Week 5 - Semantics

Question 1

When is a formula satisfiable?

Answer 1

When there is one valuation that means the entire formula is true

Question 2

When is a formula valid?

Answer 2

When every valuation satisfies it.

Question 3

When is an argument semantically valid?

Answer 3

When every valuation that evaluates all of the premises to true, also evaluates the conclusion to true.

Question 4

How can you check if an argument is semantically valid using a truth table?

Answer 4

Any row when the conclusion is false, at least one of the premises is false.

Any row when the conclusion is true, at least one of the premises is true.