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Mathematical framework for identifying causal effects
Do-calculus is a set of mathematical rules devised by Judea Pearl in 1995 to determine whether causal effects can be identified from observational data
Do-calculus
Conceptual model in philosophy of science
queries are possible, in which the do operator is applied (the value is fixed) to multiple variables. The do calculus is the set of manipulations that are
Causal_model
Branch of mathematics
infinitesimal calculus or the calculus of infinitesimals, it has two major branches, differential calculus and integral calculus. Differential calculus studies
Calculus
Error in statistical reasoning with groups
set exists, Pearl's do-calculus can be invoked to discover other ways of estimating the causal effect. The completeness of do-calculus can be viewed as offering
Simpson's_paradox
reasoning about the effects of interventions. Zhang (2008) extended Pearl's do-calculus to the context of ancestral graphs, enabling causal inference when only
Ancestral_graph
Two Advanced Placement courses and exams
Placement (AP) Calculus (also known as AP Calc, Calc AB / BC, AB / BC Calc or simply AB / BC) is a set of two distinct Advanced Placement calculus courses and
AP_Calculus
Relationship between derivatives and integrals
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Calculus of vector-valued functions
vector calculus does not generalize to higher dimensions, but the alternative approach of geometric algebra, which uses the exterior product, does (see
Vector_calculus
Mathematical-logic system based on functions
In mathematical logic, the lambda calculus (also written as λ-calculus) is a formal system for expressing computation based on function abstraction and
Lambda_calculus
Calculus on stochastic processes
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals
Stochastic_calculus
Instantaneous rate of change (mathematics)
differences. The study of differential calculus is unified with the calculus of finite differences in time scale calculus. The arithmetic derivative involves
Derivative
Specialized notation for multivariable calculus
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various
Matrix_calculus
Mathematical techniques used in probability theory and related fields
related fields, Malliavin calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic
Malliavin_calculus
Decision principle
Under such conditions, the sure-thing principle is a theorem in the do-calculus (see Bayes networks). Blyth constructed a counterexample to the sure-thing
Sure-thing_principle
2018 book by Judea Pearl and Dana Mackenzie
as lung cancer). The 'front-door criterion' and the 'do-calculus' are introduced as tools for doing this. The chapter finishes with two examples, used to
The_Book_of_Why
2.71828…, base of natural logarithms
Consequently, the exponential function with base e is particularly suited to doing calculus. Choosing e (as opposed to some other number) as the base of the exponential
E_(mathematical_constant)
Study of rates of change
differential calculus is a subfield of calculus that studies the rates at which quantities change. The primary objects of study in differential calculus are the
Differential_calculus
Calculus of functions of several variables
Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to functions of several variables: the differentiation
Multivariable_calculus
2000 book by Judea Pearl
the causal structure on other parts (the do-calculus).(2003, p F412-13). For Morgan (2004, p. 413) Pearl's do-operator is his most memorable concept. This
Causality_(book)
Extent to which the results of a study can be generalized
interventional probability, often written using Do-calculus P ( Z = z | d o ( X = x ) ) {\displaystyle P(Z=z|do(X=x))} , can sometimes be estimated from observational
External_validity
Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series
History_of_calculus
Discrete (i.e., incremental) version of infinitesimal calculus
Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of
Discrete_calculus
Simple Turing complete logic
The SKI combinator calculus is a combinatory logic system and a computational system. It can be thought of as a computer programming language, though it
SKI_combinator_calculus
Family of approaches for modelling concurrent systems
additions to the family include the π-calculus, the ambient calculus, PEPA, the fusion calculus and the join-calculus. While the variety of existing process
Process_calculus
Branch of functional analysis
