Predicate Logic The limitation of propositional logic Is

Predicate Logic

The limitation of propositional logic Is not a proposition

Predicate Logic

More on Predicate Logic •

Example of Predicate Logic •

Quantifier • A predicate becomes a proposition when we assign it fixed values. • However, another way to make a predicate into a proposition is to quantify it. • Such quantification can be done with two quantifiers: the universal quantifier and the existential quantifier

Universal Quantifier •

Universal Quantifier – Example •

Universal Quantifier – Example 2 •

Existential Quantifier •

More on Existential Quantifier which can be read “there exists a unique” there is one and only one

Quantifier - Example •

Quantifier - Example 2 •

Negating Quantified Statements •

Statement All A are B Some A are not B Some A are B Equivalent Statement There are no A that are not B Not all A are B There exists at least one A that is a B Negation of Statement Some A are not B All A are B No A are B All A are not B Some A are B

Quantifier - Example 3 • All dogs are animals. • Some kids do not like video games. • Some video games are nonviolent. • No math courses are difficult

Entailment

Definition • A sentence A entails another sentence B if, whenever A is true, B must also be true A|=B

Entailment in Propositional Logic: Examples • 1 2 3 4 A T T F F B T F T F T T T F F F A∨ ¬A T T

Another Example •