What is the difference of propositional logic and predicate logic?
Just says some statements can not be expressed in propositional logic. Propositions needs to talk in absolute values, true or false, and predicate can express quantification such as "some" "all " etc .
What parts go into the statement
(x is greater then 3) = P(x)
- P() = is greater then 3 , x = variable
- P(x) = Value of propositional function,T/F, of P at x.
- Only when x gets an assigned value "P(x)" becomes a proposition with a truth value.
What is an n-ary function?
- n-ary function. (definition)
- (1) A function with exactly n arguments.
- (2) A function which takes any number of arguments, or a variable number of arguments.
What is P(x1,x2,xn) called? two names
- (1)Propositional function P at n
- (2) N-ary predicate
When the variables are assigned values the statement becomes a proposition with a certain truth value.
What is the universal quantifier?
It says that for all, so if applied to an x it says that all elements in x domain has this quality.
What is the existential qualifier?
It says that for some, so if applied to an x it says that some elements in x domain has this quality.
What is an "argument" in logic?
It is a sequence of propositions.
What is a "permises" in Logic?
It all all except the last propositions in an argument.
What is the final proposition in an argument called?
It is called a conclusion.
When is an argument valid?
When the truth of all its premises implies that the conclusion it true.
What is a good way to show if an argument is valid if the argument is long?
Using rules of inference to reduce the length of the argument is a good idea.