functional analysis, a branch of mathematics, the Borel functional calculus is a functional calculus (that is, an assignment of operators from commutative algebras
Borel_functional_calculus
Topological space that locally resembles Euclidean space
manifolds are differentiable manifolds; their differentiable structure allows calculus to be done. A Riemannian metric on a manifold allows distances and angles
Manifold
Extremely small quantity in calculus; thing so small that there is no way to measure it
Calculus textbooks based on infinitesimals include the classic Calculus Made Easy by Silvanus P. Thompson (bearing the motto "What one fool can do another
Infinitesimal
How one process influences another
intervention. The theory of "causal calculus" (also known as do-calculus, Judea Pearl's Causal Calculus, Calculus of Actions) permits one to infer interventional
Causality
Concept in mathematics
of the tangent bundle and the cotangent bundle of that manifold. To do calculus on the tensor bundle a connection is needed, except for the special case
Tensor_bundle
Calculus of stochastic differential equations
Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important
Itô_calculus
Infinitesimal calculus on functions defined on a geometric algebra
In mathematics, geometric calculus extends geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to
Geometric_calculus
Differential calculus on function spaces
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and
Calculus_of_variations
Coordinates comprising a distance and an angle
radians throughout this section, which is the conventional choice when doing calculus. Using x = r cos φ and y = r sin φ, one can derive a relationship between
Polar_coordinate_system
Notation to express cause and effect
products. Do-calculus, and specifically the do operator, is used to describe causal relationships in the language of probability. A notation used in do-calculus
Causal_notation
Theory allowing one to apply mathematical functions to mathematical operators
In mathematics, a functional calculus is a theory allowing one to apply mathematical functions to mathematical operators. It is now a branch (more accurately
Functional_calculus
Directed graph that models causal relationships between variables
S2CID 1612893. Bareinmboim, Elias; Pearl, Judea (2014). "External Validity: From do-calculus to Transportability across Populations". Statistical Science. 29 (4):
Causal_graph
Comic character by Belgian cartoonist Hergé
Professor Cuthbert Calculus (French: Professeur Tryphon Tournesol [pʁɔ.fɛ.sœʁ tʁi.fɔ̃ tuʁ.nə.sɔl], meaning 'Professor Tryphon Sunflower' or, more scientifically
Professor_Calculus
Formation of mineral deposits in the kidneys
they may pass out of the urinary tract through the urine stream. A small calculus may pass without causing any symptoms. However, if a stone grows to more
Kidney_stone_disease
Branch of mathematical analysis
Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number
Fractional_calculus
Bias in causal inference
(3) is valid. Pearl's do-calculus provides all possible conditions under which P ( y ∣ do ( x ) ) {\displaystyle P(y\mid {\text{do}}(x))} can be estimated
Confounding
Logic formalism
The situation calculus is a logic formalism designed for representing and reasoning about dynamical domains. It was first introduced by John McCarthy in
Situation_calculus
Probabilistic graphical representation of causal relationships
with unobserved variables, one can use the three rules of "do-calculus" and test whether all do terms can be removed from the expression of that relation
Bayesian_network
Branch of statistics
(component-cause), Pearl's structural causal model (causal diagram + do-calculus), structural equation modeling, and Rubin causal model (potential-outcome)
Causal_inference
Discrete analog of a derivative
including Isaac Newton. The formal calculus of finite differences can be viewed as an alternative to the calculus of infinitesimals. Three basic types
Finite_difference
Greek mathematician and physicist (c. 287 – 212 BC)
the greatest mathematicians of all time. Archimedes anticipated modern calculus and analysis by applying the concept of the infinitesimals and the method
Archimedes
Tensor index notation for tensor-based calculations
used to be called the absolute differential calculus (the foundation of tensor calculus), tensor calculus or tensor analysis developed by Gregorio Ricci-Curbastro
Ricci_calculus
Mathematical model that predicts voting behaviour
Calculus of voting refers to any mathematical model which predicts voting behaviour by an electorate, including such features as participation rate. A
Calculus_of_voting
Process calculus
