Abstract
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).
Highlights
The article continues the series of publications on the linguistics of relations and is devoted to an introduction to the logic of natural language in relation to the approach considered in the series
This article continues a series of publications devoted to the introduction to the linguistics of relations – R-linguistics) – a formal direction in linguistics
We will talk about the logic that follows from the previously published material, and if what was stated in the series is close to the truth, the logical constructions given here are related to the foundations of natural language logic
Summary
This article continues a series of publications devoted to the introduction to the linguistics of relations – R-linguistics) – a formal direction in linguistics. The second axiom (the idempotency axiom) States that repeating the same test s (sentence) does not change the semantics of the text: Ψ(C, s) = C' = Ψ(C', s) for any semantics of C In the language, this property of interpretation is reflected by the equality s = s*s. The semantic property of the right conditional negation in the language is expressed by the rule s*s-1 = e, where “s” is a sentence and the initial meaning of the text is zero. We say that a sentence s has an unconditional right of negation, if for any sense С of equality is performed: if Ψ(С, s) = С', Ψ(C', s-1) = C. in Other words, Ψ(С, s*s-1) = С This semantic property of the sentence means that the operation * is associative for text s*s-1, i. Does this mean that logic formalizes logical operations between language sentences, separating them from meaning, but it makes meaningless any natural language to which it is applied? To clarify these issues, we will deal with in the continuation of the article
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