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Difference between First-order logic and Propositional variable

First-order logic vs. Propositional variable

First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. In mathematical logic, a propositional variable (also called a sentence letter, sentential variable, or sentential letter) is an input variable (that can either be true or false) of a truth function.

Atomic formula

In mathematical logic, an atomic formula (also known as an atom or a prime formula) is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformulas.

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Domain of discourse

In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range.

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Higher-order logic

In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics.

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Latin script

The Latin script, also known as the Roman script, is a writing system based on the letters of the classical Latin alphabet, derived from a form of the Greek alphabet which was in use in the ancient Greek city of Cumae in Magna Graecia.

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Logical conjunction

In logic, mathematics and linguistics, and (\wedge) is the truth-functional operator of conjunction or logical conjunction.

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Logical connective

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant.

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Negation

In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P to another proposition "not P", standing for "P is not true", written \neg P, \mathord P or \overline.

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Predicate variable

In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not been specifically assigned any particular relation (or meaning).

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Propositional calculus

The propositional calculus is a branch of logic.

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Quantifier (logic)

In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula.

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Truth value

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (true or false).

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