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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
Logical statement with variables, predicates, and quantifiers over objects
logic, a first-order predicate is a predicate that takes only individual(s) constants or variables as argument(s). Compare second-order predicate and higher-order
First-order_predicate
Symbol representing a property or relation in logic
all. For instance, in the first-order formula P ( a ) {\displaystyle P(a)} , the symbol P {\displaystyle P} is a predicate that applies to the individual
Predicate_(logic)
Aspect of mathematical logic
second-order predicate is a predicate that takes a first-order predicate as an argument. Compare higher-order predicate. The idea of second order predication
Second-order_predicate
not be considered a rigorous proof of the theorem. We work with first-order predicate calculus. Our languages allow constant, function and relation symbols
Original proof of Gödel's completeness theorem
Original_proof_of_Gödel's_completeness_theorem
Index of articles associated with the same name
science First-order predicate, a predicate that takes only individual(s) constants or variables as argument(s) First-order predicate calculus First-order theorem
First-order
Type of logical argument that applies deductive reasoning
Within some academic contexts, syllogism has been superseded by first-order predicate logic following the work of Gottlob Frege, in particular his Begriffsschrift
Syllogism
Philanthropy conception of meaning
constitutes the first systematic presentation of truth-conditional semantics. He proposed simply translating natural languages into first-order predicate calculus
Meaning_(philosophy)
Non-contradiction of a theory
1918[citation needed] and Emil Post in 1921, while the completeness of (first order) predicate calculus was proved by Kurt Gödel in 1930, and consistency proofs
Consistency
Fragment of first-order logic
logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic (also called predicate calculus) in which
Monadic_predicate_calculus
Knowledge base that represents semantic relations between concepts in a network
first order predicate calculus as a base, after being inspired by a demonstration of Victor Yngve. The "line of research was originated by the first President
Semantic_network
Form of logic that allows quantification over predicates
the predicate. That is, the following expression: ∃ P P ( b ) {\displaystyle \exists \mathrm {P} \,\mathrm {P} (b)} is not a sentence of first-order logic
Second-order_logic
Subject and predicate in sentences
The term predicate is used in two ways in linguistics and its subfields. The first defines a predicate as everything in a standard declarative sentence
Predicate_(grammar)
Type of mathematical variable
{\displaystyle x} . In first-order logic, they can be more properly called metalinguistic variables. In higher-order logic, predicate variables correspond
Predicate_variable
Abstract model
based on first-order predicate logic. Its core idea is to describe a database as a collection of predicates over a finite set of predicate variables
Data_model
Study of the properties of logical systems
Post 1920) Completeness of first-order monadic predicate logic (Leopold Löwenheim 1915) Completeness of first-order predicate logic (Gödel's completeness
Metalogic
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
Fundamental theorem in mathematical logic
converted into the other).[citation needed] We first fix a deductive system of first-order predicate calculus, choosing any of the well-known equivalent
Gödel's_completeness_theorem
Statement regarding whether or not an item belongs to a category
the increased expressive power of modern logic systems like the first-order predicate calculus, they still retain practical value in addition to their
Categorical_proposition
Inference rule in logic, proof theory, and automated theorem proving
not be used as p {\displaystyle p} due to its syntactic form. For first-order predicate logic, Murray's rule is generalized to allow distinct, but unifiable
Resolution_(logic)
Software able to infer logical consequences
language, and often a description logic language. Many reasoners use first-order predicate logic to perform reasoning; inference commonly proceeds by forward
Semantic_reasoner
General purpose functional programming language
PPLAMBDA, a language that was conceptually a combination of the first-order predicate calculus and the simply typed polymorphic lambda calculus, was the
ML_(programming_language)
Subfield of automated reasoning and mathematical logic
algorithms are believed to exist for general proof tasks. For a first-order predicate calculus, Gödel's completeness theorem states that the theorems
Automated_theorem_proving
Programming technique
An object–role model uses graphical symbols that are based on first order predicate logic and set theory to enable the modeler to create an unambiguous
Object–role_modeling
Rule of logical inference
subset of Q. x is not in Q. Therefore, x is not in P.") Also in first-order predicate logic: ∀ x : P ( x ) → Q ( x ) {\displaystyle \forall x:~P(x)\to
Modus_tollens
Basic notion of sameness in mathematics
the first-order logic may be regarded as a mere matter of convenience, as noted by Azriel Lévy: The reason why we take up first-order predicate calculus
