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Quantifier elimination

Index Quantifier elimination

Quantifier elimination is a concept of simplification used in mathematical logic, model theory, and theoretical computer science. [1]

32 relations: Abelian group, Algebraically closed field, Algorithm, Binary relation, Boolean algebra (structure), Conjunction elimination, Decidability (logic), Dense order, Differentially closed field, Disjunctive normal form, Elimination theory, Fourier–Motzkin elimination, Fundamenta Mathematicae, Literal (mathematical logic), Logical equivalence, Mathematical logic, Model complete theory, Model theory, Modulo (jargon), Presburger arithmetic, Quantifier (logic), Queueing theory, Random graph, Real closed field, Sentence (mathematical logic), Simplification, Springer Science+Business Media, Tarski–Seidenberg theorem, Term algebra, Theoretical computer science, Truth value, Well-formed formula.

Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.

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Algebraically closed field

In abstract algebra, an algebraically closed field F contains a root for every non-constant polynomial in F, the ring of polynomials in the variable x with coefficients in F.

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Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

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Boolean algebra (structure)

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice.

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Conjunction elimination

In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, or simplification) is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true.

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Decidability (logic)

In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas, or, more precisely, an algorithm that can and will return a boolean true or false value that is correct (instead of looping indefinitely, crashing, returning "don't know" or returning a wrong answer).

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Dense order

In mathematics, a partial order or total order.

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Differentially closed field

In mathematics, a differential field K is differentially closed if every finite system of differential equations with a solution in some differential field extending K already has a solution in K. This concept was introduced by.

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Disjunctive normal form

In boolean logic, a disjunctive normal form (DNF) is a standardization (or normalization) of a logical formula which is a disjunction of conjunctive clauses; it can also be described as an OR of ANDs, a sum of products, or (in philosophical logic) a cluster concept.

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Elimination theory

In commutative algebra and algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating some variables between polynomials of several variables, in order to solve systems of polynomial equations.

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Fourier–Motzkin elimination

Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities.

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Fundamenta Mathematicae

Fundamenta Mathematicae is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic, topology and its interactions with algebra, and dynamical systems.

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Literal (mathematical logic)

In mathematical logic, a literal is an atomic formula (atom) or its negation.

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Logical equivalence

In logic, statements p and q are logically equivalent if they have the same logical content.

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Mathematical logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.

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Model complete theory

In model theory, a first-order theory is called model complete if every embedding of models is an elementary embedding.

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Model theory

In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.

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Modulo (jargon)

The word modulo (Latin, with respect to a modulus of ___) is the Latin ablative of modulus which itself means "a small measure." It was introduced into mathematics by Carl Friedrich Gauss in 1801.

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Presburger arithmetic

Presburger arithmetic is the first-order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who introduced it in 1929.

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Quantifier (logic)

In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula.

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Queueing theory

Queueing theory is the mathematical study of waiting lines, or queues.

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Random graph

In mathematics, random graph is the general term to refer to probability distributions over graphs.

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Real closed field

In mathematics, a real closed field is a field F that has the same first-order properties as the field of real numbers.

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Sentence (mathematical logic)

In mathematical logic, a sentence of a predicate logic is a boolean-valued well-formed formula with no free variables.

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Simplification

Simplification or Simplified may refer to.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Tarski–Seidenberg theorem

In mathematics, the Tarski–Seidenberg theorem states that a set in (n + 1)-dimensional space defined by polynomial equations and inequalities can be projected down onto n-dimensional space, and the resulting set is still definable in terms of polynomial identities and inequalities.

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Term algebra

In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature.

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Theoretical computer science

Theoretical computer science, or TCS, is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.

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Truth value

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.

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Well-formed formula

In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language.

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Redirects here:

Algorithms for quantifier elimination, Elimination of quantifiers, Quantifier Elimination.

References

[1] https://en.wikipedia.org/wiki/Quantifier_elimination

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