11

There are many measures of lexical similarity or linguistic distances but neither can tell you whether something is a dialect or a language outside a very constrained context. It is easy to come up with a measure for a particular purpose such as determining historical developments or automatically recognizing different languages in a corpus. But what ...


10

Calculus can be a useful tool in quantitative linguistics. One simple example would be the deduction of the theoretical equation for the Piotrowski law modeling language change by Altmann et al. The increase of new forms p' is proportional to the product of the proportions p of new and 1-p old forms: p' ∝ p(1 - p). Introducing the factor of proportionality ...


5

A straightforward rewriting of the Wikipedia formula gives log V_R(n) = log K*n^beta = log K + log n^beta = log K + beta*log n This allows us to identify K=C and beta=-alpha (probably the WSJ uses a different formulation of Heaps' law V_R (n) = \frac{K}{n^\alpha} ). The remaining b is a strange additional parameter not present in ...


5

Definitely. This is a little obscure, probably to obscure to be of any real use, but there is a chapter from the book Aspects of Automatic Text Analysis, The Mathematics of Semantic Spaces (PDF), that models semantics as a metric space. It's general calculus on metric spaces, and this is probably the limit of mathematical abstraction in applied linguistics ...


4

Lambda calculus is often used in formal semantics to express the meaning of a sentence compositionally as a series of successive function applications. On Barbara Partee's website there's a nice lesson on how lambda calculus (or, as some say, the lambda calculus) can be used to model English semantics. Lesson 7 introduces lambda calculus, but it might be ...


3

Your question is about derivational morphology. There are mainly three strategies to create new words: 1. add affixes to a stem (as in your example), 2. combine stems (as in Chinese), 3. modify the vowels (as in Semitic). Purely agglutinative languages only apply strategy1. Indo-European languages tend to apply a mixture of all three strategies, for example ...


3

This is a good question but only in the sense that it opens a possibility for rejecting the very premise on which it is based. The short answer is, there are no laws formulated for linguistics that could be analogous to some of the laws of physics that would be constant through time and space. The last attempt at this were the sound change laws in the 19th ...


2

There's a mathematical physicist who related graphs grammars and Feynman graphs. She comes up with the, perhaps unwarranted, conclusion that any context free graph grammar determines an insertion Lie algebra and commutative Hopf algebra.


2

One research group at our university is particularly interested in the statistical properties of language. One professor, Michael Ramscar, is teaching us some classes this semester on related topics. And basically the idea is that this kind of logarithmic/exponential distribution is considered optimal in an information theory point of view, since it ensures ...


1

On the second question, I think measures of morphological productivity are what you're looking for. If you search around, you should be able to find information on productivity measures easily, e.g. this overview: Baayen, R. H. (2009). 43. Corpus linguistics in morphology: morphological productivity. Corpus linguistics: An international handbook, 900-919.


1

I assume these are your hypotheses: H0: The verb is passive 92% of the time. H1: The verb is passive 100% of the time. You can't apply a t-test in this case; there's no t-statistic that can be generated. (Typically, when we apply a t-test, it's when we have some point estimate of a variable assumed normal minus the mean under the null hypothesis divided ...


1

The entropy formula as quoted has some ideosyncrasies making it different from standard Shannon entropy There is a (not really relevant) factor of 100 (probably to produce more beautiful numbers) The term log N in the denominator is absent in Shannon entropy The term p(i) cannot mean anything but the frequency of the i-th type, obtained by dividing the ...


1

There are some laws concerning polysemy. Please look at: http://lql.uni-trier.de/index.php/Main_Page


1

For calculus to be useful, you first have to have some kind of continuous numeric function. This not being the case with grammar, calculus won't be illuminating for the study of unbounded dependencies or association relations: grammar is based on simple "does / doesn't" logic. However, it is in principle applicable to the study of linguistic behavior, e.g ...


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