80-110 The Nature of Mathematical Reasoning

Thursday, April 12 2001

Quiz 9

Name: _______________________________

1. What is the meaning of the following: "Gamma |= S", where Gamma is a set of propositional formulas, and S a propositional formula.

2. It means "Gamma entails S", i.e., when all the formulas in Gamma are true, also S is true. (Lecture).

3. What is the difference between propositional logic and predicate logic?

4. Predicate logic is propositional logic plus predicates and quantifiers, (Lecture).

5. What does the sentence "there exits x forall y ( x <= y)" mean, if the domain of the bound variables are the natural numbers and "<=" stands for "is less or equal than"? Is the sentence true or false?

6. It means that there is a number x, such that all numbers (including itself) is less or equal than it. This is true, since 0 is such a number. (Lecture).

7. Name one non-classical logic.

8. Intuitionistic, constructive, modal, fuzzy, linear... (Lecture).

9. What does a recursive definition consist of?

10. 1. Base clause(s).
2. Recursive clause(s).
3. Final clause. (Lecture).