On the Vocabulary of Grammar-Based Codes and the Logical Consistency of Texts

The article presents a new interpretation for Zipf-Mandelbrot's law in natural language which rests on two areas of information theory. Firstly, we construct a new class of grammar-based codes and, secondly, we investigate properties of strongly nonergodic stationary processes. The motivation for the joint discussion is to prove a proposition with a simple informal statement: If a text of length $n$ describes $n^\beta$ independent facts in a repetitive way then the text contains at least $n^\beta/\log n$ different words, under suitable conditions on $n$. In the formal statement, two modeling postulates are adopted. Firstly, the words are understood as nonterminal symbols of the shortest grammar-based encoding of the text. Secondly, the text is assumed to be emitted by a finite-energy strongly nonergodic source whereas the facts are binary IID variables predictable in a shift-invariant way.Comment: 24 pages, no figure

On the Vocabulary of Grammar-Based Codes and the Logical Consistency of Texts

The article presents a new interpretation for Zipf's law in natural language which relies on two areas of information theory. We reformulate the problem of grammar-based compression and investigate properties of strongly nonergodic stationary processes. The motivation for the joint discussion is to prove a proposition with a simple informal statement: If an $n$-letter long text describes $n^\beta$ independent facts in a random but consistent way then the text contains at least $n^\beta/\log n$ different words. In the formal statement, two specific postulates are adopted. Firstly, the words are understood as the nonterminal symbols of the shortest grammar-based encoding of the text. Secondly, the texts are assumed to be emitted by a nonergodic source, with the described facts being binary IID variables that are asymptotically predictable in a shift-invariant way. The proof of the formal proposition applies several new tools. These are: a construction of universal grammar-based codes for which the differences of code lengths can be bounded easily, ergodic decomposition theorems for mutual information between the past and future of a stationary process, and a lemma that bounds differences of a sublinear function. The linguistic relevance of presented modeling assumptions, theorems, definitions, and examples is discussed in parallel.While searching for concrete processes to which our proposition can be applied, we introduce several instances of strongly nonergodic processes. In particular, we define the subclass of accessible description processes, which formalizes the notion of texts that describe facts in a self-contained way

VIEWS OF PROSPECTIVE CLASSROOM TEACHERS ON LANGUAGE AND EXPRESSION OF LIFE STUDIES AND SOCIAL STUDIES TEXTBOOKS BEFORE AND AFTER 2005

This study was conducted to determine the views of prospective classroom teachers on the language and expression of Life Studies and Social Studies textbooks before and after 2005. The research employed a qualitative research method, specifically a case study. The study group consisted of 10 prospective teachers studying in the Department of Elementary Education, Faculty of Education, Çanakkale Onsekiz Mart University, Turkey selected through purposive sampling. The data for the research were collected using a Document Review Form and analyzed using inductive analysis. In the research, the 2002 and 2018 Life Studies textbooks for second-grade elementary students were compared in terms of criteria such as the use of punctuation marks, sentence structure, and adherence to spelling rules. The data obtained revealed that the textbook written in 2002 was more successful in meeting these criteria. Furthermore, the study also compared the 2019 Social Studies textbook for fourth-grade elementary students with the 2004 Social Studies textbook for the same grade. It was found that the 2019 textbook was more adequate in the use of punctuation marks, adherence to spelling rules, and the arrangement of sentence elements compared to the textbook written in 2004

The Ethics of Ambiguity in Quintilian

In a list of twelve stylistic and grammatical errors of oratory, the fourth-century grammarian Donatus includes the fault of amphibolia, a transliteration of a Greek word that Donatus further defines as an ambiguitas dictionis. This understanding of ambiguitas dictionis as a flaw in composition is unique neither to the texts of late antiquity nor to technical grammatical treatises, and one can find ample cautioning against it in pedagogical texts both before and after Donatus. In his first-century Institutio Oratoria, for instance, Quintilian similarly cautions against writing ambiguous language and encourages his students to compose lucid and straightforward Latin, particularly in regard to syntax