Equality_(mathematics)
S^{2}&&\ {\text{ (sphere path)}}\end{aligned}}} The notations of first-order predicate logic are streamlined when quantifiers are relegated to established
Lift_(mathematics)
3-volume treatise on mathematics, 1910–1913
and consistent. In 1930 Gödel's completeness theorem showed that first-order predicate logic itself was complete in a much weaker sense—that is, any sentence
Principia_Mathematica
Programming language that uses first order logic
higher-order programming. A higher-order predicate is a predicate that takes one or more other predicates as arguments. Although support for higher-order programming
Prolog
subset of first-order predicate calculus. Given positive and negative examples of some concept and a set of background-knowledge predicates, FOIL inductively
First-order_inductive_learner
Programming paradigm based on formal logic
is a relational expression, which is similar to an expression in first-order predicate logic. Other relational programming languages are based on the relational
Logic_programming
Reduction of data redundancy
of a universal data sub-language based on an applied predicate calculus. A first-order predicate calculus suffices if the collection of relations is in
Database_normalization
theoretical tool for showing the unsatisfiability of clauses in first-order predicate logic. Kundu, S (1986-12-01). "Tree resolution and generalized semantic
Semantic_resolution_tree
Programming language
Fril is a programming language for first-order predicate calculus. It includes the semantics of Prolog as a subset, but takes its syntax from the micro-PROLOG [es]
Fril
Sammartino (2009-09-01). Tim Berners-Lee: Inventor of the World Wide Web. Twenty-First Century Books. ISBN 978-0-8225-7273-2. "A.M. Turing Award Laureate – Manuel
List of pioneers in computer science
List_of_pioneers_in_computer_science
Order of syntactic constituents
In linguistics, word order (also known as linear order) is the order of the syntactic constituents of a language. Word order typology studies it from
Word_order
Hypothesis of philosopher Jerry Fodor
tallness, combined in a manner that may be expressed in first-order predicate calculus as a predicate 'T' ("is tall") that holds of the entity 'j' (John)
Language of thought hypothesis
Language_of_thought_hypothesis
Syntactically correct logical formula
propositional logic and predicate logic. A key use of formulas is in propositional logic and predicate logic such as first-order logic. In those contexts
Well-formed_formula
Organized collection of data in computing
operations to be defined in terms of the established discipline of first-order predicate calculus; because these operations have clean mathematical properties
Database
Characteristic of some logical systems
introducing an inconsistency. Truth-functional propositional logic and first-order predicate logic are semantically complete, but not syntactically complete
Completeness_(logic)
Philosophy using an idealized language
that these states of affairs can be expressed by the language of first-order predicate logic. Thus a picture of the universe can be construed by means
Ideal_language_philosophy
Extension of a formal language by the epsilon operator
operator and epsilon substitution method are typically applied to a first-order predicate calculus, followed by a demonstration of consistency. The epsilon-extended
Epsilon_calculus
Information science by discipline
documents bears a close resemblance to the Horn clause subset of first order predicate calculus. Moreover, it identified the need to extend the use of
Legal_informatics
Logical formulation of graph properties
be used in these sentences. The first-order logic of graphs concerns sentences in which the variables and predicates concern individual vertices and edges
Logic_of_graphs
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
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
American philosopher and logician (1908–2000)
philosophy students did not do justice to quantification theory or first-order predicate logic. Quine wrote this book in 6 weeks as an ad hoc solution to
Willard_Van_Orman_Quine
Database used to store info on hardware and software assets
and a semantic data model. Relational data models are based on first-order predicate logic and all data is represented in terms of tuples that are grouped
Configuration management database
Configuration_management_database
Specification of a conceptualization
its own ontology language called CycL, based on first-order predicate calculus with some higher-order extensions. DOGMA (Developing Ontology-Grounded
Ontology (information science)
Ontology_(information_science)
Formal specification language used for describing and modelling computing systems
mathematical notation used in axiomatic set theory, lambda calculus, and first-order predicate logic. All expressions in Z notation are typed, thereby avoiding
Z_notation
Study of the scope and nature of logic
contradiction. Higher-order logics extend classical first-order predicate logic by including new forms of quantification. In first-order logic, quantification
Philosophy_of_logic
Form of second-order logic
Second-order logic allows quantification over predicates. However, MSO is the fragment in which second-order quantification is limited to monadic predicates
