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Type of logical system
First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a type of formal system used in mathematics, philosophy
First-order_logic
Symbol representing a property or relation in logic
In logic, a predicate is a non-logical symbol that represents a property or a relation, though, formally, does not need to represent anything at all. For
Predicate_(logic)
Algebraization of first-order logic
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
Predicate_functor_logic
Form of logic that allows quantification over predicates
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
Second-order_logic
Approach to logic
the twelfth century with the advent of new logic, remaining dominant until the advent of predicate logic in the late nineteenth century. However, even
Term_logic
Assignment of meaning to the symbols of a formal language
formal semantics. The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard
Interpretation_(logic)
Fragment of first-order logic
In logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic (also called predicate calculus)
Monadic_predicate_calculus
Formal system of logic
first-order logic. The term "higher-order logic" is commonly used to mean higher-order simple predicate logic. Here, "simple" indicates that the underlying
Higher-order_logic
Syntactically correct logical formula
In mathematical logic, propositional logic, and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence
Well-formed_formula
System of formal deduction in logic
inference – modus ponens, for propositional logics – or two – with generalisation, to handle predicate logics, as well – and several infinite axiom schemas
Hilbert_system
Set of tuples in mathematical logic that satisfy a predicate
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
Extension_(predicate_logic)
In logic, a statement which is always true
sentences in predicate logic, which may contain quantifiers—a feature absent from sentences of propositional logic. Indeed, in propositional logic, there is
Tautology_(logic)
Formal study of linguistic meaning
and predicate logic are formal systems used to analyze the semantic structure of sentences. They introduce concepts like singular terms, predicates, quantifiers
Formal semantics (natural language)
Formal_semantics_(natural_language)
Method of deriving conclusions
First-order logic extends propositional logic by analyzing how the internal structure of propositions, like names and predicates, influences reasoning. Other logical
Rule_of_inference
Type of mathematical variable
In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not
Predicate_variable
Mathematical use of "there exists"
In predicate logic, an existential quantification is a type of quantifier which asserts the existence of an object with a given property. It is usually
Existential_quantification
Logical formalism using combinators instead of variables
variables is Quine's predicate functor logic. While the expressive power of combinatory logic typically exceeds that of first-order logic, the expressive power
Combinatory_logic
Translation of a text into a logical system
\Box } ) not found in regular predicate logic. One way to translate them is to introduce new predicates, such as the predicate R, which indicates that one
Logic_translation
Overview of and topical guide to logic
logic Non-monotonic logic Ordered logic Paraconsistent logic Philosophical logic Predicate logic Propositional logic Provability logic Quantum logic Relevance
Outline_of_logic
Mathematical logic concept
formal expression that denotes an atomic formula. For predicate logic, the atoms are predicate symbols together with their arguments, each argument being
Atomic_formula
Type of logical argument that applies deductive reasoning
some academic contexts, syllogism has been superseded by first-order predicate logic following the work of Gottlob Frege, in particular his Begriffsschrift
Syllogism
Form of second-order logic
elements for which the predicate is true). Monadic second-order logic is expressively equivalent to plural logic. Monadic second-order logic comes in two variants
Monadic_second-order_logic
Mathematical use of "for all" and "there exists"
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
Quantifier_(logic)
Topics referred to by the same term
and formal logic: Predicate (logic) Propositional function Finitary relation, or n-ary predicate Boolean-valued function Syntactic predicate, in formal
Predicate
Symbol representing a mathematical concept
untyped logic, there is an identity predicate id that satisfies id(X) = X for all X. In typed logic, given any type T, there is an identity predicate idT
Function_symbol
Study of correct reasoning
propositions. First-order logic also takes the internal parts of propositions into account, like predicates and quantifiers. Extended logics accept the basic intuitions
