Semantics

• Note: We can study grammar independently of meaning.

• Interpretation does not exactly apply to the sentence that you hear.

  • We can elide (add ellipsis) to certain parts of the sentence so that additional words are implied but not pronounced
  • Inversely, the Association with Focus (i.e., stressing different words in a sentence) shows that the interpretation of the sentence changes with how we articulate the sentence.
    • We invite a substitution on the stressed word and assert something by association.
    • Even if we focus on one word, we can invite multiple meanings (for example if focus on the word implies focus on the word alone or a phrase the word is a part of.)

• Compositionality — a hypothesis where once you specify the meanings of the parts of a sentence, you should have the meaning of the sentence.

• There are various meaning relations between words

  • Synonyms - words that mean the same thing.
  • Antonyms - words that mean the opposite thing.

• Intension - the function or procedure for determining the reference of a word / phrase (i.e., look at the thermostat)

• Extension - the value of the intension (i.e., the measurement in the thermostat)

• We have to be careful about substituting synonymous words / phrases. It has to be in line with whether or not the intension or extension is appropriate to use in the sentence.

Basic Relations §

• Entailment - entails if whenever is true, is true. (a.k.a. )
• Equivalence - and are equivalent if and entail each other (a.k.a. ).
• Contradiction - and contradict each other if each entails that the other is false (a.k.a. XOR is true.).
• Presupposition - has presupposition if is an implicit assumption required for to be true or to be false. Crucially, either or will hold but it only makes sense to talk about either if is true.
  • Accommodating presuppositions means that in discourse, people will take up their interlocutor’s presuppositions unconsciously.
• Implicature - something that is generally inferred from hearing a sentence, even if this inference is not true.

Quantifiers §

• Quantifications can be used to introduce additional meanings for a particular noun phrase (e.g. universal quantifiers, existential quantifiers, and their negations)

• Some quantifiers can be both true and false (e.g., using existential quantifiers.)

• Some quantifiers do not follow the law of excluded middle.

• Natural language quantifiers are conservative which means for a phrase involving sets and , we can replace with and get the same meaning.

• Having multiple quantifiers in a sentence can introduce ambiguities. One possible explanation of this is quantifier raising (QR) where the quantifiers are moved around the syntax tree, even though they are not moved around in the sentence (at least in English.)

  • It appears QR is limited by how quantifiers cannot escape the clauses they are in.
  • QR is subject to parallelism. That is, if one clause in the sentence has QR, then the other clause must as well.

• Downward Entailment: The following property holds for a quantifier . If ” are "" is true, and , then ” are ” is true. Examples of such a are “No”, “Few”

• Upward Entailment: The following property holds for a quantifier . If ” are ” is true, and , then ” are ” is true. An example of such a is “All”, “Every”

• Some quantifiers are neither upward nor downward entailing (i.e., “Exactly 10 of”).

• Negative Polarity Items - Linguistic items that appear only in a sentence that connotes negation. These tend to avoid upward entailing contexts.

• Positive Polarity Item - Linguistic items that appear only in a sentence that connotes affirmation. These tend to avoid downward entailing contexts.

Binding Theory §

• Given noun phrase and constituent , any noun in cannot refer to any noun dominated by

• More generally in Binding Theory we have the following principles

  • We say that binds if c-commands and corefers with . Otherwise is free.
  • Pronouns cannot corefer with something (i.e., refer to anything in the same clause / sentence). Thus, pronouns must be free within the clause.
  • Anaphors must refer to something in the same sentence. Thus, anaphors must be bound within the clause.
  • R-expressions (things that are neither pronouns or anaphors) must be free.

• Binding Theory is subject to reconstruction, that is, we consider the parse tree before any movements were performed.

• Binding Theory also reveals the presence of invisible pronouns

Copy Theory §

• Copy Theory posits that a movement operation on the parse tree is simply a merge operation with an item in the lexicon, potentially even a copy of one of the words in the sentence.
• Because this may introduce redundancies, we have rules to govern when to pronounce certain words that have been “moved”
• Thus, reconstruction really is just choosing, out of all instances of copies of the word, where to place the word.

Links §

• Linguistics