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Type of logical system
science, first-order logic (FOL), also called predicate logic, predicate calculus, or quantificational logic, is a type of formal system. First-order logic
First-order_logic
Index of articles associated with the same name
Look up first-order in Wiktionary, the free dictionary. In mathematics and other formal sciences, first-order or first order most often means either: "linear"
First-order
Topics referred to by the same term
First Order may refer to: First-order, a term used in mathematics and logic First order (religious), an institute of consecrated life for men First Order
First_Order
Fictional military power in the ''Star Wars'' franchise
The First Order is a fictional military movement in the Star Wars franchise, introduced in the 2015 film The Force Awakens. It is formed following the
First_Order_(Star_Wars)
Instantaneous rate of change (mathematics)
notation by adding additional prime marks. Higher order derivatives are used in physics; for example, the first derivative with respect to time of the position
Derivative
2015 Japanese mobile video game
special titled Fate/Grand Order: First Order (Japanese: フェイト/グランドオーダー -First Order-, Hepburn: Feito/Gurando Ōdā -First Order-) aired on 31 December 2016
Fate/Grand_Order
Differential equation containing derivatives with respect to only one variable
although note that any ODE of order greater than one can be (and usually is) rewritten as system of ODEs of first order, which makes the Jacobian singularity
Ordinary differential equation
Ordinary_differential_equation
Physical process of transition between basic states of matter
respect to pressure. Second-order phase transitions are continuous in the first derivative (the order parameter, which is the first derivative of the free
Phase_transition
Compact composite lens
classified as first through sixth order. An intermediate size between third and fourth order was added later, as well as sizes above first order and below
Fresnel_lens
Logical statement with variables, predicates, and quantifiers over objects
mathematical logic, a first-order predicate is a predicate that takes only individual(s) constants or variables as argument(s). Compare second-order predicate and
First-order_predicate
Differential equation that is linear with respect to the unknown function
can be converted into a first order system of linear differential equations by adding variables for all but the highest order derivatives. That is, if
Linear_differential_equation
Model in digital signal processing
First-order hold (FOH) is a mathematical model of the practical reconstruction of sampled signals that could be done by a conventional digital-to-analog
First-order_hold
Mendicant Catholic religious order
Elizabeth of Hungary, among many others. The Order of Friars Minor is the largest of the contemporary First Orders within the Franciscan movement. Francis
Order_of_Friars_Minor
Relation between chemical reaction rate and concentrations of the reactants
first order and second order reactions (or more often concurrent pseudo-first order and second order) reactions, and can be described as mixed first and
Rate_equation
Method for finding the extrema of a function
second-order derivative test. As shown below, the second-derivative test is mathematically identical to the special case of n = 1 in the higher-order derivative
Derivative_test
Solution technique in contract theory
In microeconomics and contract theory, the first-order approach is a simplifying assumption used to solve models with a principal-agent problem. It suggests
First-order_approach
a first-order reduction is a very strong type of reduction between two computational problems in computational complexity theory. A first-order reduction
First-order_reduction
Function that takes one or more functions as an input or that outputs a function
a function as its result. All other functions are first-order functions. In mathematics higher-order functions are also termed operators or functionals
Higher-order_function
Topics referred to by the same term
up order or Order in Wiktionary, the free dictionary. Order, ORDER or Orders most often refers to: A socio-political or established or existing order, e
Order
Inference rule in logic, proof theory, and automated theorem proving
refutation-complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution
Resolution_(logic)
Group of religious orders within the Catholic Church connected with St. Francis of Assisi
(the Order of Friars Minor being the largest contemporary male order), an order for nuns known as the Order of Saint Clare, and the Third Order of Saint
Franciscans
Semi-probabilistic reliability analysis method
The first-order reliability method (FORM) is a semi-probabilistic reliability analysis method devised to evaluate the reliability of a system. The accuracy
First-order reliability method
First-order_reliability_method
Form of logic that allows quantification over predicates
mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn
Second-order_logic
Theories in mathematical logic
In first-order logic, a first-order theory is given by a set of axioms in some language. This entry lists some of the more common examples used in model
List_of_first-order_theories
Mathematical approach to quantum physics
