Hierarchical conceptual spaces for concept combination
We introduce a hierarchical framework for conjunctive concept combination based on conceptual spaces and random set theory. The model has the flexibility to account for composition of concepts at various levels of complexity. We show that the conjunctive model includes linear combination as a special case, and that the more general model can account for non-compositional behaviours such as overextension, non-commutativity, preservation of necessity and impossibility of attributes and to some
... ent, attribute loss or emergence. We investigate two further aspects of human concept use, the conjunction fallacy and the 'guppy effect '. 205 in  , including non-compositional behaviours such as overextension, non-commutativity, preservation of necessity and impossibility of attributes and to some extent, attribute loss or emergence. An outline of the paper is as follows. Section 2 overviews a range of theoretical approaches to concept combination from the literature, and summarises the results from experimental studies that we aim to model. Section 3 describes a random set and prototype theory representational model for concepts within a conceptual space. This model provides the theoretical underpinning for our work. Section 4 introduces a framework for concept combination based on a hierarchy of conceptual spaces, and in which compound concepts are defined within Boolean spaces. We prove a number of results showing the properties of this framework and compare this approach to others in the literature. Section 5 provides a discussion of our results and indicates possible future directions.