Logic
Subject and predicate in sentences
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
Predicate_(grammar)
Concept in mathematical logic
notation).[citation needed] In traditional logic, the process of switching the subject term with the predicate term is called conversion. For example, going
Converse_(logic)
Being present, not nothing
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
Something_(concept)
In mathematical logic, a well-formed formula with no free variables
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
Sentence_(mathematical_logic)
3-volume treatise on mathematics, 1910–1913
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
Principia_Mathematica
Study of the semantics, or interpretations, of formal and natural languages
perform the kind of subject–predicate analysis in Aristotle's logic. Term logic is an attempt to modernize Aristotle's logic: find deductive systems in
Semantics_(logic)
Formal systems of logic that significantly differ from standard logical systems
significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is commonly the case, including
Non-classical_logic
Mathematical logic concept
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
Contraposition
Logical formulation of recursion
In mathematical logic, fixed-point logics are extensions of classical predicate logic that have been introduced to express recursion. Their development
Fixed-point_logic
Branch of logic
the table below. Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers. However
Propositional_logic
Whether a decision problem has an effective method to derive the answer
one other predicate symbol with two or more arguments is not decidable. Logical systems extending first-order logic, such as second-order logic and type
Decidability_(logic)
Approach to predicate logic
Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe
Intensional_logic
Programming paradigm based on formal logic
condition, where the predicate = is defined by the clause X = X : sibling(X, Y) :- parent_child(Z, X), parent_child(Z, Y), not(X = Y). Logic programming languages
Logic_programming
Mathematical use of "for all"
It expresses that a predicate can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation
Universal_quantification
Application of logical methods to philosophical problems
classical predicate logic just as predicate logic is a generalization of Aristotelian logic. On this view, classical predicate logic introduces predicates with
Philosophical_logic
Software for solving satisfiability problems
applications are extended static checking, test case generation, and predicate abstraction.[citation needed] Z3 was open sourced in the beginning of
Z3_Theorem_Prover
millennia. The Stoics, especially Chrysippus, began the development of predicate logic. Christian and Islamic philosophers such as Boethius (died 524), Avicenna
History_of_logic
Study of the scope and nature of logic
of logic. Whether this thesis is correct depends on how the term "logic" is understood. If "logic" only refers to the axioms of first-order predicate logic
Philosophy_of_logic
Study of the properties of logical systems
propositional logic (Emil Post 1920), Consistency of first-order monadic predicate logic (Leopold Löwenheim 1915) Consistency of first-order predicate logic (David
Metalogic
Sentence that resists simple formalization
problem that the logical translations had. Dynamic Predicate Logic models pronouns as first-order logic variables, but allows quantifiers in a formula to
Donkey_sentence
Rules used for constructing, or transforming the symbols and words of a language
propositional logic and first-order predicate logic are semantically complete, but not syntactically complete (for example the propositional logic statement
Syntax_(logic)
Variable that can either be true or false
Boolean algebra (logic) Boolean data type Boolean domain Boolean function Logical value Predicate variable Howson, Colin (1997). Logic with trees: an introduction
Propositional_variable
System for representing and reasoning about time
{\displaystyle a^{*}} is a one-place predicate defined by x ↦ V ( a , x ) {\displaystyle x\mapsto V(a,x)} . Temporal logic has two kinds of operators: logical
Temporal_logic
Rule of inference in predicate logic
In predicate logic, universal instantiation (UI; also called universal specification or universal elimination,[citation needed] and sometimes confused
Universal_instantiation
Inference rule in logic, proof theory, and automated theorem proving
as p {\displaystyle p} due to its syntactic form. For first-order predicate logic, Murray's rule is generalized to allow distinct, but unifiable, subformulas
Resolution_(logic)
Term in logic
