On WLI-ideal space and the properties of WLI-ideals in lattice implication algebra (LIA)

Lai, Jiajun; Xu, Yang

doi:10.1007/s12190-008-0195-4

Cited by 7 publications

(10 citation statements)

References 17 publications

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“…In the same spirit one can show that w(h) ∼ 1/h 1+ν [66]; whence γ = 1 + ν, with ν = 1/ζ or ζ * [67,68]. We do not discuss further the validity of Zip law(s) for which there is an abundant literature [54].…”

Section: Zipf Methodsmentioning

confidence: 98%

“…A large set of references on Zipf's law(s) in natural languages can be found in [54]. The idea has been applied to many various complex signals or "texts", -signals, translated through a number k of characters characterizing an alphabet, like, among many others, for time intervals between earthquakes [55], DNA sequences [56] or for financial data [50,51,52] along the lines of econophysics.…”

Section: Zipf Methodsmentioning

confidence: 99%

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Equilibrium and dynamic methods when comparing an English text and its Esperanto translation

Ausloos¹

2008

Physica A: Statistical Mechanics and its Applications

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A comparison of two english texts from Lewis Carroll, one (Alice in wonderland), also translated into esperanto, the other (Through a looking glass) are discussed in order to observe whether natural and artificial languages significantly differ from each other. One dimensional time series like signals are constructed using only word frequencies (FTS) or word lengths (LTS). The data is studied through (i) a Zipf method for sorting out correlations in the FTS and (ii) a Grassberger-Procaccia (GP) technique based method for finding correlations in LTS. Features are compared : different power laws are observed with characteristic exponents for the ranking properties, and the phase space attractor dimensionality. The Zipf exponent can take values much less than unity (ca. 0.50 or 0.30) depending on how a sentence is defined. This non-universality is conjectured to be a measure of the author style. Moreover the attractor dimension r is a simple function of the so called phase space dimension n, i.e., r = n λ , with λ = 0.79. Such an exponent should also conjecture to be a measure of the author creativity. However, even though there are quantitative differences between the original english text and its esperanto translation, the qualitative differences are very minutes, indicating in this case a translation relatively well respecting, along our analysis lines, the content of the author writing.

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Section: Zipf Methodsmentioning

confidence: 98%

Section: Zipf Methodsmentioning

confidence: 99%

Equilibrium and dynamic methods when comparing an English text and its Esperanto translation

Ausloos¹

2008

Physica A: Statistical Mechanics and its Applications

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“…Usually, for many languages, written texts, one has f ∼ R −ζ , such that one roughly sees a straight line going through the data, o a log-log plot, interestingly with a slope −1 [40]. A large set of references on Zipf's law(s) in natural languages can be found in [41]. Thus, one considers that there is a one-to-one relationship between rank and frequency.…”

Section: Data and Methdologymentioning

confidence: 99%

Punctuation effects in english and esperanto texts

Ausloos

2010

Physica A: Statistical Mechanics and its Applications

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A statistical physics study of punctuation effects on sentence lengths is presented for written texts: Alice in wonderland and Through a looking glass. The translation of the first text into esperanto is also considered as a test for the role of punctuation in defining a style, and for contrasting natural and artificial, but written, languages. Several log-log plots of the sentence length-rank relationship are presented for the major punctuation marks. Different power laws are observed with characteristic exponents. The exponent can take a value much less than unity (ca. 0.50 or 0.30) depending on how a sentence is defined. The texts are also mapped into time series based on the word frequencies. The quantitative differences between the original and translated texts are very minutes, at the exponent level. It is argued that sentences seem to be more reliable than word distributions in discussing an author style.

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“…For more details on lattice implication algebras, readers can consult Refs. [9,[12][13][14][15][16]18,22,35].…”

Section: Introductionmentioning

confidence: 99%

On WLI-ideal space and the properties of WLI-ideals in lattice implication algebra (LIA)

Cited by 7 publications

References 17 publications

Equilibrium and dynamic methods when comparing an English text and its Esperanto translation

Equilibrium and dynamic methods when comparing an English text and its Esperanto translation

Punctuation effects in english and esperanto texts

Linguistic truth-valued lattice-valued propositional logic system ℓP(X) based on linguistic truth-valued lattice implication algebra

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