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For instance, Taylor (1976) provides a recursive definition of a collection of 'states of affairs' for a given language.
In essence the axioms specify a family of possible support functions, {Pβ, Pγ, …, Pδ, …} for a given language L.
Solutions to the inference problem are evolved by optimizing the parameters of a covering grammar for a given language sample.
Groups of phones that are equivalent for a given language (not affecting the words recognized by a hearer, if interchanged) are the phonemes of the language.
Even the physicalist Bjorn Lindblom (1986, p. 495) concedes that "for a given language there seems to be no unique set of acoustic properties that will always be present in the production of a given unit (feature, phoneme, syllable) and that will reliably be found in all conceivable contexts".
Rather, when one constructs an intended model for a given language, it shows clearly how the semantic values of the relevant parts of a sentence of first-order logic — the objects, properties, relations, etc. in the world those parts signify — contribute to the actual truth value of the sentence.
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What this means is that for Humboldt, the individual sound of a given language can be formed only "in relation to the others" (in Beziehung auf die übrigen) that make up the entire 'sound system' (Lautsystem) of that language (GS Vol 7, 67).
A probabilistic grammar is consistent if a sum of probabilities of generation for all strings belonging to a given language is equal to one: (7) ∑ x ∈ Σ ∗ Pr (S ⇒ ∗ x ) = 1, where S ⇒ ∗ x denotes all possible derivations starting from S and resulting in a finite string x.
The deductive system is to capture, codify, or simply record arguments that are valid for the given language, and the semantics is to capture, codify, or record the meanings, or truth-conditions for at least part of the language.
When looking at languages to study, use Wikipedia's IPA for the given language, they are extensive and very helpful.
Building a PLV for a given Pattern Language, requires the structural, syntactic, and semantic rules of the language to be precisely defined using the presented formalism.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com