Monadic_second-order_logic
Field that studies the methods and methodologies for building ontologies
its own ontology language called CycL, based on first-order predicate calculus with some higher-order extensions. The Gellish language includes rules
Ontology_engineering
Assignment of meaning to the symbols of a formal language
line l. A formal language for higher-order predicate logic looks much the same as a formal language for first-order logic. The difference is that there
Interpretation_(logic)
Formal system of logic
those of first-order logic. The term "higher-order logic" is commonly used to mean higher-order simple predicate logic. Here, "simple" indicates that the
Higher-order_logic
Convention where symbols represent concepts
notation for specifying objects using Zermelo–Fraenkel set theory and first-order predicate logic Ordinal notation Set-builder notation, a formal notation for
Notation_system
meaning representations allow one to use the tools of classical first-order predicate calculus even for statements which, due to their use of tense, modality
Reification (information retrieval)
Reification_(information_retrieval)
Rules used for constructing, or transforming the symbols and words of a language
introducing an inconsistency. Truth-functional propositional logic and first-order predicate logic are semantically complete, but not syntactically complete
Syntax_(logic)
Study of the semantics, or interpretations, of formal and natural languages
them to some predefined mathematical domains: an interpretation of first-order predicate logic is given by a mapping from terms to a universe of individuals
Semantics_(logic)
Logical paradox
systems of logic. For instance, the following formalization in first order predicate logic would be valid via Leibniz's law: t=90 R(t) R(90) (valid conclusion
Temperature_paradox
Concept in mathematical logic
converse per accidens "Some mammals are unicorns" is clearly false. In first-order predicate calculus, All S are P can be represented as ∀ x . S ( x ) → P (
Converse_(logic)
Various systems of symbolic logic
FALSE: ⊥ → ϕ {\displaystyle \bot \to \phi } To make this a system of first-order predicate logic, the generalization rules ∀ {\displaystyle \forall } -GEN:
Intuitionistic_logic
Set of rules defining correctly structured Prolog programs
Prolog is restricted to Horn clauses, a Turing-complete subset of first-order predicate logic. There are two types of clauses: Facts and rules. A rule is
Prolog_syntax_and_semantics
Axiom of Set Theory
\varnothing =\{u\in w\mid u\neq u\}} . In many formulations of first-order predicate logic, the existence of at least one object is always guaranteed
Axiom_of_empty_set
Variable that can either be true or false
as x and y attached to predicate letters such as Px and xRy, having instead individual constants a, b, ... attached to predicate letters are propositional
Propositional_variable
Learning logic programs from data
ISBN 0-262-19218-7. Muggleton, S.H.; Buntine, W. (1988). "Machine invention of first-order predicate by inverting resolution". Proceedings of the 5th International Conference
Inductive_logic_programming
Tool for proving a logical formula
gives an assignment that falsifies A. Tableaux are extended to first-order predicate logic by two rules for dealing with universal and existential quantifiers
Method_of_analytic_tableaux
About mathematical functions
. . by a well-formed formula in the simple predicate calculus of first order in which the sole predicate constants are ε and possibly, =. ... Today an
History of the function concept
History_of_the_function_concept
System of mathematical set theory
Mendelson's modification. This means that NBG is an axiomatic system in first-order predicate logic with equality, and its only primitive notions are of classes
Von Neumann–Bernays–Gödel set theory
Von_Neumann–Bernays–Gödel_set_theory
Programming language
constructed using the universal and existential quantifiers of first-order predicate logic. SETL provides several iterators to produce a variety of loops
SETL
Overview of and topical guide to logic
(predicate logic) First-order logic First-order predicate Formation rule Free variables and bound variables Generalization (logic) Monadic predicate calculus
Outline_of_logic
utilization of parallel computer architectures. Its semantics is based on first order predicate logic. It expresses concurrency, interprocess communication, indeterminacy
Parlog
Entities that are said to be either true or false
truth-bearer. For example, a language in the first-order predicate calculus might include one or more predicate symbols and one or more individual constants
Truth-bearer
logician Thoralf Skolem showed in 1922 that every consistent theory of first-order predicate calculus, such as set theory, has an at most countable model. However
Paradoxes_of_set_theory
Framework for exploring meaning
In one sense, DRT offers a variation of first-order predicate calculus—its forms are pairs of first-order formulae and the free variables that occur
Discourse representation theory
Discourse_representation_theory
Paradox in set theory
theory is a formal theory, that is formulated in a first-order language with a binary non-logical predicate ∈ {\displaystyle \in } , and that includes the
