11.1.1 Anaphoric Pronouns

Motivation of discourse phenomena: anaphoric pronouns.

Pronouns are words that refer to objects in the text or situation in which they are uttered. We will focus on anaphoric pronoun s (pronouns that refer back to textual antecedents) and will mainly consider the personal pronouns ``he'', ``she'' and ``it''. Let's look at the following discourse with an anaphoric pronoun:

``A woman walks. She smokes.''

This discourse consists of two sentences. The second sentence contains the pronoun ``she'' which refers to the noun phrase ``a woman'' introduced by the first sentence. Let's try to translate this sentence into first-order logic, and let's try to do this in a systematic way. Recall from Chapter 1 that a sensible formula for the first sentence would be:

But what would be an appropriate first-order logic formula for the second sentence? One way to proceed is to translate the pronoun ``she'' as a free variable:

Now we can put together the translations of the two sentences together and get the following first-order formula for the entire discourse:

This formula is true in a model where there is an individual that has the properties of being a woman, walking, and smoking, and therefore correctly describes the meaning of our example discourse.

However, note that some mysterious operations took hold of the existential quantifier when we put the single translations of the two sentences together. After analysing the first sentence, the scope of the existential quantifier was restricted to . But its scope expanded after integrating the second sentence in order to include . In other words, we didn't construct this representation in a systematic way.