What are the state-of-the-art English syntax theories there are that can explain all the English syntax phenomena?

Question

Both Dependency Grammar (DG) and Constituency Grammar (CG) are a tool to describe the syntax of any natural language in general. The language whose syntax is to be described in DG or CG doesn't have to be a specific language such as English or German or French or Japanese. That means that DG or CG doesn't incorporate a complete set of syntax rules for a particular language.

Now, in order to present a theory of English syntax, whether you use DG or CG to describe the syntax, you need to be able to determine a finite number of English syntax rules -- the fewer rules, the better -- that can generate an infinite number of grammatical English sentences.

Are there such English syntax theories out there? If so, what are they called?

EDIT

I'll try to show the difference between "explaining" and "describing" English. If you have a plurality of unrelated rules, each dictating how a particular English construction works, such unrelated rules are merely "describing" English. For example, in order to form a declarative in English, the subject comes first in a canonical construction, whereas, in order to form an interrogative, an auxiliary verb (e.g., do, is, can, have, etc.) needs to be fronted before the subject in a canonical construction.

So, these are two "unrelated rules" for describing a canonical declarative construction and a canonical interrogative construction, respectively. There is no underlying principle whatsoever that explains why these different rules are applied to these different constructions. And if there is such a principle that can subsume the two apparently unrelated rules, that principle will be "explaining" English.

Answer 1

There is no theory of English syntax which contains all of the rules generating the class of English sentences, where the theory both explains why the rules are what they are, and uses just a few core principles. Such a thing is impossible in principle, since the thing that you're looking for isn't well-defined. The empirical domain is not well-defined for a number of reasons. First, "English" is too broad, so no well-defined system can simultaneously include and exclude sentences like "I might should go", which fyi is perfectly normal in some parts of the US. Other non-geographical examples are the variable acceptability of "I can has seconds?" as a question, and "If I was hungry, I would have eaten something".

It is also not clear from your question what you mean by "syntax", especially the extent to which you specifically exclude lexicon, morphology and phonology from consideration. As I understand it, minimalist syntax has relatively little by way of rules of syntax, and much of the work is shifted to the lexicon (also a feature of HPSG). Supposing we agree that *"I need" is ungrammatical, is that a fact represented in the syntax, or in the lexicon?

Somewhat finally, your concept of "explanation" needs to be clarified. The notion of "explanation" is notoriously elusive yet often-invoked in science. There is an equation in theoretical physics E=hf which states that the energy of a photon is the product of its frequency and Planck's constant. This does not explain why this particular thing should be the rule. I could assume that you are referring to Chomsky's third desideratum of theory (from Current issues in linguistic theory), namely "explanatory adequacy". This principle basically says that an explanatory metatheory allows a single grammar that generates a particular language. Explanatory adequacy can only be a requirement of a metatheory of language, not the syntax of a specific language. Since you are just asking for a grammar of English, then it is meaningless to require explanatory adequacy. And therefore, you must have in mind something completely different when you invoke the desideratum of explanation.

[EDIT]

I think it is reasonable to conclude that we do indeed have a plurality of unrelated rules in English. For example, we have a passive rule (“The cat ate the mouse” → “The mouse was eaten by the cat”) and a raising rule (“The people believe that Tom is a thief” → “The people believe Tom to be a thief”). There are also rules for placing negation in a sentence. Unless you go with Greg Lee’s general purpose rule “a sentence is any number of words”, you are going to have a plurality of unrelated rules. What is in the syntax / lexicon dichotomy for us is that this kind of scheme might work, if you have a very rich lexicon that states in great detail in what context you can insert “mouse” – that is, you put pretty much all of the syntax into the lexicon.

I suggest taking the Aspects model seriously, as implemented in Burt’s red book From Deep to Surface Structure, since it is an actual set of rules in a concrete framework, even though it has a ton of problems. It at least gives you a concrete target to shoot at. There are separate rules of Passive, Dative, Agent Deletion, Tag Formation and so on. Objecting that these are all separate unrelated rules and thus mere descriptions lacking explanatory form holds linguistics to an unrealistically high standard of idealization – not even physics as managed to reduce all laws to a single statement. If you can show us an example of a “more explanatory” theory that actually has a single rule that subsumes Passive, Dative, Agent Deletion, Tag Formation into one rule, or declarative-formation and interrogative-formation in one rule, then we might be able to address your desideratum of explanation.

Your explanation of your concept “explanation” seems to depend crucially on the validity of “construction” as a fact of grammar: that suggests then that you’re actually looking for an implementation of English syntax in Construction Grammar, or perhaps Relational Grammar.

