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Natural Language Processing and Cognitive Science by Michael Zock, Mai Yanagimura, Elena Yagunova, Svetlana Volskaya, Jordi Turmo, Susanna Tron, Rocco Tripodi, Radu Topor, Ludovic Tanguy, David Suendermann-Oeft, Elizabeth Rosenfeld, Horacio Rodriguez, Livio Robaldo, Solange O. Rezende, Michaela Regneri, Lidia Pivovarova, Marcello Pelillo, Catherine Pelachaud, Thiago S. Pardo, Ali M. Naderi, Sachiyo Muranishi, Michael Muck, Martin Mory, Francois Morlane-Hondere, Tarek Mehrez, Wieslaw Lubaszewski, Patrick Lange, Shingo Kuroiwa, Manfred Klenner, Diane King, Mohamed Hamed Kholief, Alexei V. Ivanov, Yasuo Horiuchi, Nora Hollenstein, Myriam Hernandez Alvarez, Jiri Havelka, Nabil Hathout, Marcin Hareza, Jose M. Gomez, Emiliano Giovannetti, Nadine Glas, Daniela Gifu, Izabela Gatkowska, Jean-Gabriel Ganascia, Daisuke Furukawa, Richard Frost, Cécile Fabre, Ahmed Magdy Ezzeldin, Yasser El-Sonbaty, Luigi Di Caro, Matthew Crocker, Dan Cristea, Jan Curin, Conrado S. Merley, Pawel Chrzazcz, Jesus Calvillo, Mohamed Amine Boukhaled, Guido Boella, Jared Bernstein, Alessia Bellusci, Andrea Bellandi, Raimo Bakis, Eniafe Festus Ayetiran, Michael Amsler, Nabil Abdullah, César Aguilar, Olga Acosta, Rodolfo Delmonte, Bernadette Sharp

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Nabil Abdullah and Richard Frost

Beyond Classical Set

Abstract: This work presents a novel framework for natural language semantics by augmenting the notion of the conventional set using types. Using this newly conceived set, termed “typed set”, we demonstrate the viability of this notion by showing how the meaning of non-extensional constructs can be represented and computed without resorting to metaphysically murky, psychologically unappealing and computationally expensive notions.

1 Introduction

Set theory has established its place as de facto lingua franca not only in mathematics but in many other realms, including the analysis of natural-language (NL). In NL semantics the process is not straightforward. Because of sets’ extensional character ...

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