n^{(1)}\right\rangle =0.} To obtain the first-order correction to the energy eigenstate, the expression for the first-order energy correction is inserted back
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
Type of generalized Newtonian fluid
flow behaviour index: pseudoplastic, Newtonian fluid, and dilatant. A first-order fluid is a power-law fluid with exponential dependence of viscosity on
Power-law_fluid
Axioms for the natural numbers
the second-order and first-order formulations, as discussed in the section § Peano arithmetic as first-order theory below. If the second-order induction
Peano_axioms
mathematical logic necessary to express a given query. A query is order-independent if the ordering of objects in the structure does not affect the results of
Query_(complexity)
In machine learning, first-order inductive learner (FOIL) is a rule-based learning algorithm. Developed in 1990 by Ross Quinlan, FOIL learns function-free
First-order_inductive_learner
Type of signal filter
{\operatorname {d} v_{\text{out}}}{\operatorname {d} t}}} This first-order differential equation is also the standard form of a leaky integrator
Low-pass_filter
Fictional soldiers in the Star Wars franchise
Stormtroopers remained in service to Imperial remnants, such as the First Order. The order of battle of the Stormtrooper Corps is unspecified in the Star Wars
Stormtrooper_(Star_Wars)
Limitative results in mathematical logic
that first-order logic is semantically complete. But it is not syntactically complete, since there are sentences expressible in the language of first-order
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Formal system of logic
In mathematics and logic, a higher-order logic (HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers and, sometimes
Higher-order_logic
Methods of mathematical approximation
truncating the series, often keeping only the first two terms: the solution to the known problem and the 'first order' perturbation correction. Perturbation
Perturbation_theory
Expressions for approximation accuracy
The order of the approximation is the highest power term that is kept. For example, one can refer to a zeroth-order approximation, a first-order approximation
Order_of_approximation
Inferring the speed and direction of objects
to suggest that early processing of first- and second-order motion is carried out by separate pathways. Second-order mechanisms have poorer temporal resolution
Motion_perception
Type of differential equation subject to a particular solution methodology
^{2}} and two functions I and J which are continuous on D, an implicit first-order ordinary differential equation of the form I ( x , y ) d x + J ( x ,
Exact_differential_equation
1981 book by Jean Baudrillard
is incapable of encapsulating. The first-order simulacrum is a faithful copy of the original and the third order are symbols that have come to be without
Simulacra_and_Simulation
Partial order between random variables
Statewise dominance implies first-order stochastic dominance (FSD), which is defined as: Random variable A has first-order stochastic dominance over random
Stochastic_dominance
Set of sentences in a formal language
definition, every axiom is automatically a theorem. A first-order theory is a set of first-order sentences (theorems) recursively obtained by the inference
Theory_(mathematical_logic)
Time for exponential decay to remove half of a quantity
of a first order reaction is given as the following: t 1 / 2 = ln 2 k {\displaystyle t_{1/2}={\frac {\ln 2}{k}}} The half-life of a first order reaction
Half-life
Philosophical term
higher-order volitions determined the primacy of first-order desires. This view is called compatibilism. An example for a failure to follow higher-order volitions
Higher-order_volition
Subfield of automated reasoning and mathematical logic
universe and a Herbrand interpretation that allowed (un)satisfiability of first-order formulas (and hence the validity of a theorem) to be reduced to (potentially
Automated_theorem_proving
Second-order election is a term that appeared for the first time in Karlheinz Reif and Hermann Schmitt's "Nine second-order national elections – A conceptual
Second-order_election
British magical order (1887–1903)
"Golden Dawn" was the first of three Orders, although all three are often collectively referred to as the "Golden Dawn". The First Order taught esoteric philosophy
Hermetic Order of the Golden Dawn
Hermetic_Order_of_the_Golden_Dawn
State of being real
possessed by at least one entity. A different view sees existence as a first-order property, or a property of individuals, meaning existence is similar
Existence
2018 animated television show by Dave Filoni
who is recruited by the Resistance to spy on the growing threat of the First Order shortly before and during the events of the sequel trilogy. The series
Star_Wars_Resistance
Sensory spinal pathway
that are involved in the pathway: first-order neurons, second-order neurons, and third-order neurons. The first-order neurons are sensory neurons located
Dorsal column–medial lemniscus pathway
Dorsal_column–medial_lemniscus_pathway
Star Wars character
franchise. He first appeared in the 2015 film The Force Awakens as a First Order stormtrooper. Disturbed by the Order's cruelty during his first combat mission
Finn_(Star_Wars)
