1.5.2 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 .

• 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.

• n-ary function. (definition)
• Definition:
• (1) A function with exactly n arguments.
• (2) A function which takes any number of arguments, or a variable number of arguments.

• (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.

It says that for all, so if applied to an x it says that all elements in x domain has this quality.

It says that for some, so if applied to an x it says that some elements in x domain has this quality.

It is a sequence of propositions.

It all all except the last propositions in an argument.

It is called a conclusion.

When the truth of all its premises implies that the conclusion it true.

Using rules of inference to reduce the length of the argument is a good idea.