First-Order Logic in Predicate Logic

Types of Logic

• First-order logic is considered more expressive than propositional logic.

Propositional Logic Limitations

• The assertion 'x > 1' is not a proposition in itself because it contains a variable (x) and a predicate (> 1), making it a statement that requires more context to be true or false.

First-Order Logic vs Propositional Logic

• First-order logic assumes the existence of objects and their properties, whereas propositional logic only deals with statements that can be true or false.

Predicates in First-Order Logic

• 'Brother-of', 'bigger-than', and 'part-of' are examples of predicates in first-order logic, which are used to describe properties and relationships between objects.

Limitations of Propositional Logic

• The argument 'All men are mortal. Socrates is a man. Then Socrates is mortal' cannot be expressed in propositional logic because it involves variables (men, Socrates) and predicates (mortal).

Constant Symbols in First-Order Logic

• A constant symbol in First-Order Logic is an example of a name or a label that represents a specific object, such as 'WU' or 'Socrates'.

Universal Quantifier

• The universal quantifier '∀' represents "for all" or "for every" in First-Order Logic, meaning that a statement is true for all possible values of a variable.

Representation in First-Order Logic

• The statement 'Everyone at WU is smart' can be represented in First-Order Logic using quantifiers as '∀x (WU(x) → Smart(x))', meaning "for all x, if x is at WU, then x is smart".

Existential Quantifier

• The existential quantifier '∃' indicates "there exists" or "there is at least one" in First-Order Logic, meaning that a statement is true for at least one value of a variable.

Nested Quantifiers

• The statement 'Siblinghood is a symmetric relationship' can be represented using nested quantifiers in First-Order Logic as '∀x ∀y (Sibling(x, y) → Sibling(y, x))', meaning "for all x and for all y, if x is a sibling of y, then y is a sibling of x".