Generalized Quantifiers on Dependent Types: A System for Anaphora

Abstract

We propose a system for the interpretation of anaphoric relationships between unbound pronouns and quantifiers. The main technical contribution of our proposal consists in combining generalized quantifiers ([26], [19], [2]) with dependent types ([23], [29], [20]). Empirically, our system allows a uniform treatment of the major types of unbound anaphora, with the anaphoric (dynamic) effects falling out naturally as a consequence of having generalized quantification on dependent types.

Inverse Linking, Possessive Weak Definites and Haddock Descriptions: A Unified Dependent Type Account

“…For more technical details and explanations about our notion of context, we refer the reader to our system presented in Grudzińska and Zawadowski (2017a). 1 We adopt the convention that the variables the types depend on are always explicitly written down in type specifications.…”

“…is outside the scope of the second binding occurrence of x next to Q 1 . A global restriction on variables is that each occurrence of an indexing variable be preceded by a binding occurrence of that variable-free undeclared variables are illegal (for more on this restriction, see Grudzińska and Zawadowski 2017a). As a consequence, this principle considerably restricts the number of possible readings for sentences involving multiple quantifiers and will have a major role to play in our account of the three puzzling phenomena to be discussed in the sections to follow: inversely linked interpretations, weak definite readings in possessives and Haddocktype readings.…”

“…Dependent type theoretical frameworks (Martin-Löf 1975;Martin-Löf and Sambin 1984;Makkai 1995) have been used to model linguistic phenomena of central importance, e.g., unbound anaphora (Ranta 1994;Fernando 2001;Cooper 2004;Grudzińska and Zawadowski 2014;Bekki 2014), lexical phenomena such as selectional restrictions and coercions (Asher 2011;Luo 2012;Chatzikyriakidis and Luo 2017b), adjectival and adverbial modification (Chatzikyriakidis and Luo 2017a) and long-distance indefinites (Grudzińska and Zawadowski 2017d). This paper argues that the three puzzling readings (inversely linked interpretations, weak definite readings in possessives and Haddock-type readings) provide another compelling example of application of dependent types to the study of natural language semantics.…”

Semantics with Dependent Types for Indefinites

“…In my joint work with Marek Zawadowski, we have developed a new type-theoretical semantics for natural language quantification ( [Grudzińska & Zawadowski 2014], [Grudzińska 2015], [Grudzińska & Zawadowski 2016]). The main novelty of our approach lies in combining elements from the two (sometimes considered rival) semantic frameworks: classical Montague-style semantics [Montague 1974]) and modern type theories with dependent types ( [Ranta 1994], [Fernando 2001], [Cooper 2004], [Luo 2012a], [Bekki 2014]).…”

“…The fact that the continuation in (13) can be felicitous shows that anaphoric relation with three students Semantics with Dependent Types for Indefinites involves just the three students mentioned no matter whether there were actually more than three students that came in. The overall interpretational architecture of our semantic system is twodimensional ( [Grudzińska & Zawadowski 2014], [Grudzińska & Zawadowski 2016]). The two dimensions to the meaning of a sentence in our system are: the truth value of a sentence and the dynamic effects introduced by the sentence (dynamic extensions of context).…”