In mathematical logic, a proofcalculus or a proof system is built to prove statements. A proof system includes the components: Formal language: The set...
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...
derivatives. The calculus has applications in, for example, stochastic filtering. Malliavin introduced Malliavin calculus to provide a stochastic proof that Hörmander's...
actually closely related. From the conjecture and the proof of the fundamental theorem of calculus, calculus as a unified theory of integration and differentiation...
In logic and proof theory, natural deduction is a kind of proofcalculus in which logical reasoning is expressed by inference rules closely related to...
the calculus of structures is a proofcalculus with deep inference for studying the structural proof theory of noncommutative logic. The calculus has...
has proved very important in proof theory. Gentzen (1934) further introduced the idea of the sequent calculus, a calculus advanced in a similar spirit...
we can always find a proof of a given sentence or determine that none exists. The concepts of Fitch-style proof, sequent calculus and natural deduction...
Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application...
The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes...
and other proof assistants. Some of its variants include the calculus of inductive constructions (which adds inductive types), the calculus of (co)inductive...
and in particular proof theory, a proof procedure for a given logic is a systematic method for producing proofs in some proofcalculus of (provable) statements...
This is a list of calculus topics. Limit (mathematics) Limit of a function One-sided limit Limit of a sequence Indeterminate form Orders of approximation...
distinguishes proof nets from regular proof calculi such as the natural deduction calculus and the sequent calculus, where these phenomena are present. Proof nets...
normalization of the underlying calculus if there is one) implies the consistency of the calculus: since there is no cut-free proof of falsity, there is no contradiction...
system based on the Calculus of Inductive Constructions. MINLOG – A proof assistant based on first-order minimal logic. Mizar – A proof assistant based on...
for several proof calculi there is an accepted notion. For example: In Gerhard Gentzen's natural deduction calculus the analytic proofs are those in...
called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns...
Retoré's calculus, BV, in which the two noncommutative operations are collapsed onto a single, self-dual, operator, and proposed a novel proofcalculus, the...
exponential-time algorithms are believed to exist for general proof tasks. For a first-order predicate calculus, Gödel's completeness theorem states that the theorems...
Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables:...
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The...
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...
Branch of mathematical logic Visual calculus – Visual mathematical proofs Dunham 1994, p. 120 Weisstein, Eric W. "Proof without Words". MathWorld. Retrieved...
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