In theoretical computer science, the π-calculus (or pi-calculus) is a process calculus. The π-calculus allows channel names to be communicated along the
Π-calculus
tangent to the vector manifold. Vector manifolds were introduced to do calculus on manifolds so one can define (differentiable) manifolds as a set isomorphic
Universal_geometric_algebra
Formal system in mathematical logic
typed lambda calculus ( λ → {\displaystyle \lambda ^{\to }} ), a form of type theory, is a typed interpretation of the lambda calculus with only one
Simply_typed_lambda_calculus
Mathematics of Ancient Greece and the Mediterranean, 5th BC to 6th AD
ISBN (link) Knorr 1996, pp. 67–88. Powers, J. (2020). Did Archimedes do calculus? History of Mathematics Special Interest Group of the MAA [1] Stein,
Ancient_Greek_mathematics
The join-calculus is a process calculus developed at INRIA. The join-calculus was developed to provide a formal basis for the design of distributed programming
Join-calculus
Operation in mathematical calculus
integral, called integration, is one of the two fundamental operations of calculus, along with differentiation. Integration was initially used to solve problems
Integral
Graphical language for quantum processes
The ZX-calculus is a graphical language. It was conceived for reasoning about linear maps between qubits, which are represented as string diagrams called
ZX-calculus
Mathematical notion of infinitesimal difference
differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives
Differential_(mathematics)
Algorithm in utilitarian ethics
The felicific calculus is an algorithm formulated by utilitarian philosopher Jeremy Bentham (1748–1832) for calculating the degree or amount of pleasure
Felicific_calculus
Style of formal logical argumentation
In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a
Sequent_calculus
Mathematical identities
are important identities involving derivatives and integrals in vector calculus. For a function f ( x , y , z ) {\displaystyle f(x,y,z)} in three-dimensional
Vector_calculus_identities
Indian ophthalmologist, educator and researcher
Buffalo, New York when he was three. According to his parents, Ambati was doing calculus at the age of four. The family later moved to Orangeburg, South Carolina
Balamurali_Ambati
Higher-order function Y for which Y f = f (Y f)
this way, the Y combinator implements simple recursion. The lambda calculus does not allow a function to appear as a term in its own definition as is
Fixed-point_combinator
Logical formalism using combinators instead of variables
Y\not \Vdash B} . Let A be any formula which is not provable in the calculus. Then A does not belong to the deductive closure X of the empty set, thus X ⊮
Combinatory_logic
Branch of logic
classical logic. It is also called statement logic, sentential calculus, propositional calculus, sentential logic, or sometimes zeroth-order logic. Sometimes
Propositional_logic
Physical Simulations". arXiv:2001.02892 [cs.CE]. Judea Pearl (2012). "The Do-Calculus Revisited". Proceedings of the Twenty-Eighth Conference on Uncertainty
Multifidelity_simulation
Extension of propositional modal logic
theoretical computer science, the modal μ-calculus (Lμ, Lμ, or propositional mu-calculus, sometimes just μ-calculus, although this can have a more general
Modal_μ-calculus
Circulation density in a vector field
In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional
Curl_(mathematics)
Calculus of functions generalization
In mathematics, calculus on Euclidean space is a generalization of calculus of functions in one or several variables to calculus of functions on Euclidean
Calculus_on_Euclidean_space
English polymath (1642–1727)
Gottfried Wilhelm Leibniz for formulating infinitesimal calculus, although he developed calculus years before Leibniz. Newton contributed to and refined
Isaac_Newton
Pair of small club-shaped insect organs
"How Flies Fly". Wired. Gorman, James (19 March 2014). "Flies That Do Calculus With Their Wings". The New York Times. ProQuest 1785778888. "Understanding
Halteres
Formalism for expressing dynamical domains in first-order logic
The fluent calculus is a formalism for expressing dynamical domains in first-order logic. It is a variant of the situation calculus; the main difference
Fluent_calculus
System for describing optical polarization
In optics, polarized light can be described using the Jones calculus, invented by R. C. Jones in 1941. Polarized light is represented by a Jones vector
Jones_calculus
March 2026. For the 2024 Conservative Party leadership election, Electoral Calculus conducted a multilevel regression with poststratification (MRP) opinion
