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  1. Computational Complexity of Polyadic Lifts of Generalized Quantifiers in Natural Language.Jakub Szymanik - 2010 - Linguistics and Philosophy 33 (3):215-250.
    We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multi-quantifier sentences. First, we show that the standard constructions that turn simple determiners into complex quantifiers, namely Boolean operations, iteration, cumulation, and resumption, are tractable. Then, we provide an insight into branching operation yielding intractable natural language multi-quantifier expressions. Next, we focus on a linguistic case study. We use computational complexity results to investigate semantic (...)
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  • On the Identification of Quantifiers' Witness Sets: A Study of Multi-quantifier Sentences.Livio Robaldo, Jakub Szymanik & Ben Meijering - 2014 - Journal of Logic, Language and Information 23 (1):53-81.
    Natural language sentences that talk about two or more sets of entities can be assigned various readings. The ones in which the sets are independent of one another are particularly challenging from the formal point of view. In this paper we will call them ‘Independent Set (IS) readings’. Cumulative and collective readings are paradigmatic examples of IS readings. Most approaches aiming at representing the meaning of IS readings implement some kind of maximality conditions on the witness sets involved. Two kinds (...)
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  • Formalizing GDPR Provisions in Reified I/O Logic: The DAPRECO Knowledge Base.Livio Robaldo, Cesare Bartolini, Monica Palmirani, Arianna Rossi, Michele Martoni & Gabriele Lenzini - 2020 - Journal of Logic, Language and Information 29 (4):401-449.
    The DAPRECO knowledge base is the main outcome of the interdisciplinary project bearing the same name. It is a repository of rules written in LegalRuleML, an XML formalism designed to be a standard for representing the semantic and logical content of legal documents. The rules represent the provisions of the General Data Protection Regulation, the new Regulation that is significantly affecting the digital market in the European Union and beyond. The DAPRECO knowledge base builds upon the Privacy Ontology, which provides (...)
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  • Distributivity, Collectivity, and Cumulativity in Terms of (In)dependence and Maximality.Livio Robaldo - 2011 - Journal of Logic, Language and Information 20 (2):233-271.
    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, (...)
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  • Conservativity: a necessary property for the maximization of witness sets.L. Robaldo - 2013 - Logic Journal of the IGPL 21 (5):853-878.
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  • Branching Quantification v. Two-way Quantification.Nina Gierasimczuk & Jakub Szymanik - 2009 - Journal of Semantics 26 (4):329-366.
    Next SectionWe discuss the thesis formulated by Hintikka (1973) that certain natural language sentences require non-linear quantification to express their meaning. We investigate sentences with combinations of quantifiers similar to Hintikka's examples and propose a novel alternative reading expressible by linear formulae. This interpretation is based on linguistic and logical observations. We report on our experiments showing that people tend to interpret sentences similar to Hintikka sentence in a way consistent with our interpretation.
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  • The European Legal Taxonomy Syllabus: A multi-lingual, multi-level ontology framework to untangle the web of European legal terminology.Gianmaria Ajani, Guido Boella, Luigi di Caro, Livio Robaldo, Llio Humphreys, Sabrina Praduroux, Piercarlo Rossi & Andrea Violato - 2016 - Applied ontology 11 (4):325-375.
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  • Pragmatic identification of the witness sets.Livio Robaldo & Jakub Szymanik - 2012 - Proceeding of the 8th Conference on Language Resources and Evaluation.
    Among the readings available for NL sentences, those where two or more sets of entities are independent of one another are particularly challenging from both a theoretical and an empirical point of view. Those readings are termed here as ‘Independent Set (IS) readings'. Standard examples of such readings are the well-known Collective and Cumulative Readings. (Robaldo, 2011) proposes a logical framework that can properly represent the meaning of IS readings in terms of a set-Skolemization of the witness sets. One of (...)
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