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Lasix For Sale, In the 70's, Joan Bresnan, a student of Chomsky's, came out with a new model of grammar called Lexical-Functional Grammar (LFG). At the time it was perhaps one of the only real alternatives to the then-contemporary versions of generative grammar espoused by Chomskyans. Bresnan's model was different in that instead of treating the whole of linguistic phenomena in terms of purely syntactic categories and phrase structure rules, and so forth, she added a second layer to the nature of linguistic representation, a "functional" layer, which would represent more traditional notions of grammatical functions like subject, object, and so forth. The phenomena traditionally handled via transformational processes applied to underlying syntactic structures were instead taken to be constraint relationships that apply between syntactic rules and objects, and their corresponding functional structures.

Constituent Structure (C-structure)

As with Chomskyan syntax of the time, LFG employs a version of x-bar syntax for it's trees and the structuring of constituents wherein (major) head words project phrases, with potential intermediate nodes between the phrasal node and the head word node (or the pre-terminal node), japan, craiglist, ebay, overseas, paypal. Unlike normal x-bar syntax, however, not all phrases have to be projected by heads. So while any given noun, let's say book, projects up through the preterminal N, then the non-terminals N' then NP, not all NP nodes have to have an N' or N, Lasix For Sale. In the phrase structure rules for LFG, all daughter nodes are, in principle, optional. Other than this, LFG's structural descriptions are relatively straight-forwardly representable as context-free rules.

Functional Structure (F-structure)

Along side s-structure, LFG has a layer of functional structures that are used to describe mostly if not entirely abstract relationships within a sentence. F-structures correspond to syntactic objects (nodes within trees), Order Lasix online c.o.d, so it's easy to introduce the notion by talking about the f-structures of particular objects. The simplest sorts of functional structures are for nominal elements like proper names. A name like Susan have a corresponding functional structure like the following (denoted with an attribute-value matrix (AVM)).




The functional structure here has three "functions" — the pred function can be seen as an abstract grammatical (but not semantic) predicate whose arguments are to be found in the f-structure that the pred Lasix For Sale, function belongs to, and the absence of an argument list for this particular pred can be seen as indicating that it predicates on whatever the reference of the word Susan is at time of use; the num function denotes the abstract grammatical number of the word; and the pers function similarly denotes the abstract grammatical person of the word. The ideas aren't enormously new to anyone who's studied more traditional notions of grammar, and the LFG formalism takes them as serious core conceptual notions.

Let's take a look at some more f-structures to really drive the point home. Here we have the f-structure for the sentence the boy danced:




What we can see here is a slightly more complicated f-structure corresponding to the sentence as a whole. We have two new functions, tense and subj, corresponding to abstract grammatical tense, and abstract grammatical subject, respectively, and also def which corresponds to definiteness, here being binary valued as + denoting 'definite', as opposed -, where can i buy Lasix online, which would denote 'indefinite'. The value for subj is itself an f-structure, in this case the f-structure corresponding to the noun phrase the boy in the sentence. The little letters before the AVMs for these f-structures are just labels that we can use to talk about the different f-structures, so the f-structure f is the f-structure for the sentence as a whole, and g is the f-structure of the noun phrase, as previously described, Lasix For Sale. The labels will be used in various ways for convenience and often omitted when they're irrelevant.

Let's look at one more, this time for the sentence "the small dog will bark loudly".




Again we have a new function, specifically, adj, which is used to denote a sort of modification arrangement, and notice that since modification is not exclusive (e.g. the dog could be both small and furry), the adj function takes a set of f-structures, Lasix online cod, not just a single f-structure. The precise collection of functions and the value types they take are numerous and depend on what brand of LFG you're looking at, so I won't bother to try and list and explain all of the possible ones you might come across.

Correspondences and Phrase Structure Rules

As discussed before, these f-structures correspond to various syntactic nodes. Using example (2), the f-structure f belongs to the sentence node S, and we can describe this with a correspondence function ϕ such that ϕ(S) = f. Lasix For Sale, Similarly, in (2), ϕ(NP) = g. LFG's phrase structure rules take advantage of this notion of a correspondence structure so that constraints can be placed on the relations between f-structures of various nodes. The simplest of these constraints is a sort of "propagation" constraint that is used to ensure that the f-structure of a verb/preterminal is the same as the V' and VP that it projects (I will omit the objects of the verb for clarity).



    1. VP → V'

    2. ϕ(VP) = ϕ(V')


    1. VP → V

    2. ϕ(VP) = ϕ(V)


    1. V' → V

    2. ϕ(V') = ϕ(V)

Here we can see that these functional equations in the (b) entries associated with each phrase structure rule in (a) require an equality of the functional structures corresponding to each node. It's cumbersome, however, to have to have a number of equations like this, and to write the node labels multiple times, is Lasix addictive, so LFG introduces a number of layers of notational shorthand which I will now explain.

