The ability to link variables is critical to many high-order cognitive functions, including reasoning. It has been proposed that limits in relating variables depend critically on relational complexity, defined formally as the number of variables to be related in solving a problem. In humans, the prefrontal cortex is known to be important for reasoning, but recent studies have suggested that such processes are likely to involve widespread functional brain networks. To test this hypothesis, we used functional magnetic resonance imaging and a classic measure of deductive reasoning to examine changes in brain networks as a function of relational complexity. As expected, behavioral performance declined as the number of variables to be related increased. Likewise, increments in relational complexity were associated with proportional enhancements in brain activity and task-based connectivity within and between 2 cognitive control networks: A cingulo-opercular network for maintaining task set, and a fronto-parietal network for implementing trial-by-trial control. Changes in effective connectivity as a function of increased relational complexity suggested a key role for the left dorsolateral prefrontal cortex in integrating and implementing task set in a trial-by-trial manner. Our findings show that limits in relational processing are manifested in the brain as complexity-dependent modulations of large-scale networks.

Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilised in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual combinations are compositional, and so can be considered as a function of the semantics of the constituent concepts, or not. While the systematicity and productivity of language provide a strong argument in favor of assuming compositionality, this very assumption is still regularly questioned in both cognitive science and philosophy. Additionally, the principle of semantic compositionality is underspecified, which means that notions of both "strong" and "weak" compositionality appear in the literature. Rather than adjudicating between different grades of compositionality, the framework presented here contributes formal methods for determining a clear dividing line between compositional and non-compositional semantics. In addition, we suggest that the distinction between these is contextually sensitive. Compositionality is equated with a joint * Corresponding author Email addresses: p.bruza@qut.edu.au (Peter D. Bruza), kirsty.kitto@qut.edu.au (Kirsty Kitto), brentynramm@gmail.com (Brentyn J. Ramm), laurianne.sitbon@qut.edu.au (Laurianne Sitbon) Preprint submitted to ElsevierNovember 24, 2014 probability distribution modeling how the constituent concepts in the combination are interpreted. Marginal selectivity is introduced as a pivotal probabilistic constraint for the application of the Bell/CH and CHSH systems of inequalities.Non-compositionality is equated with a failure of marginal selectivity, or violation of either system of inequalities in the presence of marginal selectivity. This means that the conceptual combination cannot be modeled in a joint probability distribution, the variables of which correspond to how the constituent concepts are being interpreted. The formal analysis methods are demonstrated by applying them to an empirical illustration of twenty-four non-lexicalised conceptual combinations.

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.

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Measures and theories of information abound, but there are few formalised methods for treating the contextuality that can manifest in different information systems. Quantum theory provides one possible formalism for treating information in context. This paper introduces a quantum inspired model of the human mental lexicon. This model is currently being experimentally investigated and we present a preliminary set of pilot data suggesting that concept combinations can indeed behave non-separably.