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Semantic Complexity of Aggregate Noun Phrases - ESSLLI 2013

This course is intended as a 1-week (5x90min) introductory course on the formal (Montague) semantic analysis of aggregate noun phrases, and on the computational properties that arise thereof (i.e., their semantic complexity). An aggregate noun phrase is a definite noun phrase like "the total number of vegans in New York", expressing a second order query-language-like aggregation function (a sum in the example). Such noun phrases, while frequent in some natural language datasets, have a little understood semantics and unknown computational properties. This course will show students a possible analysis of such expressions leveraging on Barwise and Cooper's generalized quantifier theory and Pratt and Third's semantic complexity theory. It targets students with some prior exposure to logic and formal semantics. Students are encouraged to have a look at the following literature references (more will be given during the course): Day 1. Computing meaning. This lecture will introduce the problem of aggregate noun phrase semantics within a computational semantics framework. It will very briefly recall formal semantic and generalized quantifier theory. It will also outline how such formal logic semantic representations can be computed via syntax-driven semantic analysis. The slides are here.
Day 2. Formal semantics of aggregation. This lecture will provide a formal semantic analysis of aggregation in English, introduce the notion of "aggregate function" and distinguish between their set- and bag-valued interpretations. The slides are here.
Day 3. Semantic complexity of aggregation. This lecture will briefly recall the basic concepts of complexity theory and will then apply them both to provide a definition and study the semantic complexity of aggregation. The slides are here.
Day 4. Distribution of aggregate quantifiers. This lecture will show how semantic complexity can be used to predict the distribution of aggregations in (selected) English corpora. The slides are here.
Day 5. Lab session and discussion. The last session will be devoted to discussing the concepts and results seen during the course via a number of simple exercises. The exercise sheet is here. If time permits, the lecturer will demonstrate how to implement the framework in the NLTK Python NLP software package.