Russell's_paradox
Number representing a continuous quantity
the classical logic of first-order predicates. This is one of the reasons for which higher-order logics were developed in the first half of the 20th century
Real_number
Standard system of axiomatic set theory
common. The signature has a single predicate symbol, usually denoted ∈ {\displaystyle \in } , which is a predicate symbol of arity 2 (a binary relation
Zermelo–Fraenkel_set_theory
20th-century tradition of Western philosophy
states of affairs can be expressed and mirrored by the language of first-order predicate logic. Thus, a picture of the universe can be constructed by expressing
Analytic_philosophy
Branch of logic
предикатов" [Volume and fraction of satisfiability of formulae of the first-order predicate calculus]. Kibernetika. 5 (2): 17–27. Also available as;"Range and
Finite_model_theory
Topics referred to by the same term
relational calculus Relational model, a database model based on first-order predicate logic Relational operator, a programming language construct or operator
Relational
Axioms for the natural numbers
one can consider a first-order axiom schema of induction. Such a schema includes one axiom per predicate definable in the first-order language of Peano
Peano_axioms
Topics referred to by the same term
rights supporting organization based in the United States First-order predicate calculus First Parish in Cambridge, a church in Massachusetts, United States
FPC
Formal argument for the existence of God
{\displaystyle x} has property φ {\displaystyle \varphi } " (notation for first-order predicates) ⇒ {\displaystyle \Rightarrow } : "implies" (material implication)
Gödel's_ontological_proof
Limitative results in mathematical logic
provability used in the proof of the first incompleteness theorem can be formalized within a system S using a formal predicate P for provability. Once this is
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Term that does not contain any variables
particular, predicates cannot be ground terms). Roughly speaking, the Herbrand universe is the set of all ground terms. A ground predicate, ground atom
Ground_expression
Smallest grammatical unit that can express a complete proposition
predicand (expressed or not) and a semantic predicate. A typical clause consists of a subject and a syntactic predicate, the latter typically a verb phrase composed
Clause
Mathematical use of "for all" and "there exists"
quantification requires first-order predicate calculus with equality. This means there is given a distinguished two-placed predicate "="; the semantics is
Quantifier_(logic)
Style of formal logical argumentation
A {\displaystyle A} and B {\displaystyle B} denote formulas of first-order predicate logic (one may also restrict this to propositional logic), Γ , Δ
Sequent_calculus
Mathematical-logic system based on functions
comparison predicates of natural numbers, using recursion. When Y combinator is coded directly in a strict programming language, the applicative order of evaluation
Lambda_calculus
Mathematical theory
The system of ω-logic includes all axioms and rules of the usual first-order predicate logic, together with, for each T-formula P(x) with a specified free
Ω-consistent_theory
Framework in lambda calculus
impredicative way in second and higher order logics. In the weak higher order logics, there are variables for higher order predicates, but no quantification on those
Lambda_cube
Concept in information technology
purpose language such as XML. Languages with the full power of first-order predicate logic may be required for many tasks. Human languages are highly
Semantic_interoperability
Algebraization of first-order logic with equality
algebra.[example needed] It is easier to connect the semantics of first-order predicate logic with cylindric set algebra. (For more details, see § Further
Cylindric_algebra
Method of deriving conclusions
conclusions. First-order logic extends propositional logic by analyzing how the internal structure of propositions, like names and predicates, influences
Rule_of_inference
Symbol representing a mathematical concept
only if Y = F(X). Many treatments of predicate logic don't allow functional predicates, only relational predicates. This is useful, for example, in the
Function_symbol
Overview of and topical guide to databases
model – for database management is a database model based on first-order predicate logic, first formulated and proposed in 1969 by Edgar F. Object–relational
Outline_of_databases
Database in which records or objects are found by following references from other objects
recursive: the mathematics originally underpinning SQL (specifically, first-order predicate calculus) does not have sufficient power to support recursive queries
Navigational_database
results confirm the validity of the argument A Some arguments need first-order predicate logic to reveal their forms and they cannot be tested properly by
Corresponding_conditional
Generalized polyadic quantifier
intuitively states that first-order logic is the "strongest" logic having both properties. Lindstrom, P. (1966). "First order predicate logic with generalized
Lindström_quantifier
FIRST ORDER-PREDICATE
FIRST ORDER-PREDICATE
Boy/Male
Hindu, Indian, Punjabi, Sikh
Order
Boy/Male
Indian
Order, Decree
Boy/Male
Greek
Order.
