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Formalisation and Quantification of a Cognitively Motivated Conceptual Space Model Based on the Prototype Theory

The realist approach in meaning definition posits that meanings exist independently from the observer. In contrast, the cognitive approach holds that the meanings are “in the head” and are inseparable from the reasoning agent’s interpretation. Cognitive linguistics adopts the latter approach and regards the linguistic knowledge as structurally and functionally inseparable from the rest of the knowledge. It posits that language competence arises from language use. The prototype theory is an essential theory in cognitive semantics. Confirmed by many behavioural empirical findings on object categorisation, pioneered by Eleanor Rosch in the 1970s, it illuminates the idea of graded category membership, meaning that some category members are more representative than others. The most representative category member is called the prototype. The idea of graded membership causes a departure from the Aristotelian view of category membership claiming there is a set of necessary conditions for category membership. Instead, cognitive categories are essentially fuzzy, with exceptions that do have binary boundaries, imposed by the encyclopaedic knowledge, while the membership is still graded (e.g., odd number). There have been quite a few attempts of introducing formalisms into cognitive linguistics, with the aim to make the computational models more cognitively relevant and thus arguably increase their performance in semantic tasks. Gärdenfors’ conceptual space model provided a very elaborate theoretical and formal framework for modelling concepts as complex matrices of regions of quality domains that span the conceptual space. The proposed µw-model represents concept instances as vectors and provides a formal apparatus for the quantification of their representativeness. The model uses two parameters: the membership function µ that quantifies the contribution of each of its features (quality domain values) to the level of representativeness of a concept instance with respect to the observed concept ; and the weight w of each property. Additionally, the application of the model to the quantification of the representativeness of situations is proposed, as well as its utilisation for defining measures of language acquisition on different levels of processing (syntax, morphology, and phonology). A notable shortcoming of the extant models is that they do not adequately address specificities of conceptual structure arising from different statuses of properties regarding the concept structure. Properties that are less transformable are considered more central and influential with regards to concept coherence. Natural kind concepts, referring to plants and animals, exhibit structured bundled correlations of features, creating cognitive theories. Extensive empirical evidence suggests that humans are biologically predisposed for effortlessly utilising developed theories and structured correlations of concept features in categorising objects. The property weight parameter w of µw-model is interpreted as concept centrality indicator. An empirical crowdsourcing study is conducted in order to test whether the invariability of property values across concept instances predicts its impact on instance typicality. The hypothesis is confirmed, which means it is possible to automate the quantification of the w parameter by using text corpora. The proposed means of concept centrality quantification is validated by enhancing the distributional semantic model with the w parameter. It is shown that such enhanced, cognitively motivated model demonstrates statistically relevant improvement in the task of word similarity quantification. The results suggest that it is beneficial to enhance the extant computational linguistic models with cognitively motivated parameters, especially the semantic models.

conceptual space; semantic model; concepts; prototype theory

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