Opinion polling for the next United Kingdom general election
Opinion_polling_for_the_next_United_Kingdom_general_election
Pattern calculus bases all computation on pattern matching of a very general kind. Like lambda calculus, it supports a uniform treatment of function evaluation
Pattern_calculus
Subset of lambda calculus
computer science, kappa calculus is a formal system for defining first-order functions. Unlike lambda calculus, kappa calculus has no higher-order functions;
Kappa_calculus
Mathematical formalism
The lambda calculus is a formal mathematical system consisting of constructing lambda terms and performing reduction operations on them. The definition
Lambda_calculus_definition
Visual mathematical proofs
Visual calculus, invented by Mamikon Mnatsakanian (known as Mamikon), is an approach to solving a variety of integral calculus problems. Many problems
Visual_calculus
Statistical paradox
differences between groups and (2) Why the data appear paradoxical. Pearl's do-calculus further answers question (1) for any causal model assumed, including
Lord's_paradox
Mathematical notation used for calculus
dy dx d2y dx2 In calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz, uses
Leibniz's_notation
Light rays follow quickest paths
Instinct contains a chapter, "Elvis the Welsh Corgi Who Can Do Calculus", that discusses the calculus "embedded" in some animals as they solve the "least time"
Fermat's_principle
writing definitions for existing ones. This glossary of calculus is a list of definitions about calculus, its sub-disciplines, and related fields. Contents:
Glossary_of_calculus
Theorem in theoretical computer science
lambda calculus, the Church–Rosser theorem states that, when applying reduction rules to terms, the ordering in which the reductions are chosen does not
Church–Rosser_theorem
Framework in lambda calculus
the different dimensions in which the calculus of constructions is a generalization of the simply typed λ-calculus. Each dimension of the cube corresponds
Lambda_cube
Formula for the derivative of a product
In calculus, the product rule (or Leibniz rule or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions
Product_rule
Language for reasoning and representing events
The event calculus is a logical theory for representing and reasoning about events and about the way in which they change the state of some real or artificial
Event_calculus
Modern application of infinitesimals
mathematics, nonstandard calculus is the modern application of infinitesimals, in the sense of nonstandard analysis, to infinitesimal calculus. It provides a rigorous
Nonstandard_calculus
German polymath (1646–1716)
diplomat who is credited, alongside Isaac Newton, with the creation of calculus in addition to many other branches of mathematics, such as binary arithmetic
Gottfried_Wilhelm_Leibniz
Extension of a formal language by the epsilon operator
In logic, Hilbert's epsilon calculus is an extension of a formal language by the epsilon operator, where the epsilon operator substitutes for quantifiers
Epsilon_calculus
Field of knowledge
names or are otherwise commonly considered part of geometry. Algebra and calculus do not appear as first-level areas but are split into several first-level
Mathematics
Quantity of a three-dimensional space
formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. Zero-, one- and two-dimensional
Volume
1943 paper proposing artificial neural networks
"A Logical Calculus of the Ideas Immanent in Nervous Activity" is a 1943 paper written by Warren Sturgis McCulloch and Walter Pitts, published in the journal
A Logical Calculus of the Ideas Immanent in Nervous Activity
A_Logical_Calculus_of_the_Ideas_Immanent_in_Nervous_Activity
Collection of notes
mathematical notes where he attempted to derive the foundations of infinitesimal calculus from first principles. The notes that Marx took have been collected into
Mathematical manuscripts of Karl Marx
Mathematical_manuscripts_of_Karl_Marx
Calculus of predispositions is a basic part of predispositioning theory and belongs to the indeterministic procedures. "The key component of any indeterministic
Calculus_of_predispositions
Multivariate derivative (mathematics)
In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued
Gradient
Intelligence of machines
(1998, chpt. 18.3) Representing events and time:Situation calculus, event calculus, fluent calculus (including solving the frame problem): Russell & Norvig
Artificial_intelligence
Globalization meta-process
calculus and programs written as functions. However it does not demonstrate the soundness of lambda calculus for deduction, as the eta reduction used in lambda