for example sentential calculus and predicate calculus, partly with the purpose of revealing the underlying logic of natural-language statements, the
Atomic_sentence
Various systems of symbolic logic
logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by
Intuitionistic_logic
Metatheorem in mathematical logic
⊢ A → B {\displaystyle \vdash A\to B} . The deduction theorem for predicate logic is similar, but comes with some extra constraints (that would for example
Deduction_theorem
Rule defining the correct structure of expressions in formal grammar
logic and α as a variable then we can take ( ∀ {\displaystyle \forall } α)Φ and ( ∃ {\displaystyle \exists } α)Φ each to be formulas of our predicate
Formation_rule
Form of conditionals in computer programming
with a predicate (the word here used similarly to its usage in predicate logic) and that the instruction will only be executed if the predicate is true
Predication (computer architecture)
Predication_(computer_architecture)
Mathematical theory
second-order logic. This is because predicates such as "are shipmates", "are meeting together", "are surrounding a building" are not distributive. A predicate F
Plural_quantification
Apparent logical paradox
drinker's principle, or the drinking principle) is a theorem of classical predicate logic that can be stated as "There is someone in the pub such that, if he
Drinker_paradox
Reformulation of Floyd-Hoare logic
semantics are a reformulation of Floyd–Hoare logic. Whereas Hoare logic is presented as a deductive system, predicate transformer semantics (either by weakest-preconditions
Predicate transformer semantics
Predicate_transformer_semantics
True when either but not both inputs are true
(conjunction) and ∨ {\displaystyle \lor } (disjunction) are very useful in logic systems, they fail a more generalizable structure in the following way:
Exclusive_or
Range of application for a quantifier or connective in a logical formula
which may stand for symbols in a formal language for propositional or predicate logic. In particular, ϕ {\displaystyle \phi } and ψ {\displaystyle \psi }
Scope_(logic)
consequent. anti-extension In set theory and logic, the complement of the extension of a concept or predicate, consisting of all objects that do not fall
Glossary_of_logic
Logical connective AND
In logic, mathematics and linguistics, and ( ∧ {\displaystyle \wedge } ) is the truth-functional operator of conjunction or logical conjunction. The logical
Logical_conjunction
System including an indeterminate value
represent predicates that are "undecidable by [any] algorithms whether true or false" As with bivalent logic, truth values in ternary logic may be represented
Three-valued_logic
Logical operation
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P {\displaystyle P} to another proposition
Negation
Characteristic of some logical systems
propositional logic and first-order predicate logic are semantically complete, but not syntactically complete (for example, the propositional logic statement
Completeness_(logic)
Constructed human language based on predicate logic
translated in some of its parts into predicate logic. There are also analogies between Lojban and combinatory logic. There have been proposals to use Lojban
Lojban
In scholastic logic, predicable is a term applied to a classification of the possible relations in which a predicate may stand to its subject. It is not
Predicable
Testing device for logical soundness
in natural language, but it can be formalized in many-sorted predicate logic or modal logic; such a formalisation is called a "T-theory."[citation needed]
T-schema
Rule of inference in predicate logic
In predicate logic, existential generalization (also known as existential introduction, ∃I) is a valid rule of inference that allows one to move from
Existential_generalization
Rule of inference in predicate logic
In predicate logic, existential instantiation (also called existential elimination) is a rule of inference which says that, given a formula of the form
Existential_instantiation
Subfield of mathematics
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory
Mathematical_logic
Topics referred to by the same term
Law of logic may refer to: Basic laws of Propositional Logic or First Order Predicate Logic Rules of inference, which dictate the valid use of inferential
Laws_of_logic
Type of diagrammatic notation for propositional logic
found the algebraic notation (i.e. symbolic notation) of logic, especially that of predicate logic, which was still very new during his lifetime and which
Existential_graph
Mathematical model for deduction or proof systems
arithmetic. Early logic systems includes Indian logic of Pāṇini, syllogistic logic of Aristotle, propositional logic of Stoicism, and Chinese logic of Gongsun
Formal_system
Sequence of words formed by specific rules
In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet".
