The superposition calculus is a calculus for reasoning in equational logic. It was developed in the early 1990s and combines concepts from first-order resolution with ordering-based equality handling as developed in the context of (unfailing) Knuth–Bendix completion. It can be seen as a generalization of either resolution (to equational logic) or unfailing completion (to full clausal logic). Like most first-order calculi, superposition tries to show the unsatisfiability of a set of first-order clauses, i.e. it performs proofs by refutation. Superposition is refutation complete—given unlimited resources and a fair derivation strategy, from any unsatisfiable clause set a contradiction will eventually be derived.
Many (state-of-the-art) theorem provers for first-order logic are based on superposition (e.g. the E equational theorem prover), although only a few implement the pure calculus.
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The superpositioncalculus is a calculus for reasoning in equational logic. It was developed in the early 1990s and combines concepts from first-order...
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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:...
Computer Science and using the superpositioncalculus. The name originally stood for Synergetic Prover Augmenting Superposition with Sorts. The theorem-proving...
context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis...
Mueller calculus is a matrix method for manipulating Stokes vectors, which represent the polarization of light. It was developed in 1943 by Hans Mueller...
instead that quantum-mechanical phenomena, such as entanglement and superposition that cause nonlocalized quantum effects, interacting in smaller features...
computer scientist who together with Leo Bachmair developed the superpositioncalculus, which is (as of 2007) used in most of the state-of-the-art automated...
Quantum calculus, sometimes called calculus without limits, is equivalent to traditional infinitesimal calculus without the notion of limits. The two...
The general solution to the electromagnetic wave equation is a linear superposition of waves of the form E ( r , t ) = g ( ϕ ( r , t ) ) = g ( ω t − k ⋅...
known as Faltung (which means folding in German), composition product, superposition integral, and Carson's integral. Yet it appears as early as 1903, though...
that just a few terms already produce a fairly good approximation. The superposition of several terms in the expansion of a sawtooth wave are shown underneath...
distinguish between an "input" and "output" of a process. In the diagrammatic calculus, it allows wires to be bent, allowing for a less restricted transfer of...
function of being compatible with addition and scaling, also known as the superposition principle. Linearity of a polynomial means that its degree is less than...
AC circuits magnetic and electric fields in matter wave properties superposition interference diffraction geometrical optics light polarization Doppler...
box description. A system is linear if and only if it satisfies the superposition principle, or equivalently both the additivity and homogeneity properties...
are known as the retarded Lorenz gauge potentials. They represent a superposition of spherical light waves traveling outward from the sources of the waves...
strike", and was used in the context of wave superposition by Thomas Young in 1801. The principle of superposition of waves states that when two or more propagating...
Daniel was the son of Johann Bernoulli (one of the early developers of calculus) and a nephew of Jacob Bernoulli (an early researcher in probability theory...
known as linearity of differentiation, the rule of linearity, or the superposition rule for differentiation. It is a fundamental property of the derivative...
representation. This power series expresses a function as a linear superposition of moments of the function. This perspective has applications in probability...
definition because, as Remmert 2012 explains, differential calculus typically precedes integral calculus in the university curriculum, so it is desirable to...
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