Structural ambiguity occurs when the grammar can assign more than one parse
to a sentence. Two common kinds of ambiguity are attachment ambiguity and coordination ambiguity. A sentence has an attachment ambiguity if a particular constituent can be attached to the parse tree at more than one place. For instance, in the following example the gerundive-VP flying to Paris can be part of a gerundive sentence whose subject is the Eiffel Tower or it can be an adjunct modifying the VP headed by saw:
We saw the Eiffel Tower flying to Paris.
In coordination ambiguity phrases can be conjoined by a conjunction like and. For example, the phrase old men and women can be bracketed as [old [men and women]], referring to old men and old women, or as [old men] and [women], in
which case it is only the men who are old.
The fact that there are many grammatically correct but semantically unreasonable parses for naturally occurring sentences is an irksome problem that affects all parsers. Fortunately, the CKY algorithm is designed to efficiently handle structural ambiguities.

Ambiguity 

Instead of providing numerosity of all possible parsing trees, span-based neural constituency parsing only offer the best parsing tree. Its intuition is to train a neural classifier to assign a score to each constituent and find out the best-scoring parse tree based on those assigned scores.


Span-Based Neural Constituency Parsing

The CKY parsing allows each non-terminal paired with entires from which it was derived and multiple versions of the same non-terminal to be entered into the same table. It can return every possible parse for a sentence, which may not be very helpful.

 CKY Parsing

Also referred to as probabilistic parsing, this is when a probabilistic component is added to constituency parsing. Probabilistic Parsers compute the probability of each interpretation of a sentence and choose the most probable interpretation.

Statistical Constituency Parsing

Many language processing tasks do not require complex, complete parse trees for all inputs. In such cases, a partial parse, or shallow parse, of input sentences may be sufficient, where not all possible information are extracted from a text.

Partial Parsing in NLP

Constituency Parsing focuses on constituency structures, those assigned by context-free grammars. In order to know which parse tree is the right one, we need to augment CKY with scores for each possible constituent. 

University of Michigan - Ann Arbor

Parsing, syntax analysis, or syntactic analysis is the process of analyzing a string of symbols, either in natural language, computer languages or data structures, conforming to the rules of a formal grammar.



Within computational linguistics the term is used to refer to the formal analysis by a computer of a sentence or other string of words into its constituents, resulting in a parse tree showing their syntactic relation to each other, which may also contain semantic and other information (p-values). Some parsing algorithms may generate a parse forest or list of parse trees for a syntactically ambiguous input.



Simply speaking, parsing in NLP is the process of determining the syntactic structure of a text by analyzing its constituent words based on an underlying grammar (of the language).

Parsing

Syntactic constituency is the idea that groups of words can act as single units, which are called constituents

Constituency

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

Research papers, articles and examples about parsing in NLP

NLP Parsing References

A context-free grammar consists of a set of rules or productions and a lexicon of words and symbols.  Each of those rules expresses the ways that symbols of the language can be grouped and ordered together.
For example, one rule for noun phrase, like "the flight", is that a noun phrase can be composed of a determiner and a nominal.
$$ NP --> Det \quad Nominal$$



Context-Free Grammars


A parse tree is one way to represent the syntactic structure of a string according to some context-free grammar. In parsing trees, each sentence starts with the start symbol $$S$$.


Parse Tree

The syntactic structure can also be expressed by bracketed notation, which is more compact than the parse tree.
$$ [\mathit{S}[NP [Pro\,\textrm{I}]] [VP [V \,\textrm{perfer}] [NP [Det \,\textrm{a}] [Nom [N \,\textrm{morning}] [Nom [N \,\textrm{flight}]]]]]]$$



Bracketed Notation


Categorical grammar is an early lexicalized grammar model which consists of three major elements: a set of categories, a lexicon that associates words with categories, and a set of rules that govern how categories combine in context.

Categorical Grammar

Unfortunately, the basic categorial approach does not give us any more expressive power than we had with traditional CFG rules; it just moves information from the grammar to the lexicon. To move beyond these limitations CCG is a modern extension of categorical grammar and includes operations that operate over functions.

Combinatory Categorical Grammar (CCG)

Constituency Parsing

Dependency Parsing is fundamentally based on the dependency grammars in terms of grammar formalisms. In these formalisms, phrasal constituents and phrase-structure rules do not play a direct role as Constituent Parsing. Instead, the syntactic structure of a sentence is describe solely in terms of the words in a sentence and an associated set of directed binary grammatical relations that hold among the words.

Dependency Parsing

Given a sequence of sentences, automatically determine the coherence relations between them.

Discourse Structure Parsing

The Penn Discourse TreeBank (PDTB) is a second commonly used dataset that embodies model of coherence relations.

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