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Quantifiers and Cognition: Logical and Computational Perspectives

Part of the Studies in Linguistics and Philosophy Book Series (volume 96)

DOI: 10.1007/978-3-319-28749-2

ISBN: 978-3-319-28747-8

Publisher: Springer International Publishing - Springer Journals

Feb 20, 2016

1 - 10 of 12 Chapters

LitStream

Algorithmic Theory of Meaning

Szymanik, Jakub

Pages: 3 –8

[In this chapter, I describe the philosophical conception that identifies the meaning of a sentence with a procedure for finding its truth-value. I also give a short historical overview of this idea. The procedural approach to meaning seems reasonable for a large part of natural language in many...
LitStream

Complexity in Linguistics

Szymanik, Jakub

Pages: 9 –19

[The topic of language complexity has surfaced in many different contexts and can be measured in many different ways. In this chapter, I discuss notions relevant to the computational and descriptive complexity of language. I introduce the notion of ‘complexity class’ (e.g. P and NP), the...
LitStream

Basic Generalized Quantifier Theory

Szymanik, Jakub

Pages: 23 –39

[This chapter is a crash course in generalized quantifier theory, which is one of the basic tools of today’s linguistics. In its simplest form generalized quantifier theory assigns meanings to statements by defining the semantics of the quantifiers, like ‘some’, ‘at least 7’, and ‘most’. I...
LitStream

Computing Simple Quantifiers

Szymanik, Jakub

Pages: 41 –49

[In this Chapter I introduce the idea of semantic automata—simple computational devices corresponding to basic quantifiers in natural language. In line with a procedural approach to semantics, given a quantified sentence and a finite model, a semantic automaton computes the truth-value of this...
LitStream

Cognitive Processing of Quantifiers

Szymanik, Jakub

Pages: 51 –83

[In this chapter, I set out to study the cognitive task of sentence verification. In particular, I investigate the cognitive capacity to recognize the truth-value of sentences with simple quantifiers (like ‘some’, ‘an even number of’, ‘more than 7’, ‘less than half’). As the exact strategies...
LitStream

Standard Polyadic Lifts

Szymanik, Jakub

Pages: 87 –100

[This chapter is devoted to a logical and computational study of multi-quantifier sentences, like: ‘Three explorers discovered most of the islands.’ First, I show how to compositionally construct the meaning of such sentences from the meaning of single quantifiers using special semantic...
LitStream

Complexity of Polyadic Quantifiers

Szymanik, Jakub

Pages: 101 –121

[In this chapter, rather mathematical in nature, I provide a top-down computational perspective on polyadic quantification in natural language, that is, starting with a general computational model of Turing machines I investigate complexity differences between various polyadic constructions. I...
LitStream

Complexity of Quantified Reciprocals

Szymanik, Jakub

Pages: 123 –141

[This chapter is concerned with the linguistic case study. I investigate the computational complexity of different interpretations of reciprocal expressions, like ‘each other’ in English. I show that Ramsey quantifiers express the semantics of reciprocal sentences with a quantifier in the...
LitStream

Branching Quantifiers

Szymanik, Jakub

Pages: 143 –162

[This chapter is devoted to a particularly intriguing quantifier construction: branching. Branching interpretations of some natural language sentences are intractable, and therefore, their occurrence in natural language is far from obvious. I start by discussing the thesis formulated by Hintikka,...
LitStream

Complexity of Collective Quantification

Szymanik, Jakub

Pages: 165 –184

[Generalized quantifier theory tends to focus on distributive readings of natural language determiners. In contrast, this last chapter is devoted to collective readings of quantifiers, e.g., “Most students played poker together”. I start by introducing the common strategy of formalizing...

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