Consider the concept combination “pet human.” In word association experiments, human subjects often produce the associate “slave” in relation to this combination. The striking aspect of this associate is that it is not produced as an associate of “pet” or “human” in isolation. In other words, the associate “slave” cannot be recovered from the constituent concepts. Such examples have been used in both cognitive science and philosophy to argue that concept combinations have a non-compositional semantics. This chapter will feature how various non-compositional accounts of concept combinations can be provided from quantum theory. Quantum theory is a theory which caters for the modelling of non-compositionality because the state of a quantum entangled system cannot be constructed from the states of its individual subsystems. Utilizing probabilistic methods developed for analyzing composite systems in quantum theory, we show that it is possible to classify concept combinations as having “classically compositional,” “pseudo-classically non-compositional,” or “non-classically non-compositional” semantics by determining whether the joint probability distribution modelling the combination is factorizable or not.

Concept combinations and cognition

The principle of semantic compositionality states the meaning of a (syntactically complex) whole is a function only of the meanings of its (syntactic) parts together with the manner in which these parts were combined (Pelletier, 1994). Whether the semantics of concepts are compositional, or not, has been somewhat of a battleground. On the one hand, there are authors like Fodor (1994) who are adamant that concepts are, and must be, compositional, but this position stands in contrast with the computational linguist Zadrozny (1994), who produced a theorem suggesting that: “the standard definition of compositionality is formally vacuous.”