Formal_language
Fifth letter of the Latin alphabet
electric charge carried by a single proton). ∃: existential quantifier in predicate logic. It is read "there exists ... such that". ∈: the symbol for set membership
E
Subfield of automated reasoning and mathematical logic
essentially modern predicate logic. His Foundations of Arithmetic, published in 1884, expressed (parts of) mathematics in formal logic. This approach was
Automated_theorem_proving
Propositional formula
In logic, a clause is a propositional formula formed from a finite collection of literals (atoms or their negations) and logical connectives. A clause
Clause_(logic)
British computer scientist
and computational logic "Curriculum Vitae: Keith Leonard Clark" (PDF). AIST. 1984. pp. 4–5. Retrieved 3 September 2025. Predicate logic as a computational
Keith Clark (computer scientist)
Keith_Clark_(computer_scientist)
Approach to natural language semantics
on mathematical logic, especially higher-order predicate logic and lambda calculus, and makes use of the notions of intensional logic, via Kripke models
Montague_grammar
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
Vector_logic
Rules to verify computer program correctness
command establishes the postcondition. Assertions are formulae in predicate logic. Hoare logic provides axioms and inference rules for all the constructs of
Hoare_logic
Database model
managing data using a structure and language consistent with first-order predicate logic, first described in 1969 by English computer scientist Edgar F. Codd
Relational_model
Resource-sensitive logic allowing each assumption to be used at most once
comprehension axiom. Likewise, the logic formed the basis of a decidable sub-theory of predicate logic, called 'Direct logic' (Ketonen & Wehrauch, 1984; Ketonen
Affine_logic
Topics referred to by the same term
(disambiguation) Allyl group "For all", a universal quantification in predicate logic, represented by ∀ This disambiguation page lists articles associated
All
Programming language that uses first order logic
schemata, logic description schemata, and higher-order programming. A higher-order predicate is a predicate that takes one or more other predicates as arguments
Prolog
Formalism for knowledge representation
representation and reasoning model. In this approach, a formula in first-order logic (predicate calculus) is represented by a labeled graph. A linear notation, called
Conceptual_graph
Logical connective OR
In logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated
Logical_disjunction
Term that does not contain any variables
In mathematical logic, a ground term of a formal system is a term that does not contain any variables. Similarly, a ground formula is a formula that does
Ground_expression
Intelligence of machines
such as "and", "or", "not" and "implies") and predicate logic (which also operates on objects, predicates and relations and uses quantifiers such as "Every
Artificial_intelligence
Category of constructed language
typically based on predicate logic but can also be based on any system of formal logic. The two best-known logical languages are the predicate languages Loglan
Engineered_language
System for reasoning about vagueness
Łukasziewicz fuzzy logic. A generalization of the classical Gödel completeness theorem is provable in EVŁ. Similar to the way predicate logic is created from
Fuzzy_logic
Concept in mathematics or computer science
in other disciplines involving formal languages, including mathematical logic and computer science, a variable may be said to be either free or bound
Free variables and bound variables
Free_variables_and_bound_variables
Reasoning about equations with free variables
Stanford Encyclopedia of Philosophy. Willard Quine, 1976, "Algebraic Logic and Predicate Functors" pages 283 to 307 in The Ways of Paradox, Harvard University
Algebraic_logic
Classification of definitions in mathematics, philosophy, and logic
Comprehension (logic) – Totality of intensions of an object Extension (predicate logic) – Set of tuples in mathematical logic that satisfy a predicate Extension
Extensional and intensional definitions
Extensional_and_intensional_definitions
Kind of proof calculus
