Foundations

Question 1

What is a formal language?

Answer 1

It is a language where one can unambiguously decide if a sentence is grammatically correct.

Question 2

Why is the study of logic important?

Answer 2

It provides a foundation for all of mathematics and reasoning. In addition, formal checking of reasoning systems can avoid costly flaws.

Question 3

What are some examples of formal logic methods could have been applied to save money and lives?

Answer 3

Software bug in Therac-25, a radiation therapy machine, lead to the death of 6 patients.

Ariane 5 rocket failure in 1996 due to a software bug cost 370 million dollars.

Intel floating arithmetic bug in 1994 cost 475 million dollars.

So this stuff can matter. Big time.

Question 4

What are the two primary approaches to logic?

Answer 4

(1) model-theoretic approach

(2) proof-theoretic approach

Question 5

Are there many logics?

Answer 5

Yes there are many logics not just classical logic.

Question 6

Do logics have levels? If so, what levels?

Answer 6

Yes, multiple: propositional logic, first order, second order, etc…