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, quantificational logic—is a collection of formal systems used in mathematics, philosophy...

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

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

In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms,...

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 -- First-order predicate -- First-order predicate calculus -- First-order resolution -- Fitch-style calculus -- Fluidic logic -- Fluidics...

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...

calculus Predicate (mathematical logic) Predicate logic Predicate variable Quantification Second-order predicate Sentence (mathematical logic) Universal...

In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order quantification is limited to quantification...

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

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

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, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", or "for any"...

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...

functions from them to some predefined mathematical domains: an interpretation of first-order predicate logic is given by a mapping from terms to a universe...

models of second-order logic. They do hold however for Henkin models.: xi  Predicate logic was introduced to the mathematical community by C. S. Peirce...

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory...

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

quantification over predicates (higher-order logic) didn't meet the requirements to be a logic, saying that it was "set theory in disguise". Classical logic is the...

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

In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of...

used in mathematical logic and computer science. Mathematical induction in this extended sense is closely related to recursion. Mathematical induction...

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

In mathematical logic, a first-order predicate is a predicate that takes only individual(s) constants or variables as argument(s). Compare second-order...

Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell...

addresses the mathematical properties of formal systems of logic. However, it can also include attempts to use logic to analyze mathematical reasoning or...

is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and...