Abstract
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper.
Highlights
Theories of concepts struggle to capture the creative flexibility with which concepts are used in natural language, and combined into larger complexes with emergent meaning, as well as the context-dependent manner in which concepts are understood (Geeraerts, 1989)
This improved quantum model illustrates how the prototype of Fruits (Vegetables) changes under the influence of the context Vegetables (Fruits) in the combination Fruits or Vegetables. The latter combination is represented using the quantum-mathematical notion of linear superposition in a complex Hilbert space, which entails the genuine quantum effect of “interference.” our model shows that the prototypes of Fruits and Vegetables interfere in the disjunction Fruits or Vegetables
In this paper we showed that a generalization of prototype theory can address the “Pet-Fish problem” and related combination issues
Summary
Theories of concepts struggle to capture the creative flexibility with which concepts are used in natural language, and combined into larger complexes with emergent meaning, as well as the context-dependent manner in which concepts are understood (Geeraerts, 1989). This improved quantum model illustrates how the prototype of Fruits (Vegetables) changes under the influence of the context Vegetables (Fruits) in the combination Fruits or Vegetables. Data collected on combinations of two concepts systematically exhibit deviations from classical set-theoretical modeling, and traditional probabilistic approaches have difficulty coping with this In this sense, the success of the quantumtheoretic modeling can be interpreted as a confirmation of the effectiveness of quantum theory to model conceptual combinations. The fact that our “theory derived model” reproduces different sets of experimental data is a convincing argument to support its advantage over traditional modeling approaches and to extend its use to more complex combinations of concepts
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