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Clarification and Generalized Quantifiers
Abstract
Purver and Ginzburg introduce the Reprise Content Hypothesis (RCH) and use it to argue for a non-generalized quantifier approach to certain quantifiers. In previous work we contrasted their approach with an approach which employs a more classical
generalized quantifier analysis. In the present paper we synthesize the two approaches and suggest that this gives us the best account of the dialogue phenomena associated with RCH.
... The classical account of generalized quantifiers (Barwise and Cooper, 1981;Peters and Westerståhl, 2006, and much other literature) treats such quantifier relations as relations between sets. Here we will follow Cooper (2011Cooper ( , 2013a in relating our treatment directly to the classical relation between sets, although, as argued in Cooper (2012a) based on earlier work by Keenan and Stavi (1986), there are ultimately good reasons for exploiting the intensionality of properties. If P is a property, the relevant set is the set of individuals which have the property, which we will represent as [↓P]. ...
... Somehow we have to coordinate the frame which is chosen in connection with the interpretation of temperature with the frame which is chosen in connection with the interpretation of rise. The solution to this that we wish to propose rests on the treatment of generalized quantifiers proposed in Cooper (2011Cooper ( , 2013a. ...
The aim of this book is to characterize a notion of type which will cover both linguistic and non-linguistic action and to lay the foundations for a theory of action based on a theory of types called TTR (a Theory of Types with Records). The book argues that a theory of language based on action allows us to take a perspective on linguistic content which is centred on interaction in dialogue and that this is importantly different to the traditional view of natural languages as being essentially similar to formal languages such as logics developed by philosophers or mathematicians. At the same time it will argue that the tremendous technical advances made by the formal language view of semantics can be incorporated into the action-based view and that this can lead to important improvements both of intuitive understanding and empirical coverage. In this enterprise we use types rather than possible worlds as commonly employed in studies of the semantics of natural language. Types are more tractable than possible worlds and give us more hope of understanding the implementation of semantics both on machines and in biological brains.
... quantifiers. In Cooper (2011Cooper ( , 2013Cooper ( , 2016 and elsewhere, we have been developing a view of generalized quantifiers as relations between properties in the TTR sense. This view is based on classical generalized quantifier theory. ...
The classical view of semantics that we inherited from Montague is that natural languages are formal languages where semantics specifies the interpretations which can be associated with expressions of the language. In this context coercion might be seen as a slight but formally specifiable disturbance in the formal semantics which shows how the canonical interpretation of an expression can be modified by its linguistic context. In recent years an alternative to the formal language view of natural language has developed which sees the interpretation of language as a more local and dynamic process where the interpretation of expressions can be modified for the purposes of the utterance at hand. This presents linguistic semantics as a dynamic, somewhat chaotic, system constrained by the need to communicate. An interpretation of an expression will work in communication if it is close enough to other interpretations your interlocutor might be familiar with and there is enough evidence in the ambient context for her to approximate the interpretation you intended. On this view of language as a system in flux, coercion is not so much a disturbance in the semantic system but rather a regularization of available interpretations leading to a more predictable system.
I will present some of the reasons why I favour the view of language in flux (but nevertheless think that the techniques we have learnt from formal semantics are important to preserve). I will look at some of the original examples of coercion discussed in the Pustejovskian generative lexicon and suggest that the possibilities for interpretation are broader than might be suggested by Pustejovsky’s original work. Finally, I will suggest that coercion can play a central role in compositional semantics taking two examples: (1) individual vs. frame-level properties and (2) dynamic generalized quantifiers and property coercion.
... In dialogue all words and phrases are, in principle, subject to clarification interaction (see (Ginzburg and Cooper, 2004;Purver, 2006;Ginzburg, 2012;Cooper, 2013a This is a conventionalized process: as corpus studies have shown, there are a very small number of possible construals of CRs-as request for confirmation, repetition, intended content resolution (see Purver et al (2001); Rodriguez and Schlangen (2004)). There are thus in the aftermath of an utterance (and indeed while it is ongoing) two essential branches: ...
Quotation has been much studied in philosophy. Given that quotation allows one to diagonalize out of any grammar, there have been comparatively few attempts within the linguistic literature to develop an account within a formal linguistic theory. Nonetheless, given the ubiquity of quotation in natural language, linguists need to explicate the formal mechanisms it employs. The central claim of this paper is that once one assumes a dialogical perspective on language such as provided by the KoS (KoS is not an acronym, despite emphasizing a Konversationally Oriented Semantics) framework, formalized in a rich type theory like Type Theory with Records, much of the mystery evaporates. In particular, one can utilize as denotations for quotative constructions entities that are independently motivated for dialogue processing—utterance types and locutionary propositions, Austinian propositions about speech events.
... 5 See (Kripke, 1977), and (Bach, 1994). 6 The suggestion goes back to (Barwise and Cooper, 1981). Jason Stanley and Zoltán Szabó contend that this is the only sound view of incomplete descriptions. ...
“Incomplete” definite descriptions (i.e. descriptions that violate the uniqueness constraint) have been offered various accounts in semantics. Among them, the so-called ellipsis account, which analyzes “the F” as elliptical for “the F which is that F”. I begin by arguing that the objections raised against this account have not been conclusive, and go on to supply a new argument against it, which consists in showing such demonstrative completions to be semantically redundant.
