The extension of a predicate – a truth-valued function – is the set of tuples of values that, used as arguments, satisfy the predicate. Such a set of tuples...

In logic, a predicate is a symbol that represents a property or a relation. For instance, in the first-order formula P ( a ) {\displaystyle P(a)} , the...

formal semantics. The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard...

First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics,...

intensions of an object Extension (predicate logic) – Set of tuples in mathematical logic that satisfy a predicate Extension (semantics) – In the context...

the twelfth century with the advent of new logic, remaining dominant until the advent of predicate logic in the late nineteenth century. However, even...

In mathematical logic, fixed-point logics are extensions of classical predicate logic that have been introduced to express recursion. Their development...

as propositional and predicate logic. There are several ways in which this is commonly the case, including by way of extensions, deviations, and variations...

domain Extension (predicate logic) First-order logic First-order predicate Formation rule Free variables and bound variables Generalization (logic) Monadic...

In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not...

6, 8..., -2, -4, -6, -8..." In logic, the extension of a predicate is the set of all things for which the predicate is true. The logical term was introduced...

In mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can...

variables is Quine's predicate functor logic. While the expressive power of combinatory logic typically exceeds that of first-order logic, the expressive power...

cardinal Extension (model theory) Extension (proof theory) Extension (predicate logic), the set of tuples of values that satisfy the predicate Extension (semantics)...

exists an x" proposition, one needs to show that the predicate is false for all x. In classical logic, every formula is logically equivalent to a formula...

In logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic in which all relation symbols[clarification...

In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic...

structure of propositions. Basic propositions in first-order logic consist of a predicate, symbolized with uppercase letters like P {\displaystyle P} and...

negation of the subject and predicate, and is valid only for the type "A" and type "O" propositions of Aristotelian logic, while it is conditionally valid...

first-order logic. The term "higher-order logic" is commonly used to mean higher-order simple predicate logic. Here "simple" indicates that the underlying...

while still retaining the ability to talk about the extensions of a predicate. Thus, the plural logic comprehension schema ∃ x ¯ . ∀ y . y ≺ x ¯ ↔ F ( y...

Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe...

In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands...

least one other predicate with two or more arguments is not decidable. Logical systems extending first-order logic, such as second-order logic and type theory...

mathematics, logicism is a programme comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some...

higher-order logic, such as predicate variables. Such languages include the Prolog extensions HiLog and λProlog. Basing logic programming within linear logic has...

In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence...

Second-order logic allows quantification over predicates. However, MSO is the fragment in which second-order quantification is limited to monadic predicates (predicates...

propositions. First-order logic also takes the internal parts of propositions into account, like predicates and quantifiers. Extended logics accept the basic intuitions...

classical predicate logic just as predicate logic is a generalization of Aristotelian logic. On this view, classical predicate logic introduces predicates with...