 With this in mind, let’s return to the idea that each complex expression of natural language has semantic properties that are determined by (i) the semantic properties of its constituents, and (ii) the ways in which these constituents are grammatically arranged. If this is correct, then following Davidson, one might say that the logical forms of expressions (of some natural language) just are the structures that determine the corresponding meanings given the relevant word meanings; see Lepore and Ludwig (2002). In which case, the phenomenon of valid inference may be largely a by-product of semantic compositionality. If principles governing the meanings of (37–40) have the consequence that (40) is true iff an existential claim like (40a) is true, perhaps this is illustrative of the general case. Given a sentence of some natural language NL, the task of specifying its logical form may be inseparable from the task of providing a compositional specification of what the sentences of NL mean.