This paper is part of a broader project whose aim is to present a coherent unified approach to natural language dialogue semantics using tools from type theory. Here we explore aspects of our approach which relate to situation theory and situation semantics. We first point out a relationship between type theory and the Austinian notion of truth. We then consider how records in type theory might be used to represent situations and how dependent record types can be used to model constraints on situations. We then sketch treatments of attitude phenom-ena for which Barwise and Perry proposed situation semantic analyses (perception complements, belief, the Pierre puzzle) as well as two other intensional phenomena (intensional verbs and intentional identity). Finally we give a characterisation of the type theory used and a small illustrative fragment of English.
We shall consider a formulation of generalised quantifiers using type theory with records (TTR). TTR follows closely the development of record types in Martin-Löf or constructive type theory but differs in that the type theory is defined on a classical set theoretic basis. This means that the classical set-theoretic approach to generalised quantifiers can be imported into the type theoretic framework. The result is, I believe, equivalent to the proposal for dynamic generalised quantifiers in Chier-chia (1995). The use of dependent types provides us with an elegant approach to the formulation of dynamic quantifiers. We use a notion of hypothetical context which we have used elsewhere to give accounts of intentional identity, answers to questions and information state up-dates in dialogue management. We suggest that this points towards a general theory of hypothetical context in natural language. We suspect also that our analysis using records will support analyses of common noun phrase and verb-phrase anaphora and also facilitate representa-tions which are underspecified with respect to quantifier scope, though we leave the investigation of this to future research.
Reprise questions are a common dialogue device allowing a conversational participant to request clarification of the meaning intended by a speaker when uttering a word or phrase. As such they can act as semantic probes, providing us with information about what meaning can be associated with word and phrase types and thus helping to sharpen the principle of compositionality. This paper discusses the evidence provided by reprise questions concerning the meaning of nouns, noun phrases and determiners.
In this book we hope to acquaint the reader with the fundamentals of truth conditional model-theoretic semantics, and in particular with a version of this developed by Richard Montague in a series of papers published during the 1960's and early 1970's. In many ways the paper 'The Proper Treatment of Quantification in Ordinary English' (commonly abbreviated PTQ) represents the culmination of Montague's efforts to apply the techniques developed within mathematical logic to the semantics of natural languages, and indeed it is the system outlined there that people generally have in mind when they refer to "Montague Grammar". (We prefer the term "Montague Semantics" inasmuch as a grammar, as conceived of in current linguistics, would contain at least a phonological component, a morphological component, and other subsystems which are either lacking entirely or present only in a very rudi mentary state in the PTQ system. ) Montague's work has attracted increasing attention in recent years among linguists and philosophers since it offers the hope that semantics can be characterized with the same formal rigor and explicitness that transformational approaches have brought to syntax. Whether this hope can be fully realized remains to be seen, but it is clear nonetheless that Montague semantics has already established itself as a productive para digm, leading to new areas of inquiry and suggesting new ways of conceiving of theories of natural language. Unfortunately, Montague's papers are tersely written and very difficult to follow unless one has a considerable background in logical semantics.
Purver and Ginzburg introduce the Reprise Content Hypothesis (RCH) and use it to argue for a non-generalized quantifier ap-proach to certain quantifiers. Here we will contrast their approach with an approach which employs a more classical general-ized quantifier analysis and examine what predictions it has for possible clarifica-tions and reexamine the data which Purver and Ginzburg present in the light of this.
onnich has worked both on the use of type theory in semantics and on formal aspects of gram- mar formalisms. This paper suggests a way of bringing together type theory and unification as found in unification-based grammar formalisms like HPSG by using records in type theory which provide us with feature structure like objects. It represents a small offering to Uwe to thank him for many kindnesses over the years sprinkled with insights and rigorous comments.
In 1957, the Polish logician Andrej Mostowski pointed out that there are many mathematically interesting quantifiers that are not definable in terms of the first-order ∀, ∃ and initiated study of so-called generalized quantifiers (cf. Mostowski, 1957). Since then logicians have discovered and studied a large number of generalized quantifiers. At last count there were well over 200 research papers in this area. Most of this work has been directed toward cardinality quantifiers (e.g. Keisler, 1969) and topological quantifiers (e.g. Sgro, 1977) which are not particularly relevant to natural language, but even so, it has forced logicians to rethink the traditional theory of quantification.
Type theory and semantics in flux
- Robin Cooper
Robin Cooper. Type theory and semantics in flux. In Ruth Kempson, Nicholas Asher, and Tim
Fernando, editors, Handbook of the Philosophy of Science, volume 14: Philosophy of Linguistics,
pages 271-323. Elsevier BV, 2012. General editors: Dov M. Gabbay, Paul Thagard and John
Woods.
Interrogative Investigations: The Form, Meaning, and Use of English Interrogatives. Number 123 in CSLI Lecture Notes
- Jonathan Ginzburg
- Ivan A Sag
Jonathan Ginzburg and Ivan A. Sag. Interrogative Investigations: The Form, Meaning, and Use
of English Interrogatives. Number 123 in CSLI Lecture Notes. CSLI Publications, Stanford,
California, 2000.