intended it as a technical device for clarifying the consistency of predicate logic. Kleene, in his seminal 1952 book Introduction to Metamathematics,
Natural_deduction
Topics referred to by the same term
theory) Extension (proof theory) Extension (predicate logic), the set of tuples of values that satisfy the predicate Extension (semantics), the set of things
Extension
Software able to infer logical consequences
ontology language, and often a description logic language. Many reasoners use first-order predicate logic to perform reasoning; inference commonly proceeds
Semantic_reasoner
{\text{ (sphere path)}}\end{aligned}}} The notations of first-order predicate logic are streamlined when quantifiers are relegated to established domains
Lift_(mathematics)
PREDICATE LOGIC
PREDICATE LOGIC
Girl/Female
Tamil
Viviktha | விவீகà¯à®¤à®¾Â
Distinguished, Pure, Deep, Logically intelligent
Viviktha | விவீகà¯à®¤à®¾Â
Girl/Female
Tamil
Arpitha | à®…à®°à¯à®ªà®¿à®¤à®¾
Dedicate, Presenting
Arpitha | à®…à®°à¯à®ªà®¿à®¤à®¾
Girl/Female
Arabic
Dark Night; Dedicate
Girl/Female
Bengali, Indian
Dedicate
Girl/Female
Hindu
Distinguished, Pure, Deep, Logically intelligent
Girl/Female
Indian
Dedicate, Presenting
Girl/Female
Tamil
Trick, Power, Strategy, Solution by logic, By reasoning
Boy/Male
Hindu
Love and kindness, Analytical, Logical
Boy/Male
Hindu, Indian, Tamil
Sun; Moon; Dedicate
Girl/Female
Tamil
Vivikta | விவிகதா
Distinguished, Pure, Deep, Logically intelligent
Vivikta | விவிகதா
Girl/Female
Hindu
Trick, Power, Strategy, Solution by logic, By reasoning
Girl/Female
Tamil
Trick, Power, Strategy, Solution by logic, By reasoning
Boy/Male
Indian
Intelligent, Logical
Boy/Male
Tamil
Full of feathers, Full of logic, Name of sage, Vatsyayan
Girl/Female
Bengali, Indian
Dedicate
Girl/Female
Tamil
Arpita | à®…à®°à¯à®ªà®¿à®¤à®¾
Dedicate, Presenting
Arpita | à®…à®°à¯à®ªà®¿à®¤à®¾
Girl/Female
Hindu, Indian, Malayalam, Marathi, Tamil, Telugu
Devotee of God; Daughter of God; Dedicated; Tribute; To Dedicate Something
Girl/Female
Indian
Dedicate, Presenting
Girl/Female
Indian
One who Willingly Dedicate Herself
Biblical
respiration; conversion; taking captive;man sitting in Nob;dweller on the mount, he that predicts;
PREDICATE LOGIC
PREDICATE LOGIC
Biblical
finished; complete; perfect
Boy/Male
Indian, Sanskrit
Transcendental; Without Cast
Girl/Female
Indian
Safe, Healthy, Happy
Surname or Lastname
English (Oxfordshire, Warwickshire)
English (Oxfordshire, Warwickshire) : patronymic from a pet form of the personal name Gill.
Boy/Male
Scottish Celtic Greek Irish English
Youth.
Girl/Female
Afghan, Arabic, Australian, Iranian, Muslim, Parsi
Sweetheart
Girl/Female
Indian, Sanskrit
Female Elephant
Male
Egyptian
, an Egyptian officer.
Boy/Male
Arabic, Muslim
Unprecedented; Unique
Girl/Female
Greek
Pure.
PREDICATE LOGIC
PREDICATE LOGIC
PREDICATE LOGIC
PREDICATE LOGIC
PREDICATE LOGIC
v. t.
That which is affirmed or denied of the subject. In these propositions, "Paper is white," "Ink is not white," whiteness is the predicate affirmed of paper and denied of ink.
v. i.
To affirm something of another thing; to make an affirmation.
a.
Predicated.
v. t.
To assert to belong to something; to affirm (one thing of another); as, to predicate whiteness of snow.
a.
Capable of being predicated or affirmed of something; affirmable; attributable.
imp. & p. p.
of Eradicate
imp. & p. p.
of Prejudicate
p. pr. & vb. n.
of Eradicate
v. t.
The word or words in a proposition which express what is affirmed of the subject.
v. t.
To found; to base.
a.
Joining subject and predicate; copulative.
p. pr. & vb. n.
of Predicate
imp. & p. p.
of Predict
v. t.
To root out; to destroy utterly; to extirpate; as, to eradicate diseases, or errors.
a.
Expressing affirmation or predication; affirming; predicating, as, a predicative term.
p. pr. & vb. n.
of Prejudicate
v. t.
To set apart and consecrate, as to a divinity, or for sacred uses; to devote formally and solemnly; as, to dedicate vessels, treasures, a temple, or a church, to a religious use.
v. t.
To tell or declare beforehand; to foretell; to prophesy; to presage; as, to predict misfortune; to predict the return of a comet.
imp. & p. p.
of Predicate
n.
One who predicates, affirms, or proclaims; specifically, a preaching friar; a Dominican.