, to mean that every construct of the syntax should be associated by a clause of the T-schema with an operator in the semantics that specifies how the meaning of the whole expression is built from constituents combined by the syntactic rule.
[citation needed] Most proponents of the principle, however, make certain exceptions for idiomatic expressions in natural language.
[8] The principle of compositionality usually holds when only syntactic factors play in the increased complexity of sentence processing, while it becomes more problematic and questionable when the complexity increase is due to sentence or discourse context, semantic memory, or sensory cues.
[9] Among the problematic phenomena for traditional theories of compositionality is that of logical metonymy, which has been studied at least since the mid 1990s by linguists James Pustejovsky and Ray Jackendoff.
[10] The problem for compositionality is that the meaning of reading or writing is not present in the words of the sentence, neither in "begin" nor in "book".