Mmm Mmm Ambiguous Advertising (includes vagueness and a spelling error )

This is a screen shot from the website of one of my family's favorite pizza places.

Is the advertised special a [[large family] [deal]] ?

Or a [[large][family deal]] ?
If the advertised special is for a [[large family] [deal]] as the ad layout suggests, is it for a family that is large in number or a family whose members are large in size?

I'm pretty sure the advertisers meant the advertised special to be interpreted as a [[large][family deal]] because the special includes a large pizza and a large salad, but the word choice and the way the words are arranged on the two different lines make the deal both ambiguous and vague at the same time.

Also, no matter how "mmm, mmm good" their pizza is, I still don't like the extra "m" in the box about on-line ordering.

Would That Be an Example of Ambiguity or Vagueness?

The answer is both when talking about the word "triangle."
The word "triangle" is ambiguous when it is unclear on whether it is denoting the shape, the musical instrument or the drafting tool. The word "triangle" is vague when it is referencing the shape because it is indefinite about whether it denotes a scalene, isosceles, obtuse, right, acute or equilateral triangle.

Ambiguous words have more than one meaning, for example: the word "light" meaning "not heavy" and the word "light" meaning "not dark."

Vague words have more than one sense of the same meaning, for example: the word "child" is defined as "a young person" and that young person could be either male or female.

A test to help determine a word's ambiguity status is whether or not the word has two unrelated antonyms, for example: the word "hard" is ambiguous because it has the antonyms "soft" and "easy."

Crossword Puzzle Clues and Semantics

I have always been a huge fan of crossword puzzles and, in a round-about way, my love of crossword puzzles was partly responsible for my decision to study linguistics in graduate school. So naturally, I tend to semantically analyze crossword puzzle clues while working a puzzle. As a result, I believe that the relationship between crossword puzzles and semantics should be seen as reciprocal because working a puzzle not only calls on semantic knowledge, it also reinforces and adds to a person's semantic knowledge, whether consciously or not.

The role semantic knowledge plays in solving a crossword should become clear by looking at some of the common crossword puzzle clue categories and the semantic concepts with which they can be compared.

Traditional dictionary definitions = reference
Thesaurus = synonymy
Encyclopedic = reference
Names = reference
Opposites = antonymy
Puns and wordplay = vagueness and ambiguity, polysemy
“A kind of” = hyponymy
Indirect = vagueness and ambiguity

Pragmatics and Crossword Puzzles

Where crossword puzzles are concerned, pragmatics can be viewed as the ability of the solver to interpret correctly the meaning or sense the constructor had in mind when writing a clue. When a clue appears as a single word without other words to give it a context, the puzzle itself can be thought of as the context. Oftentimes, even a multi-word clue can leave open more than one interpretation of the meaning or sense of the clue and this is part of the art of writing clues.

A constructor can intentionally use a vague expression in a clue to challenge the solver by not giving an appropriate amount of information. Ambiguities, too, are used in a similar way because the possible alternative denotations provide the challenge. With homonyms, it is specifically homographs that pose a problem to solvers because in written language they can not be distinguished without context, whereas homophones can. Polysemes are similarly problematic as they too have the same spelling for different senses of a word.

A perfect example of how a constructor can creatively mislead a solver even with some contextual information would be the homographic clue; bank deposit. The answer could be cash if the referenced bank is a financial institute or silt if the referenced bank is a river bank. An example of misleading with a one-word clue using a polysemic word is the clue; hire. The answer could be engage or employ. With both examples each possible answer has the same number of letters and each of the answers would be acceptable for the clue. It is in instances such as these that a solver must also take into consideration answers from the crossing clues in the grid to help them choose the best response.