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Distributivity, Collectivity, and Cumulativity in Terms of (In)dependence and Maximality

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Abstract

This article proposes a new logical framework for NL quantification. The framework is based on Generalized Quantifiers, Skolem-like functional dependencies, and Maximality of the involved sets of entities. Among the readings available for NL sentences, those where two or more sets of entities are independent of one another are particularly challenging. In the literature, examples of those readings are known as Collective and Cumulative readings. This article briefly analyzes previous approaches to Cumulativity and Collectivity, and indicates (Schwarzschild in Pluralities. Kluwer, Dordrecht, 1996) as the best proposal so far to deal with these readings. Then, it incorporates its insights in the logical framework defined in Robaldo (J Philos Log 39(1):23–58, 2009a), leading to a scalable logical account for NL quantification.

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Authors and Affiliations

  1. Department of Computer Science, University of Turin, Turin, Italy

    Livio Robaldo

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  1. Livio Robaldo
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Correspondence to Livio Robaldo.

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This work has partially been funded by the project “TOCAI.IT: Knowledge-oriented technologies for enterprise aggregation in Internet” (RBNE05BFRK) of the Italian Ministry for University and Research.

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Robaldo, L. Distributivity, Collectivity, and Cumulativity in Terms of (In)dependence and Maximality. J of Log Lang and Inf 20, 233–271 (2011). https://doi.org/10.1007/s10849-010-9131-8

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