The first of these is based on the fact that in LFG, there is an assumption that the functional equations can only refer to the mother node and a single daughter node at any one time. That is to say, functional equations relate something about the non-terminal node on the left of → to a something about single node on the right of the →. We can simplify the notation by doing the following: first, we write equations under the single node that they pertain to (the one other than the non-terminal on the left of →), Lasix For Sale. This helps separate things out visually. Thus (4) can be rewritten as:





  1. VPV'
    ϕ(VP) = ϕ(V')

With this simplification it's obvious that repeating the name of the node beneath the node in the equations that constrain that node is silly, so we can make a shorthand, ∗, which denotes "the non-parent node that this equation applies to". It's similarly silly to keep repeating the name of the parent node that's on the left of the →, since it's the same in any given rule, Lasix results, so we can denote that by ∗̂ (the little up-hat is like an arrow pointing to the node "above" the node denoted by ∗).





  1. VPV'
    ϕ(∗̂ ) = ϕ(∗)

And again, because we're going to be referring to ϕ(∗) and ϕ(∗̂ ) a lot, if not exclusively, it makes sense to just reduce these to something simpler as well, and LFG chose ↑ and ↓, respectively, giving us the final shorthand version.





  1. VPV'
    ↑ = ↓

If we want to add in objects to the rule in (5), we can do so relatively simply, here given in each of the three ways just described.





  1. VPVNP
    ϕ(VP) = ϕ(V')ϕ(VP) OBJ = ϕ(NP)




  2. VPVNP
    ϕ(∗̂ ) = ϕ(∗)ϕ(∗̂ ) OBJ = ϕ(∗)




  3. VPVNP
    ↑ = ↓↑ OBJ = ↓

What we can see here is the introduction of a useful notation. With the VP-V' equations we only need to ensure the equality of the two f-structures, but with the VP-V-NP rule we don't need the f-structure of VP to equal the f-structure of NP, we need the object attribute of ϕ(VP) to equal ϕ(NP), and so we use the notation given here, buy Lasix from canada, with an f-structure followed by an attribute name, to denote the value of that attribute for that f-structure.

For the terminals the rules are subtly different. Lasix For Sale, Rules that govern non-terminals and pre-terminals just need to constraint the relative equality of different f-structures and function values, but terminals — actual words — have to introduce those values, presumably because in LFG, terminals themselves have no f-structures (f-structures are apparently reserved to things that are build by rules, not the things that define how things are build, e.g. the nodes in rules). Therefore we have lexical/terminal rules like the following:





  1. Vdanced
    ↑ PRED = 'dance⟨subj⟩'
    ↑ TENSE = past

Because lexical rules are a bit different than other rules, they're sometimes just written as lexical entries like so:




  1. dancedV↑ PRED = 'dance⟨subj⟩'
    ↑ TENSE = past

When we represent linguistic expressions as trees, we still want to show the functional equations that pertain, so we can write the relevant equations over or under their associated nodes in the tree, rather than writing them over or under the nodes in the rule (over is preferable because then the ↑ and ↓ symbols really do point to correct things). Thus for an NP like the boy we might have the tree in (15).




While for the whole sentence the boy danced we might have (16).




We can now use this tree to check whether or not the f-structure of (2) matches, and as it turns out, it does. Buy Lasix from mexico, For the sake of exposition, however, let's go through it piece by piece to see. We'll go left to right, bottom to top, starting with the word the and working up as far as possible, laying them out in a list looking like the: ....


  • the: ϕ(D) DEF = +

  • D: ϕ(NP) = ϕ(D)

  • boy: ϕ(N) PRED = 'boy', ϕ(N) NUM = sg, ϕ(N) PERS = 3p

  • N: ϕ(NP) = ϕ(N)

  • NP: ϕ(S) SUBJ = ϕ(NP)
  • danced: ϕ(V) PRED = 'dance⟨subj⟩'

  • V: ϕ(VP) = ϕ(V)>

  • VP: ϕ(S) = ϕ(VP)

Solving this, and using temporary variables f and g again, we find:


  • ϕ(S) = ϕ(VP) = ϕ(V) = f

  • ϕ(NP) = ϕ(D) = ϕ(N) = g

  • f PRED = 'dance⟨subj⟩'

  • f TENSE = past

  • f SUBJ = g

  • g DEF = +

  • g PRED = 'boy'

  • g NUM = sg

  • g PERS = 3p

We could then construct two f-structure AVMs to represent f and g, and we would find that they match what we said the f-structures should be in (2), Lasix For Sale. In this way we can see that this sentence has a valid f-structure. For the present tense version, the lexical item dances would instead have the equations (↑ PRED) = 'dance⟨subj⟩', (↑ TENSE) = present, and (↑ SUBJ NUM) = sg. This last one has two function names, which act as a path, denoting "the number of the subject of the node above dances". In this way, the lexical item dances enforces that it's subject must have singular number, Lasix brand name, and if we were to use a plural root noun like boys, which specifies (↑ NUM) = pl, the functional equations would not be satisfied, because (ϕ(S) SUBJ NUM) would have to be both sg and pl. Lasix For Sale, This is how LFG handles agreement phenomena. The total set of kinds of equations permitted is a bit larger than just those listed above. For instance, there are ways of denoting that a function must be defined (regardless of value), or undefined, or different comparators can be used, etc.