Assignment of meaning to the symbols of a formal language
discuss] they include the usual interpretations of propositional and first-order logic. The sentences that are made true by a particular assignment are
Interpretation_(logic)
Statement that is taken to be true
requires the use of second-order logic. The Löwenheim–Skolem theorems tell us that if we restrict ourselves to first-order logic, any axiom system for
Axiom
Standard system of axiomatic set theory
regularity (first proposed by John von Neumann), to Zermelo set theory yields the theory ZFC. Formally, ZFC is a one-sorted theory in first-order logic. The
Zermelo–Fraenkel_set_theory
Pattern defining an infinite sequence of numbers
n} ; this number k {\displaystyle k} is called the order of the relation. If the values of the first k {\displaystyle k} numbers in the sequence have been
Recurrence_relation
Type of functional equation (mathematics)
containing only first-order derivatives is a first-order differential equation, an equation containing the second-order derivative is a second-order differential
Differential_equation
Star Wars character
struggle with Kylo Ren for the First Order leadership, and being exceeded only by Supreme Leader Snoke. The character first featured in The Force Awakens
General_Hux
Branch of logic
zeroth-order logic. Sometimes, it is called first-order propositional logic to contrast it with System F, but it is distinct from first-order logic. It
Propositional_logic
The Order of Berthold the First (German: Orden Berthold des Ersten) was a dynastic order in the Grand Duchy of Baden. It was established on 29 April 1877
Order_of_Berthold_the_First
Limited form of tree data structure
special case of this. See depth-first search for more information. Contrasting with depth-first order is breadth-first order, which always attempts to visit
Binary_tree
Type of electronic circuit or optical filter
capacitor or an inductor can be configured as a first-order high-pass filter. The simple first-order capacitive high-pass filter shown in Figure 1 is
High-pass_filter
Fragment of first-order logic
the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic (also called predicate calculus) in which all
Monadic_predicate_calculus
individuals, so their order is "1" (first-order classes). Metaclasses that are classes of first-order classes' order is "2" (second-order classes), and so
Metaclass (knowledge representation)
Metaclass_(knowledge_representation)
In logic, a statement which is always true
propositional logic, and uniformly replacing each propositional variable by a first-order formula (one formula per propositional variable). The set of such formulas
Tautology_(logic)
Theory relating to sampling from finite populations
inclusion probability is also termed the "first-order inclusion probability" to distinguish it from the "second-order inclusion probability", i.e. the probability
Sampling_probability
Term in numerical analysis
general, all numerical errors correctly. The size of the error of a first-order accurate approximation is directly proportional to h {\displaystyle h}
Order_of_accuracy
In mathematics, a first-order partial differential equation is a partial differential equation that involves the first derivatives of an unknown function
First-order partial differential equation
First-order_partial_differential_equation
Approach to finding numerical solutions of ordinary differential equations
science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs)
Euler_method
Roman Catholic monastic order
The Order of Saint Paul the First Hermit (Latin: Ordo Fratrum Sancti Pauli Primi Eremitæ; abbreviated OSPPE), commonly called the Pauline Fathers, is
Order of Saint Paul the First Hermit
Order_of_Saint_Paul_the_First_Hermit
Algorithmic process of solving equations
expressions are considered equivalent. In first-order syntactic unification, variables range over first-order terms and equivalence is syntactic. This
Unification (computer science)
Unification_(computer_science)
Spectral line splitting in electrical field
converges fast, so only a few first terms give an accurate approximation. Namely, keeping only the zeroth- and first-order terms, ϕ ( r ) ≈ ϕ ( 0 ) − ∑
Stark_effect
Changing the balance of frequency components in an audio signal
each a first-order filter in which the balance of frequencies above and below a point are varied using a single knob. A special case of first-order filters
Audio_equalization
Organization in the Star Wars franchise
Remnant, and the First Order, are shown to have originated from the Sith. Sith, known as Sith Lords, are by nature ruthless. Members of the order have the power
Sith
Fictional state in the Star Wars universe
the First Order, under Supreme Leader Snoke's direction, in Star Wars: The Force Awakens. In the Star Wars chronology, the destruction of the first Death
Galactic_Republic
Type of ordinary differential equation
differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written
Homogeneous differential equation
Homogeneous_differential_equation
Area of mathematical logic
theory, which is semantic in nature. This article focuses on finitary first order model theory. The relative emphasis placed on the class of models of
Model_theory
Subfield of mathematics
When applied to first-order logic, the first incompleteness theorem implies that any sufficiently strong, consistent, effective first-order theory has models
