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

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...

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

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...

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

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

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...

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...

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

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

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

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

semantics are a reformulation of Floyd–Hoare logic. Whereas Hoare logic is presented as a deductive system, predicate transformer semantics (either by weakest-preconditions...

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

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

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

logic Non-monotonic logic Ordered logic Paraconsistent logic Philosophical logic Predicate logic Propositional logic Provability logic Quantum logic Relevance...

second-order logic. This is because predicates such as "are shipmates", "are meeting together", "are surrounding a building" are not distributive. A predicate F...

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

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...

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

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

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...

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

first-order monadic predicate logic (Leopold Löwenheim 1915) Proof of the semantic completeness of first-order monadic predicate logic (Leopold Löwenheim...

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”...

propositional variables. Predicate logic can be represented as a vector space of the same type in which the axes represent the predicate letters S {\displaystyle...

algebra (logic) Boolean data type Boolean domain Boolean function Logical value Predicate variable Propositional logic Howson, Colin (1997). Logic with trees:...