Answer 2

The "word-star" grammar describes all the sentences of every human language with a single rule: S -> word*. The rule says that a sentence is a string of words. Of course, you need a lexicon, also.

Answer 3

In some way, this question just underscores the fundamental problem with 'syntax' theory. It takes an idealized notion of 'a correct sentence in a language' and tries to come up with formal rules for generating all possible sequences of lexemes in such a way that all correct possible sequences are generated by those rules and no incorrect possible sequences are. The notions of dependency and constituency are just ways of arranging those rules with respect to putative relationships among the words within a correct sentence. But even if they were successful in that (which they aren't) they wouldn't get around the fundamental problem of the consequence of the initial idealization. If you assume the fundamental unit of syntax to be sentence (or even clause), you are mostly limited to written language for your universe of sentences. But even then you have all those 'imperfectly' formed sentences or varying judgements on acceptability among native speakers as to the acceptability of those sentences. In spontaneous speech, you don't even have sentences.

So your next step is to posit an arbitrary distinction between competence and performance and ignore all the aspects of performance. But you then get the problem of bootstrapping your target set of sentences from this imperfect 'real' set of performed sentences, then rejecting them, and defining language only through the rules. Therefore, in a formal (constraint-based) theory of syntax, you can never account for the totality of the syntactic phenomena you encounter in the real world.

The construction grammar framework was explicitly designed to deal with this issue. But it thinks of syntax very differently, so you cannot think of it as a third alternative to dependency or constituency. It simply does not think of sentence or clause structure in terms of heads but rather abstract schemas into which words can fit. So instead of S --> NP VP you get something like The ___ Verbed ____ into a _____. These constructions are considered to be part of an inventory alongside traditional lexemes. This means that you have a lot of 'rules' that are difficult to abstract away into structures (like trees) that are directly translatable into algorithms. Instead, you have to model them as they are. You get a lot more linguistic and cognitive plausibility this way but not a 'grammar' framework that can be evaluated on the same criteria - ie. positing of just the right constraints to produce only acceptable strings (sentences).

Answer 4

Now that the question has been edited to clarify that it is really explanation you're interested in, I find that I have something to add to my previous answer.

What's an explanation? It tells you why something happens the way it does, when you didn't know that before you heard the explanation. Obviously, there is no known theory which explains all known syntactic phenomena. In fact, it's tough to find a syntactic theory that explains anything at all. But not impossible.

Consider the constraints on movement described by John Ross -- in particular the Coordinate Structure Constraint (CSC) and the Complex NP Constraint (CNPC). There is a theoretical explanation for these constraints.

Now, stop me if you've heard this one. I said an explanation tells you why something happens, when you didn't previously know why. So, do you know why there is a CSC or a CNPC? Does your syntactic theory, DG, CG, Minimalism, or whatever, tell you why? If so, read no further, because I can tell you nothing you didn't know already.

The reason for these two constraints (and others) is that there are no transformations. Note that although I've couched the matter rather theoretically, this is a factual matter. Speaker-hearers, by and large, find sentences that violate the Ross constraints to be unacceptable, and it's not obvious why.

We generally have a choice between describing movement constructions directly with phrase structure rules or appealing to a movement transformation. Gerald Gazdar exploited a notation from Categorial Grammar to show how we can describe constructions that seem to involve movement: we append to a phrase structure grammar a finite number of "slash categories", which represent constituents out of which something has been moved, and a finite number of phrase structure rules to describe the composition of such categories. The numbers of categories and phrase structure rules have to be finite, because this is a fundamental restriction on phrase structure grammar.

1. The CNPC. Suppose there were no CNPC, then to describe a relative clause construction, we'd need a category S/NP, sentence missing a NP, to describe the relative clause, and if the missing NP was inside another relative clause, the main relative clause would have to be of a new category S/NP/NP, and further, if the missing NP of the relative clause inside a relative clause was inside another relative clause, the main relative clause would have to be a S/NP/NP/NP (a sentence missing three NPs), and so on, ad infinitum. Thus, if there were no CNPC, there would have to be constructions which are impossible in phrase structure grammar (which can have only a finite number of categories). So the CNPC is shown to follow from general principles.
2. The CSC. There is an independently motivated constraint on coordinate structures that requires the constituents coordinated to be of the same category. But if there are no transformations, a constituent from which nothing has been extracted is never of the same category as the corresponding constituent from which something has been extracted. So, there must (appear to be) a CSC.
3. The across-the-board exception to the CSC. Two constituents which are otherwise the same but from which the same things have been extracted are of the same category. So it should be possible to remove something from both conjuncts of a coordinate construction, as it is. This part of the CSC is utterly mysterious in transformational grammar, but makes perfect sense in the corresponding account without transformations.