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Open Access 2023 | Open Access | Buch

Vector Semantics

verfasst von: András Kornai

Verlag: Springer Nature Singapore

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Inhaltsverzeichnis

Über dieses Buch

This open access book introduces Vector semantics, which links the formal theory of word vectors to the cognitive theory of linguistics.

The computational linguists and deep learning researchers who developed word vectors have relied primarily on the ever-increasing availability of large corpora and of computers with highly parallel GPU and TPU compute engines, and their focus is with endowing computers with natural language capabilities for practical applications such as machine translation or question answering. Cognitive linguists investigate natural language from the perspective of human cognition, the relation between language and thought, and questions about conceptual universals, relying primarily on in-depth investigation of language in use.

In spite of the fact that these two schools both have ‘linguistics’ in their name, so far there has been very limited communication between them, as their historical origins, data collection methods, and conceptual apparatuses are quite different. Vector semantics bridges the gap by presenting a formal theory, cast in terms of linear polytopes, that generalizes both word vectors and conceptual structures, by treating each dictionary definition as an equation, and the entire lexicon as a set of equations mutually constraining all meanings.

Inhaltsverzeichnis

Frontmatter

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1. Foundations of non-compositionality

Abstract

For the past half century, linguistic semantics was dominated by issues of compositionality to such an extent that the meaning of the atomic units (which were generally assumed to be words or their stems) received scant attention. Here we will put word meaning front and center, and base the entire plan of the book on beginning with the lowest meaningful units, morphemes, and building upward.

András Kornai

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2. From morphology to syntax

Abstract

Our goal is to develop a semantic theory that is equally suitable for the lexical material (words) and for the larger constructions (sentences) put together from these. In 2.1 we begin with the system of lexical categories that are in generative grammar routinely used as preterminals mediating between syntax and the lexicon. Morphology is discussed in 2.2, where subdirect composition is introduced. This notion is further developed in 2.3, where the geometric view is expanded from the standard word vectors and the voronoids introduced in Chapter 1 to include non-vectorial elements that express binary relations.

András Kornai

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3. Time and space

Abstract

We owe the recognition of a deep connection between time, space, and gravity to the 20th century, but people have used language to speak about spatial and temporal matters long before the development of Euclidean geometry, let alone general relativity. Throughout this book, we approach problems through language use, in search of a naive theory that can be reasonably assumed to underlie human linguistic competence.

András Kornai

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4. Negation

Abstract

Our goal in this chapter is to provide a formal theory of negation in ordinary language, as opposed to the formal theory of negation in logic and mathematics. In order to provide for a linguistically and cognitively sound theory of negation, we argue for the introduction of a dyadic negation predicate lack and a force dynamic account of affirmation and negation in general.

András Kornai

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5. Valuations and learnability

Abstract

In this chapter we describe a rational, but low resolution, model of probability. We do this for two reasons: first, to show how a naive theory, using only discrete categories, can still explain how people think about uncertainty, and second, as a model for fitting discrete theories of valuation (which arise in many other contexts from moral judgments to household finance) into the overall 4lang framework.

András Kornai

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6. Modality

Abstract

The notion of modality is almost inextricably intertwined with metaphysics, some kind of theory of what is real, what exists, and why (a theory of ‘first causes’). At the center of the commonsensical theory is the real world, but the idea is that there exist, or at least there can exist, other worlds.

András Kornai

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7. Adjectives, gradience, implicature

Abstract

Adjectives are present in most, though not necessarily all, natural languages. In 7.1 we begin by discussing the major properties of adjectival roots and the vector semantics associated to the base, comparative, and superlative forms. We discuss the logic associated to these, and extend the analysis to intensifiers.

András Kornai

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8. Trainability and real-world knowledge

Abstract

Until this point, we concentrated on the lexicon, conceived of as the repository of shared linguistic information. In 8.1 we take on the problem of integrating real-world knowledge, nowadays typically stored in knowledge graphs as billions of RDF triples, and linguistic knowledge, stored in a much smaller dictionary, typically compressible to a few megabytes. We present proper names as point vectors (rather than the polytopes we use for common nouns and most other lexical entries), and introduce the notion of content continuations, algorithms that extend the lexical entries to more detailed hypergraphs that can refer to technical nodes, such as Date, FloatingPointNumber, or Obligation (see 9.1) that are missing from the core lexicon.

András Kornai

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9. Applications

Abstract

We started with Lewin’s aphorism, “there is nothing as practical as a good theory”. Vector semantics, the broad theory that was raised from a Firthian slogan to a computational theory by Schütze, 1993, has clearly proven its practicality on a wide range of tasks from Named Entity Recognition (see 8.1) to sentiment analysis. But the farther we move from basic labeling and classification tasks, the more indirect the impact becomes, until we reach a point where some conceptual model needs to be fitted to the text. Perhaps the best known such problem is time extraction and normalization, where our target model is the standard (Gregorian) calendar rather than the simple (naive) model we discussed in 3.2. In 9.1, based almost entirely on the work of Gábor Recski and his co-workers at TU Wien, we outline a system that probes for matches with a far more complex conceptual model, that of building codes and regulations in effect in the city of Vienna.

András Kornai

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Backmatter

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Titel: Vector Semantics
verfasst von: András Kornai
Verlag: Springer Nature Singapore
Electronic ISBN: 978-981-19-5607-2
Print ISBN: 978-981-19-5606-5
DOI: https://doi.org/10.1007/978-981-19-5607-2