Constraining the Grammar

With just these tools — f-structures and phrase structure rules with functional equations — there is little that can't be found to be acceptable. The grammar needs constraints, Fast shipping Lasix, and LFG provides these in the form of well-formedness constraints on f-structures. Just as every sentence must be generable using the phrase structure rules, every f-structure must satisfy the well-formedness constraints, and failure to do so renders a linguistic expression ungrammatical.

The first of these constraints is completeness, which says that every argument inside the ⟨ ⟩ of an f-structure's pred (the arguments that the predicate "governs") must have a corresponding function in that f-structure. For example, dance⟨subj⟩ has subj, and so the avm that this belongs too must have a subj function defined, Lasix For Sale. Or, break⟨subj,obj⟩ requires it's f-structure to have both a defined subj and obj. The rule is slightly more subtle, in that some of those arguments governed by pred might be stipulated by the particular model of LFG as being irrelevant to completeness, that is, ungovernable. We can reword the rule more precisely as all governable functions that are governed by an f-structure's pred must appear in that f-structure, online buying Lasix hcl. The completeness constraint is what renders the sentence John broke ungrammatical. The lexical item broke Lasix For Sale, requires, after we solve the functional equations, that (ϕ(S) PRED) = 'break⟨subj,obj⟩, but there would be no (ϕ(S) OBJ) for this sentence, and the f-structure is therefore incomplete thus bad.

The second of these constraints is sort of like the converse of completeness, and in the precise formulation is all the governable functions that appear in an f-structure must be governed by that f-structure's pred. In simpler terms, if it's in the f-structure and can be governed by the pred, then it must be governed by pred. The converse of the example for completeness would be the sentence the boy danced the girl. Since dance requires, after solving the functional equations, (ϕ(S) PRED) = 'dance⟨subj⟩', and since this f-structure would have an obj function defined that isn't present in pred, the f-structure is incoherent thus bad.

The last of these constraints is consistency, which we've already seen, Lasix no rx, which is simply that f-structure functions have only one value, which amounts to requiring that functional equations have a solution.

Long-distance Dependencies

Long-distance dependencies in LFG, for instance, topicalized elements, are not handled using movement, as they would be in mainstream generative grammar but instead by a notion called functional uncertainty combined with function path patterns. Functional uncertainty is relatively simple: you have a pseudo-function named GF that means "some function", and you define functional equations in terms of that. So for example (f GF) = g requires that some function of f is valued with g, Lasix For Sale. Maybe it's the subj function, maybe it's adj, who knows. As long as some function in the f-structure of f is valued with g, the equation is satisfied, Lasix mg. Function path patterns are a bit tricker.

I already briefly described function paths above to show how agreement is handled but let's look more deeply at this issue.




Here we see an f-structure, f, with two functions, foo and bar. The f-structures g and h are similar in their function content. Lasix For Sale, Notice also that (f BAR) = g and (g BAR) = h, so we can say that (f BAR BAR) = h. We could continue this down for as long as we want. What we can imagine now is that we want one of these, f, (f BAR), or (f BAR BAR), or (f BAR BAR BAR), Purchase Lasix online, etc. for as many BAR's as necessary, to be equal to some particular f-structure, call it k. That is, we want at least one of these equations to be true:


  • f = k

  • (f BAR) = k

  • (f BAR BAR) = k

  • (f BAR BAR BAR) = k

  • (f BAR BAR BAR BAR) = k

  • ...

Well obviously there are an infinite number of equations here, and writing infinitely many things is complicated, so we can take advantage of the obvious repetition and use a Kleene star like we had back in simple formal grammars to condense this down to just one equation:


  • f BAR* = k

We can do the same for any part of a function path, so we might have (f BAR* BAZ), or (f BAR BAZ* QUUX*), or whatever. Similarly, you could use a Kleene plus, where can i order Lasix without prescription. In this fashion, LFG can handle long distance dependencies with the a phrase structure rule like so:





  1. CPXPC'
    (↑ TOPIC) = (↑ COMP* GF) = ↓↑ = ↓

In plain English, we can have a fronted topic element XP if that object's f-structure is the topic of it's parent CP, and if it's also the value of some function in the CP, or COMP in the CP, or the COMP of the COMP of the CP, etc. As long as that is possible, this equation is satisfied.

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