User:Ken H/gf

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If grammar is seen as studying the relations and architectures of language, such relations and structures would then have supports and anchors, forces and motions, features and property equivalencies, and roles galore just as a building or organism has. If one treats grammar similarly to the descriptive disciplines of mathematics, logic and computation, then a possibly uncountable number of functions are present since language recklessly allows seemingly anything.

Certainly we can find many many routine grammatical functions everywhere in daily speech.

If a utilitarian POV is held, then everything in our buildings or organism (our language) is there for a reason. Our inventions and edifices all conect with various kinds of performance. Even static or apparently still performances may actually be space -or shape-making, or identity-bearing, even passive objects are busy receiving or load-sharing.

Necessarily every word (each a part-of-speech) has both a functions associated with it. Some languages are very free in the positions that wordPOS can occupy within grammatical or sentences. Their syntax may be loose but through one method or another, relationships are nonetheless reliably fixed such that users mostly agree on what a particular sentence is about.

Languages that are less free have a more fixed syntax. Again, somehow grammatically correct sentences express a fairly clear meaning as a result of their word ordering or syntactic functions. Among the tasks linguists pursue is the discovery of these functions within general theories of language, or for the understanding of a particular language.

A language such as English has a fair number of constraints. For example:
 * generally a head that is a single word follows its modifier(s)
 * prefixes modify the following head; affixes modify the preceding head; infixes modify the surrounding head
 * a preposition usually precedes its object and relates to its case function
 * subjects (when present) usually precede their predicates (when present).
 * adverbs generally precede verbs or adjectives; adjectives generally precede nouns; etc.

The above shows a general left&rarr;right pattern, just as how English is read left to right. This also fits with the general English sentence pattern of subject&rarr;verb&rarr;object. This precedence relation also allies with an over-arching functional dominance, that can be expressed both informally (descriptively or reflectively) or formally (painted by math and logic and embedded in hardware).

So then trees. But trinary trees. Logic does not have a zero. TF only. So nodes against each other can only X-bar unless weighted. That metaphor means grounded on their canvas of other objects. Nonetheless, at least for pixel generation one might strive for some kind of a sphere squishiness and then, even better, toroidal acuity. What kind of qualities would a real GF have?

some informal gf definitions
Quantification, mapping, control, scope, range, boundary, head/modifier, specifier/head, individual part-of-speech functions, relevance.

some formal gf definitions
Quantification &lambda;f  precedence dominance [op[op]] permutations binding indexing c-cmd m-cmd, etc.,

gf references

 * Wikipedia: &lambda;f    |   X-bar   |   exocentric   |   endocentric   |   algorithm   |   sphere&toroid
 * Function: Phil  |   Comp   |   Math   |   Logic
 * Function: itself can be found in its disambiguation page.

academic references

 * Minsky  |   Talmy   |   Rizzi   |   Kayne   |   Chomsky LGB Min   |   PPs    |   PSGs   |   CG, etc.