A probabilistic framework for analysing the compositionality of conceptual combinations

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Journal Article
Journal of Mathematical Psychology, 2015, 67 pp. 26 - 38
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© 2015. Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilised in everyday language. While the systematicity and productivity of language provide a strong argument in favour of assuming compositionality, this very assumption is still regularly questioned in both cognitive science and philosophy. 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. 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. Compositionality is equated with a joint probability distribution modelling how the constituent concepts in the combination are interpreted. Marginal selectivity is emphasised as a pivotal probabilistic constraint for the application of the Bell/CH and CHSH systems of inequalities (referred to collectively as Bell-type). Non-compositionality is then equated with either a failure of marginal selectivity, or, in the presence of marginal selectivity, with a violation of Bell-type inequalities. In both non-compositional scenarios, the conceptual combination cannot be modelled using a joint probability distribution with variables corresponding to the interpretation of the individual concepts. The framework is demonstrated by applying it to an empirical scenario of twenty-four non-lexicalised conceptual combinations.
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