Mathematical Logic. W. V. Quine

Introduction. The article continues the series of publications on the linguistics of relations (hereinafter R–linguistics) and is devoted to an introduction to the logic of natural language in relation to the approach considered in the series. The problem of natural language logic still remains relevant, since this logic differs significantly from traditional mathematical logic. Moreover, with the appearance of artificial intelligence systems, the importance of this problem only increases. The article analyzes logical problems that prevent the application of classical logic methods to natural languages. This is possible because R-linguistics forms the semantics of a language in the form of world model structures in which language sentences are interpreted.Methodology and sources. The results obtained in the previous parts of the series are used as research tools. To develop the necessary mathematical representations in the field of logic and semantics, the formulated concept of the interpretation operator is used.Results and discussion. The problems that arise when studying the logic of natural language in the framework of R–linguistics are analyzed. These issues are discussed in three aspects: the logical aspect itself; the linguistic aspect; the aspect of correlation with reality. A very General approach to language semantics is considered and semantic axioms of the language are formulated. The problems of the language and its logic related to the most General view of semantics are shown.Conclusion. It is shown that the application of mathematical logic, regardless of its type, to the study of natural language logic faces significant problems. This is a consequence of the inconsistency of existing approaches with the world model. But it is the coherence with the world model that allows us to build a new logical approach. Matching with the model means a semantic approach to logic. Even the most General view of semantics allows to formulate important results about the properties of languages that lack meaning. The simplest examples of semantic interpretation of traditional logic demonstrate its semantic problems (primarily related to negation).

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Ω-Bibliography of Mathematical Logic

10.1007/978-3-662-09055-8 ◽

1987 ◽

Cited By ~ 2

Keyword(s):

Mathematical Logic

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PHILOSOPHICAL CONCEPTIONS OF LANGUAGE VS. MATHEMATICAL LOGIC IN SEMANTIC TRADITION

Философия науки ◽

10.15372/ps20180103 ◽

2018 ◽

Keyword(s):

Mathematical Logic

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A Study on the Small Unit of the Mojia in Mathematical Logic

THE EASTERN CLASSIC STUDIES ◽

10.25086/hsdy.2018.39.147 ◽

2018 ◽

Vol 39 ◽

pp. 147-167

Author(s):

Gwang Yeon Lee ◽

◽

Ki Soeb Park

Keyword(s):

Mathematical Logic ◽

Small Unit

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Recursive generation in language

10.1093/oso/9780198785156.003.0003 ◽

2017 ◽

Author(s):

David J. Lobina

Keyword(s):

Mathematical Logic ◽

Production System ◽

General Property ◽

Recent Literature ◽

Expressive Power ◽

The Self ◽

Recursive Structure ◽

Embedded Structures ◽

Mechanical Procedure ◽

The 1950S

The introduction of recursion into linguistics was the result of applying some of the results of mathematical logic to the study of language. In particular, recursion was introduced in the 1950s as a general property of the mechanical procedure underlying the grammar, in order to account for language’s discrete infinity and expressive power—in the 1950s, this mechanical procedure was a production system, whereas more recently, of course, it is the set-operator merge. Unfortunately, the recent literature has confused the general recursive property of a grammar with specific instances of (recursive) rules/operations within a grammar; more worryingly still, there has been a general conflation of these recursive rules with some of the self-embedded structures these rules can generate, adding to the confusion. The conflation is manifold but always fallacious. Moreover, language manifests a much more generally recursive structure than is usually recognized: bundles of the universal (Specifier)-Head-Complement(s) geometry.

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