Mathematical_logic
Order whose elements are all comparable
mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation ≤
Total_order
Performing order of mathematical operations
computer programming, the order of operations is a collection of conventions about which arithmetic operations to perform first in order to evaluate a given
Order_of_operations
they are implicit in the structure. Abstract syntaxes are classified as first-order abstract syntax (FOAS), if the structure is abstract but names (identifiers)
Abstract_syntax
Class of algorithms
There are three common ways to traverse them in depth-first order: in-order, pre-order and post-order. Beyond these basic traversals, various more complex
Tree_traversal
Method of deriving conclusions
logical operators like "not" and "if...then..." support conclusions. First-order logic extends propositional logic by analyzing how the internal structure
Rule_of_inference
Components of a mathematical or logical formula
phrase refers to an object and a whole sentence refers to a fact. A first-order term is recursively constructed from constant symbols, variable symbols
Term_(logic)
Mathematical system
axiomatization of second-order arithmetic is denoted by Z2. Second-order arithmetic includes, but is significantly stronger than, its first-order counterpart Peano
Second-order_arithmetic
Index of articles associated with the same name
Zeroth-order logic First-order logic Second-order logic Higher-order logic Order (journal), an academic journal on order theory Dense order, a total order wherein
Order_(mathematics)
Model parameters in mathematical finance
Greeks are the quantities (known in calculus as partial derivatives; first-order or higher) representing the sensitivity of the price of a derivative
Greeks_(finance)
In mathematical logic, a first-order language of the real numbers is the set of all well-formed sentences of first-order logic that involve universal
Decidability of first-order theories of the real numbers
Decidability_of_first-order_theories_of_the_real_numbers
Non-contradiction of a theory
explosive formal system (e.g., classical or intuitionistic propositional or first-order logics) every inconsistent theory is trivial. Consistency of a theory
Consistency
Concept in quantum optics
experiment and Mach-Zehnder interferometry are characterized only by the first order coherence. The 1956 Hanbury Brown and Twiss experiment brought to light
Higher_order_coherence
Branch of mathematical logic
logarithmic time. First-order logic in a signature with only the order relation corresponds to the set of star-free languages. First-order logic gains substantially
Descriptive_complexity_theory
Paradox in set theory
strong higher-order logic, while Zermelo employed second-order logic, and ZFC can also be given a first-order formulation. The first-order 'description'
Russell's_paradox
Scientific theory
Higher-order theories of consciousness postulate that consciousness consists in perceptions or thoughts about first-order mental states. In particular
Higher-order theories of consciousness
Higher-order_theories_of_consciousness
Fundamental theorem in mathematical logic
semantic truth and syntactic provability in first-order logic. The completeness theorem applies to any first-order theory: If T is such a theory, and φ is
Gödel's_completeness_theorem
Template that specifies one or more axioms
Some axiom schemata in first-order theories can be replaced by single axioms in a higher-order language. For example, the first-order induction schema for
Axiom_schema
Fictional state in the Star Wars franchise
the First Order) Star Wars: Episode VII – The Force Awakens (2015) (As the First Order) Star Wars: Episode VIII – The Last Jedi (2017) (As the First Order)
Galactic_Empire
Axiom of set theory
theorem for first-order logic: every consistent set of first-order sentences has a completion. That is, every consistent set of first-order sentences can
Axiom_of_choice
Movement of a drug into the bloodstream or lymph
intravenous injection. Zero-order absorption: rate of absorption is constant. A common example is continuous intravenous infusion. First-order absorption: rate of
Absorption_(pharmacology)
Kth smallest value in a statistical sample
\x_{(2)}&=6\\x_{(3)}&=7\\x_{(4)}&=9\end{aligned}}} The first order statistic (or smallest order statistic) is always the minimum of the sample, that is
Order_statistic
Theorem in mathematical logic
In mathematical logic, the compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model
Compactness_theorem
Logical generalization for symbolic expressions
allowed in an expression, the process is called "higher-order anti-unification", otherwise "first-order anti-unification". If the generalization is required
Anti-unification
Discretization method for differential equations
above will show that it is first-order accurate in space and time. Modified wavenumber analysis shows that the first-order upwind scheme introduces severe
Upwind_scheme
Mapping function that preserves data point locality
Morton order). It is named in France after Henri Lebesgue, who studied it in 1904, and named in the United States after Guy Macdonald Morton, who first applied
Z-order_curve
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