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...

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

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...

is not a sentence of first-order logic, but this is a legitimate sentence of second-order logic. Here, P is a predicate variable and is semantically a set...

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

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

In mathematical logic, predicate functor logic (PFL) is one of several ways to express first-order logic (also known as predicate logic) by purely algebraic...

In formal logic and related branches of mathematics, a functional predicate, or function symbol, is a logical symbol that may be applied to an object...

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

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

sentences in predicate logic, which may contain quantifiers—a feature absent from sentences of propositional logic. Indeed, in propositional logic, there is...

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

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 predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least...

some academic contexts, syllogism has been superseded by first-order predicate logic following the work of Gottlob Frege, in particular his Begriffsschrift...

formal expression that denotes an atomic formula. For predicate logic, the atoms are predicate symbols together with their arguments, each argument being...

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

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...

true, but means something different. These problems are addressed in predicate logic by using a variable for the problematic term, so that “X is a philosopher”...

inference – modus ponens, for propositional logics – or two – with generalisation, to handle predicate logics, as well – and several infinite axiom schemas...

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...

impossible the kind of subject–predicate analysis that governed Aristotle's account, although there is a renewed interest in term logic, attempting to find calculi...

equivalent either. These sections concern what is now known as predicate logic, and predicate logic with identity (equality). NB: As a result of criticism and...

clearly as does thing itself, a word always classified as a noun". In predicate logic, what is described in layman's terms as "something" can more specifically...

notation).[citation needed] In traditional logic, the process of switching the subject term with the predicate term is called conversion. For example, going...

significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is commonly the case, including...

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

traces back to Aristotelian logic. A predicate is seen as a property that a subject has or is characterized by. A predicate is therefore an expression...

formal logic: Predicate (mathematical logic) Propositional function Finitary relation, or n-ary predicate Boolean-valued function Syntactic predicate, in...

for example sentential calculus and predicate calculus, partly with the purpose of revealing the underlying logic of natural-language statements, the...