One of the central challenges in cognitive neuroscience has been the study of internal mental representations of the external objects, events and relations that allow us to predict and interact with the world. Recently, researchers have uncovered parallels between the neural processing of physical space and of abstract knowledge, such that the established neural mechanisms for spatial navigation may also shed light on how we represent conceptual knowledge. In this thesis, we present a set of behavioural experiments examining the representational format of knowledge structures such as concepts and schemas, and develop learning paradigms that test algorithmic-level theories of spatial and non-spatial processing.

We start by discussing classical geometric models of knowledge representation, which view concepts as regions in abstract, multidimensional spaces organised by metric principles. These models have been supported by recent neuroimaging studies that suggest shared neural representations for spatial and non-spatial reasoning. We consider an older set of behavioural results that uncovered violations of the metric axioms of such representations, and discuss augmented geometric models that have been developed in response. One such model – the distance-density model – is examined in Chapter 2, using similarity judgments on a novel one-dimensional stimulus space. We did not find support for the basic prediction that psychological density affects similarity. In Chapter 3, we adapted the conceptual stimulus spaces used in the recent neuroimaging studies, and found that violations of metric requirements depend on the nature of the dimensions defining the stimuli. Nonetheless, using simulations and considering the prior psychological literature, we argue that another type of augmented model – the attention-weighted geometric model – is unlikely to account for such violations. These chapters therefore cast doubt on geometric models as adequate algorithmic-level theories for human knowledge representation. The next two chapters develop schema learning tasks that lay the foundation for continued study of parallels between spatial and non-spatial reasoning. In Chapter 4, we examined how a non-spatial schema acquired in one conceptual space can influence learning in a different conceptual space. Across two experiments, we found effects consistent with generalisation of knowledge, but only for certain counterbalancing conditions. We argue for the importance of further refining our task and stimuli to develop a fast and flexible knowledge-transfer paradigm for studying relations between spatial and non-spatial processing, which could also be extended to analogical reasoning, categorisation and schemas. In Chapter 5, we examined the nature of representational elements constituting spatial schemas. The prior literature has defined such schemas as networks of stimulus-location associative elements that can benefit learning. An unexamined possibility is that, instead of forming a cohesive network, such elements act independently to influence acquisition of new knowledge only within their local neighbourhood. Across two experiments involving learning of image-location associations on 2D boards, we find evidence consistent with this interpretation, and we outline how our paradigm can be adapted to address analogous questions for non-spatial schemas.

Taken together, our results question spatial representation of knowledge at the algorithmic level, as well as the nature of spatial schema, and emphasize the importance of continued research for elucidating commonalities and differences between spatial and non-spatial reasoning.