Example with a quantifier for the ''Jane Eyre'' context
Task 6
1. Write down one formula with a quantifier.
2. For each individual in your universe, indicate whether the restrictor and the scope are true for that individual.
3. Given your results from (b), is the formula true in your model?
4. In which way would your model have to be different to make the formula false (or, in case the formula is false: to make it true in your model)?
1. Formula with a quantifier
Corresponding English sentence: Mr Rochester is every women's husband.
Formula: ∀x (woman(x) : husband-of(edward,x))
Note: The interpretation of the relation husband-of is as given above. The interpretation of the predicate woman is the same as that of the predicate female above.
2. Evaluation of restrictor and scope by individual
| U | woman(x) | husband-of(edward,x) |
| JaneEyre | 1 | 1 |
| BerthaMason | 1 | 1 |
| MrRochester | 0 | 0 |
| StJohn | 0 | 0 |
3. Truth of the formula
For every individual for which the restrictor is true, the scope is true as well. Therefore the entire formula is true in our model.
4. Change the model
The formula would be false, if we included another female individual from the novel. We could, for example, introduce another female individual, the individual MrsFairfax who is Mrs. Alice Fairfax, Mr Rochester's housekeeper. In this case, the restrictor is true for MrsFairfax, but the scope is not.
Back to the assignment sheet for Chapter 2.