From compositional to systematic semantics

Abstract

We prove a theorem stating that any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous. We then show that when compositional semantics is required to be "systematic" (that is, the meaning function cannot be arbitrary, but must belong to some class), it is possible to distinguish between compositional and non-compositional semantics. As a result, we believe that the paper clarifies the concept of compositionality and opens a possibility of making systematic formal comparisons of different systems of grammars.

Towards structural systematicity in distributed, statically bound visual representations

“…Without loss of generality (cf. (Zadrozny, 1994), section 2), we may only treat here the relation above, which we denote by the symbol (e.g., A B standing for "A above B"). Left: an interpretation function, f , maps the two primitive shapes into their corresponding atomic symbols, as follows: f (A) = a, f (B) = b.…”

The Processing Consequences of Compositionality

“…It is often argued that the principle of compositionality is formally vacuous: any grammar can be given a compositional semantics (Janssen 1986;Zadrozny 1994), 1 which implies the principle is also empirically vacuous: if a compositional analysis of any linguistic structure can be given, compositionality is always upheld by the data. To be sure, the meaning of any 5 complex expression can be viewed as a function of the meanings of its constituents and the syntactic mode of combination, provided enough complexity is built into the structures involved, that is the lexicon and the syntax.…”

Problems of Compositionality

“…21 Janssen (1983) and Zadrozny (1994) discuss this example in a related context. £ is a language that does not have a semantics parallel to its syntax.…”