AMBIGUITY

What is the picture? a saxophone player or a woman?
It is an ambiguous picture.

         Ambiguity is a type of uncertainty of meaning in which several interpretations are plausible. It is thus an attribute of any idea or statement whose intended meaning cannot be definitively resolved according to a rule or process with a finite number of steps. (The ambi- part of the name reflects an idea of "two" as in two meanings.)        The concept of ambiguity is generally contrasted with vagueness. In ambiguity, specific and distinct interpretations are permitted (although some may not be immediately apparent), whereas with information that is vague, it is difficult to form any interpretation at the desired level of specificity. Context may play a role in resolving ambiguity. For example, the same piece of information may be ambiguous in one context and unambiguous in another.
There are three types of ambiguity:1. Semantic Ambiguity (Usually an Idiom)
       
The notions of `meaning' and `sense' just discussed are the starting point for the semantic account of the notion of ambiguity and its relation with vagueness developed by Pinkal ((1985), translated as (Pinkal , 1995)). Pinkal introduces the notion of indefiniteness to subsume both ambiguity and vagueness. 
De nition 2.1 A sentence is semantically indefinite if and only if in certain situations, despite su cient knowledge of the relevant facts, neither \true" nor \false" can be clearly assigned as its truth value 
De nition 2.2 Expression in context c can be precisified to s if and only if (i) s is a sense that can assume according to its meaning; and (ii) s is more precise than the sense of inc.   
for example: 
Even after the syntax and the meanings of the individual words have been resolved, there are two ways of reading the sentence. "Lucy owns a parrot that is larger than a cat", "a parrot" is extenstensionally quantified, "a cat" is either universally quantified or means "typical cats." Other examples: "The dog is chasing the cat." vs. "The dog has been domesticated for 10,000 years." In the first sentence, "The dog" means to a particular dog; in the second, it means the species "dog". 
"John and Mary are married." (To each other? or separately?) Compare "John and Mary got engaged last month. Now, John and Mary are married." vs. "Which of the men at this party are single? John and Jim are married; the rest are all available."
"John kissed his wife, and so did Sam". (Sam kissed John's wife or his own?)
Compare "Amy's car", "Amy's husband", "Amy's greatest fear", "Michaelangelo's David" etc. 
2. Structural or Syntactic ambiguity (When a headline may have more than one alternative structure and ambivalent structure)  
         Although the number of logical form permutations that one can obtain for a particular sentence by, e.g., considering all the permutations of its operators may be rather large, constraints of a syntactic and/or semantic nature drastically reduce this number.  for example:
This ambiguous sentence represented two alternative ambivalent structures:
- After 18 years they didn’t meet, and finally they meet in the check in counter. or
- After 18 years in the check in counter, they just reunited.

3. Lexical Ambiguity (A word or  phrase that has more than one meaning while it stands in a sentence). 
        Lexical ambiguity is the one case of ambiguity for which a `generate and test' strategy may well be compatible with the psychological results, therefore the one for which the need for underspeci ed representations is less clear. for example: 
This sentence use homonym and homophone to create a complex sentence structure. It is very ambiguous in the class of word. Rose can be a noun (the name of person and a name of flower). Meanwhile rose can be a verb (the past form of rise (grow or stood). 
The analyzing of the sentence is: 
Rose (a girl name) rose (the past form of rise “stood”) to put a rose (The name of flower) rose (grown) on her rows of roses (Rose Flowers)

          It can be read in another way:
         The girl named Rose stood to put a grown rose flower on her rows of roses. 


Source: https://en.wikipedia.org/wiki/Ambiguity
            http://cswww.essex.ac.uk/poesio/publications/vandeemter_book.pdf