Male
Swedish
Old Swedish form of Old Norse Oddr, ODDER means "point of a weapon."
Surname or Lastname
English
English : topographic name for someone who lived at the edge of a village or by some other boundary, Middle English border, from Old French bordure ‘edge’.
Boy/Male
Muslim
Order. Discipline.
Boy/Male
Arabic, Australian, Muslim
Order
Girl/Female
Indian, Traditional
Order
Boy/Male
Greek
Order.
Girl/Female
Australian, French, German, Greek, Italian
Order
Boy/Male
Tamil
Pradarsh | பà¯à®°à®¤à®°à¯à®·
Appearance, Order
Pradarsh | பà¯à®°à®¤à®°à¯à®·
Surname or Lastname
English
English : variant of Cordier.Catalan : occupational name for a maker of cord or string, from an agent derivative of Catalan corda ‘string’, ‘cord’.
Boy/Male
Australian, French, German, Greek
Order
Girl/Female
Greek
Order.
Girl/Female
Indian, Marathi, Sindhi
Order
Boy/Male
English
From the Thicket of Trees
Girl/Female
German, Greek
Order
Boy/Male
Muslim
Order, Decree
Boy/Male
Greek
Order.
Girl/Female
Indian, Telugu
Order
FIRST ORDER-PREDICATE
FIRST ORDER-PREDICATE
Boy/Male
Hindu
Ambidextrous while shooting
Girl/Female
Sikh
Absorbed in the light of God, Love illuminated
Boy/Male
Hindu
Philosophical verses, Activity, Dancer, Actress
Surname or Lastname
English
English : patronymic from the personal name Ray.
Boy/Male
Indian, Punjabi, Sikh
Lamp of War
Girl/Female
Muslim
Rose garden, Inhabited town, Flourishing
Boy/Male
Tamil
Boy/Male
Muslim/Islamic
Religious Scholar
Girl/Female
Arabic, Muslim
Princess
Boy/Male
Hindu
A name of Lord Krishna
FIRST ORDER-PREDICATE
FIRST ORDER-PREDICATE
FIRST ORDER-PREDICATE
FIRST ORDER-PREDICATE
FIRST ORDER-PREDICATE
n.
An ecclesiastical grade or rank, as of deacon, priest, or bishop; the office of the Christian ministry; -- often used in the plural; as, to take orders, or to take holy orders, that is, to enter some grade of the ministry.
v. i.
To give orders; to issue commands.
a.
Most eminent or exalted; most excellent; chief; highest; as, Demosthenes was the first orator of Greece.
n.
Rank; degree; thus, the order of a curve or surface is the same as the degree of its equation.
n.
Right arrangement; a normal, correct, or fit condition; as, the house is in order; the machinery is out of order.
adv.
In the first place; first in order.
v. t.
To make a border for; to furnish with a border, as for ornament; as, to border a garment or a garden.
n.
Conformity with law or decorum; freedom from disturbance; general tranquillity; public quiet; as, to preserve order in a community or an assembly.
v. t.
To gripe with the fist.
n.
To give an order for; to secure by an order; as, to order a carriage; to order groceries.
v. t.
To strike with the fist.
a.
Preceding all others of a series or kind; the ordinal of one; earliest; as, the first day of a month; the first year of a reign.
n.
To give an order to; to command; as, to order troops to advance.
n.
An assemblage of genera having certain important characters in common; as, the Carnivora and Insectivora are orders of Mammalia.
n.
A number of things or persons arranged in a fixed or suitable place, or relative position; a rank; a row; a grade; especially, a rank or class in society; a group or division of men in the same social or other position; also, a distinct character, kind, or sort; as, the higher or lower orders of society; talent of a high order.
n.
To admit to holy orders; to ordain; to receive into the ranks of the ministry.
a.
Of the best class; of the highest rank; in the first division; of the best quality; first-rate; as, a first-class telescope.
n.
A body of persons having some common honorary distinction or rule of obligation; esp., a body of religious persons or aggregate of convents living under a common rule; as, the Order of the Bath; the Franciscan order.
n.
To put in order; to reduce to a methodical arrangement; to arrange in a series, or with reference to an end. Hence, to regulate; to dispose; to direct; to rule.