Predicate logic

Also know as first order logic. It Introduces quantifiers over non-logical objects.

The best way to understand this is with an example. The phrase: $\exists xP(x),$means “there is an $x$ with the property $P$”.

• The symbol '$P$' represents the property and is named a predicate.
• The symbol '$x$' is named a variable. It represents an arbitrary object within the domain of the theory considered. For example, if I use the logic to make statements about numbers, $x$ represents a number.

Predicate logic is an extension of Zeroth order logic needed to deal with non-logical objects.

Notes

• Predicates are not logical symbols (like e.g. $\vee$ and $\wedge$) because they don’t have a meaning independent of the language and its interpretation.
• Variables, like $x$, are sometimes lumped with logical symbols.

Zeroth order logic

• Logic of propositions
• Only deals with logical objects (propositions) and logical connectors
• Example: Socrates is a man