Lambda_lifting
Notation of differential calculus
In differential calculus, there is no single standard notation for differentiation. Instead, several notations for the derivative of a function or a dependent
Notation_for_differentiation
calculus of structures (CoS) is a proof calculus with deep inference for studying the structural proof theory of noncommutative logic. The calculus has
Calculus_of_structures
Typed lambda calculus
polymorphic lambda calculus or second-order lambda calculus) is a typed lambda calculus that introduces, to simply typed lambda calculus, a mechanism of
System_F
Norwegian economist and Nobel Laureate (1911–1999)
Pearl's "do"-calculus and to a mathematical theory of counterfactuals in econometric models. Pearl further speculates that the reason economists do not generally
Trygve_Haavelmo
API Calculus is a program that solves calculus problems using operating systems within a device. In 1989, the PI Calculus was created by Robin Milner
API-Calculus
Theoretical framework for analysing performance guarantees in computer networks
Network calculus is "a set of mathematical results which give insights into man-made systems such as concurrent programs, digital circuits and communication
Network_calculus
DO CALCULUS
DO CALCULUS
Boy/Male
Muslim
To do with paper, Leaf
Boy/Male
Arabic, Malaysian, Muslim
Well to do; Wealthy
Boy/Male
Indian, Sanskrit
Who do Great Things
Boy/Male
Indian, Sanskrit, Tamil
Leader; Do Anything
Girl/Female
Hindu
A way to do work
Girl/Female
Gujarati, Hindu, Indian, Sanskrit
Right Thing to do
Girl/Female
Indian
Will to do
Girl/Female
Bengali, Indian
To do Something
Boy/Male
Tamil
Capable to do anything
Boy/Male
Hindu
Capable to do anything
Girl/Female
Hindu, Indian
Never do Bad
Boy/Male
Hindu
Capable to do anything
Boy/Male
Tamil
Hitakrit | ஹிதாகà¯à®°à®¿à®¤Â
Well wisher, Well to do
Hitakrit | ஹிதாகà¯à®°à®¿à®¤Â
Boy/Male
Indian, Tamil
Planner; Plan to do
Girl/Female
African, Australian, Ghana
First Child After Twins; From Ewe
Boy/Male
Tamil
Capable to do anything
Boy/Male
Muslim/Islamic
To do something which others cannot do; a miracle; inimitability
Boy/Male
Hindu
Well wisher, Well to do
Boy/Male
English, Modern
A Miracle; Inimitably; Do Something which Others cannot do
Girl/Female
Tamil
Shelly | ஷேலà¯à®²à¯€  Â
A way to do work
DO CALCULUS
DO CALCULUS
Boy/Male
Welsh
Guardian of the sea. Great chief. This name can be given to children of either gender, but is...
Girl/Female
Indian
Near of heart
Girl/Female
Tamil
Limitless, Boundless, Unmeasurable, Infinite, Eternal
Girl/Female
Indian
The First Person; The Winner in Every Thing; Beauty Like a Sunshine
Boy/Male
Hebrew American English
Promise.
Surname or Lastname
English
English : unexplained.
Female
Native American
Native American Hopi name ZIHNA means "spins."
Boy/Male
Greek
Christ bearer.
Boy/Male
American, Australian, French, German
Nobility
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu
New
DO CALCULUS
DO CALCULUS
DO CALCULUS
DO CALCULUS
DO CALCULUS
2d pers. sing. pres.
of Do.
v. t. / auxiliary
To cheat; to gull; to overreach.
n.
Deed; act; fear.
v. t. / auxiliary
To bring to an end by action; to perform completely; to finish; to accomplish; -- a sense conveyed by the construction, which is that of the past participle done.
v. t. / auxiliary
To put or bring into a form, state, or condition, especially in the phrases, to do death, to put to death; to slay; to do away (often do away with), to put away; to remove; to do on, to put on; to don; to do off, to take off, as dress; to doff; to do into, to put into the form of; to translate or transform into, as a text.
v. i.
To succeed; to avail; to answer the purpose; to serve; as, if no better plan can be found, he will make this do.
imp.
of Do
v. i.
To act or behave in any manner; to conduct one's self.
p. pr. & vb. n.
of Do
n.
Ado; bustle; stir; to do.
v. i.
To fare; to be, as regards health; as, they asked him how he did; how do you do to-day?
v. t. / auxiliary
To cash or to advance money for, as a bill or note.
v. t. / auxiliary
To see or inspect; to explore; as, to do all the points of interest.
n.
Alt. of Do-nothingness
n.
A cheat; a swindle.
v. t. / auxiliary
To perform, as an action; to execute; to transact to carry out in action; as, to do a good or a bad act; do our duty; to do what I can.
a.
Doing nothing; inactive; idle; lazy; as, a do-nothing policy.
p. p.
of Do
3d pers. sing. pres.
of Do.
v. t. / auxiliary
To make ready for an object, purpose, or use, as food by cooking; to cook completely or sufficiently; as, the meat is done on one side only.