PHIL222 Lecture 8: Quantification and Syntax of MPL

Flashcards covering key vocabulary and concepts related to quantification and syntax in Mathematical Predicate Logic.

Universal Quantifier

A symbol (∀) that indicates that a statement applies to all elements in a specific domain.

Existential Quantifier

A symbol (∃) that indicates that there exists at least one element in a specific domain that satisfies a given property.

Bound Variable

A variable that is either directly involved in a quantifier or is within the scope of a quantifier.

Free Variable

A variable in a well-formed formula (wff) that is not bound by a quantifier.

Closed Formula

A well-formed formula with no free variables, indicating that the statement can be evaluated as true or false.

Open Formula

A well-formed formula that contains one or more free variables, and thus does not have a definite truth value.

Restricted Quantification

Quantification that applies only to a subset of a larger domain, rather than to all elements in that domain.

Well-formed formula (wff)

A syntactically correct expression in mathematical logic, built from predicates, quantifiers, and terms.

Predicate

A symbol that represents a property or relation that can be true or false depending on the arguments.

Atomic Formula

The most basic type of well-formed formula, consisting of a predicate and its arguments.

Quantifier Scope

The part of a well-formed formula that is affected by a quantifier, determined by the position of the quantifier in relation to other expressions.

Syntax of MPL

The formal structure and rules governing the construction of expressions in Mathematical Predicate Logic.