Compositionality is a frequently made assumption in linguistics, and yet many human subjects reveal highly non-compositional word associations when confronted with novel concept combinations.This article will show how a non-compositional account of concept combinations can be supplied by modelling them as interacting quantum systems.
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.”
The question of under what conditions conceptual representation is compositional remains debatable within cognitive science.This paper proposes a well developed mathematical apparatus for a probabilistic representation of concepts, drawing upon methods developed in quantum theory to propose a formal test that can determine whether a specific conceptual combination is compositional, or not.This test examines a joint probability distribution modeling the combination, asking whether or not it is factorizable.Empirical studies indicate that some combinations should be considered non-compositionally.
Consider the concept combination ‘pet human’. In word association experiments, human subjects 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’ seems to be emergent. Such emergent associations sometimes have a creative character and cognitive science is largely silent about how we produce them. Departing from a dimensional model of human conceptual space, this article will explore concept combinations, and will argue that emergent associations are a result of abductive reasoning within conceptual space, that is, below the symbolic level of cognition. A tensor-based approach is used to model concept combinations allowing such combinations to be formalized as interacting quantum systems. Free association norm data is used to motivate the underlying basis of the conceptual space. It is shown by analogy how some concept combinations may behave like quantum-entangled (non-separable) particles. Two methods of analysis were presented for empirically validating the presence of non-separable concept combinations in human cognition. One method is based on quantum theory and another based on comparing a joint (true theoretic) probability distribution with another distribution based on a separability assumption using a chi-square goodness-of-fit test. Although these methods were inconclusive in relation to an empirical study of bi-ambiguous concept combinations, avenues for further refinement of these methods are identified.
Human memory experiments appear to be generating "nonlocal" effects cite{Nelson:McEvoy:2007}. In this paper the possibility that words might be entangled in human semantic space is seriously entertained. This approach leads to a very natural picture of the way in which context might affect word association via the standard interpretation of quantum measurement. Two possible scenarios for testing such a hypothesis are suggested, both based upon potential violations of the CHSH inequality.
Objectives: This research is first of its kind to investigate the application of quantum mechanics and related mathematical models to cognitive science, specifically focusing on the challenge of modeling how the human mind assigns meaning to combinations of words. The primary objective is to classify whether given word combinations are compositional or non-compositional. Methods: The author introduces the "WWW method," which leverages the World Wide Web (WWW) as an experimental tool in place of human subjects, which makes this method cheaper and handy in comparison to the earlier methods which used human subjects for spoken and sign language studies and robots as non-human subjects. The "WWW method" involves checking the adherence to Bell inequalities and marginal selectivity. The term "meaning bound" is introduced to quantify the extent to which two words influence each other's meaning within a combination. This concept proves instrumental in devising a method for assessing compositionality using the WWW method. Findings: When the WWW serves as the information space, the verification of whether a word combination adheres to Bell inequalities entails determining if the meaning bound for the word combination (AB & C) exceeds that of its constituent parts (A & C, B & C) within the conceptual combination AB. Marginal selectivity is evaluated by establishing a vector model for grammatically framed word combinations, utilizing the WWW to collect data. If the word combination 'A then B' yields an equivalent number of hits as 'B then A,' it signifies that the word combination AB satisfies marginal selectivity. Novelty: Consequently, this research presents an accessible approach to identifying entangled pairs of word combinations using the WWW method, eliminating the need for human subject experiments. The earlier studies which include human subjects are costly and cannot be replicated anytime-anywhere, for obvious reasons. Keywords: Quantum cognition, Marginal selectivity, Compositionality, WWW method, CHSH inequality
We present modeling for conceptual combinations which uses the mathematical formalism of quantum theory. Our model faithfully describes a large amount of experimental data collected by different scholars on concept conjunctions and disjunctions. Furthermore, our approach sheds a new light on long standing drawbacks connected with vagueness, or fuzziness, of concepts, and puts forward a completely novel possible solution to the 'combination problem' in concept theory. Additionally, we introduce an explanation for the occurrence of quantum structures in the mechanisms and dynamics of concepts and, more generally, in cognitive and decision processes, according to which human thought is a well structured superposition of a 'logical thought' and a 'conceptual thought', and the latter usually prevails over the former, at variance with some widespread beliefs.