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...
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First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy...
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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...
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In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not...
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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...
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related uses in mathematics and formal logic: Predicate (mathematical logic) Propositional function Finitary relation, or n-ary predicate Boolean-valued...
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In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms,...
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Well-formed formula (redirect from Formula (mathematical logic))
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence...
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First-order logic -- First-order predicate -- First-order predicate calculus -- First-order resolution -- Fitch-style calculus -- Fluidic logic -- Fluidics...
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calculus Predicate (mathematical logic) Predicate logic Predicate variable Quantification Second-order predicate Sentence (mathematical logic) Universal...
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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...
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Atomic formula (redirect from Atom (logic))
formal expression that denotes an atomic formula. For predicate logic, the atoms are predicate symbols together with their arguments, each argument being...
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In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order quantification is limited to quantification...
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Universal quantification (redirect from All (logic))
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"...
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first-order logic. The term "higher-order logic" is commonly used to mean higher-order simple predicate logic. Here "simple" indicates that the underlying...
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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...
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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...
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the twelfth century with the advent of new logic, remaining dominant until the advent of predicate logic in the late nineteenth century. However, even...
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Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory...
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formal semantics. The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard...
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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...
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In mathematical logic, fixed-point logics are extensions of classical predicate logic that have been introduced to express recursion. Their development...
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In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of...
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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...
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used in mathematical logic and computer science. Mathematical induction in this extended sense is closely related to recursion. Mathematical induction...
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In mathematical logic, a first-order predicate is a predicate that takes only individual(s) constants or variables as argument(s). Compare second-order...
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Existential quantification (redirect from Mathematical existence)
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least...
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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...
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addresses the mathematical properties of formal systems of logic. However, it can also include attempts to use logic to analyze mathematical reasoning or...
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Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell...
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