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Calculus of structures information


In mathematical logic, the calculus of structures is a proof calculus with deep inference for studying the structural proof theory of noncommutative logic. The calculus has since been applied to study linear logic, classical logic, modal logic, and process calculi, and many benefits are claimed to follow in these investigations from the way in which deep inference is made available in the calculus.

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Calculus of structures

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the calculus of structures is a proof calculus with deep inference for studying the structural proof theory of noncommutative logic. The calculus has...

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Proof calculus

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hypersequents, the calculus of structures, and bunched implication. Propositional proof system Proof nets Cirquent calculus Calculus of structures Formal proof...

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Calculus

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Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations...

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Structural proof theory

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notion of normal form in term rewriting. The term structure in structural proof theory comes from a technical notion introduced in the sequent calculus: the...

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Noncommutative logic

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proof calculus, the calculus of structures to accommodate the calculus. The principal novelty of the calculus of structures was its pervasive use of deep...

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Multivariable calculus

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Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables:...

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Simply typed lambda calculus

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typed lambda calculus ( λ → {\displaystyle \lambda ^{\to }} ), a form of type theory, is a typed interpretation of the lambda calculus with only one...

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Vector calculus

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Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional...

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AP Calculus

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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...

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Deep inference

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breaks with the classical sequent calculus by generalising the notion of structure to permit inference to occur in contexts of high structural complexity. The...

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Discrete mathematics

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study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural...

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Fundamental theorem of calculus

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fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point...

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Lambda calculus

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Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application...

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Typed lambda calculus

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Structures. Handbook of Logic in Computer Science. Vol. 2. Oxford University Press. pp. 117–309. ISBN 9780198537618. Brandl, Helmut (2022). Calculus of...

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Discrete calculus

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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 shape...

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Stochastic calculus

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Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals...

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Differentiable manifold

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type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts...

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Cirquent calculus

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logic”. Logic Journal of the IGPL 20 (2012), pp. 317–330. W.Xu and S.Liu, “Cirquent calculus system CL8S versus calculus of structures system SKSg for propositional...

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Knights of the Lambda Calculus

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The Knights of the Lambda Calculus is a semi-fictional organization of expert Lisp and Scheme hackers. The name refers to the lambda calculus, a mathematical...

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Propositional calculus

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The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes...

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Kidney stone disease

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known as renal calculus disease, nephrolithiasis or urolithiasis, is a crystallopathy where a solid piece of material (renal calculus) develops in the...

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Ricci calculus

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In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with...

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Integral

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process of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation. Integration was initially used to solve...

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Process calculus

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examples of process calculi include CSP, CCS, ACP, and LOTOS. More recent additions to the family include the π-calculus, the ambient calculus, PEPA, the...

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SKI combinator calculus

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The SKI combinator calculus is a combinatory logic system and a computational system. It can be thought of as a computer programming language, though...

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Mathematical analysis

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context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis...

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Interaction nets

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massive parallelism. Interaction nets are at the heart of many implementations of the lambda calculus, such as efficient closed reduction and optimal, in...

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