Table of Contents
49 relations: Academic Press, Affine transformation, Algebra of sets, Arity, Boolean algebra, Boolean algebra (structure), Boolean domain, Boolean expression, Boolean function, Cambridge University Press, Charles Sanders Peirce, Clone (algebra), De Morgan's laws, Digital electronics, Disjunctive normal form, Emil Leon Post, Fredkin gate, Hadamard transform, Henry M. Sheffer, Isomorphism, Lattice (order), Logic gate, Logical biconditional, Logical conjunction, Logical connective, Logical disjunction, Logical NOR, Majority function, Material conditional, Mathematical logic, McGraw Hill Education, Monotonic function, NAND gate, Negation, NOR gate, Post's lattice, Propositional calculus, Quantum computing, Reversible computing, Russell's paradox, Set (mathematics), Sheffer stroke, Singleton (mathematics), Subset, Toffoli gate, Truth table, Truth value, Unary operation, Universal set.
- Propositional calculus
Academic Press
Academic Press (AP) is an academic book publisher founded in 1941.
See Functional completeness and Academic Press
Affine transformation
In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles.
See Functional completeness and Affine transformation
Algebra of sets
In mathematics, the algebra of sets, not to be confused with the mathematical structure of ''an'' algebra of sets, defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion.
See Functional completeness and Algebra of sets
Arity
In logic, mathematics, and computer science, arity is the number of arguments or operands taken by a function, operation or relation.
See Functional completeness and Arity
Boolean algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra.
See Functional completeness and Boolean algebra
Boolean algebra (structure)
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. Functional completeness and Boolean algebra (structure) are boolean algebra.
See Functional completeness and Boolean algebra (structure)
Boolean domain
In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true. Functional completeness and Boolean domain are boolean algebra.
See Functional completeness and Boolean domain
Boolean expression
In computer science, a Boolean expression is an expression used in programming languages that produces a Boolean value when evaluated. Functional completeness and Boolean expression are boolean algebra.
See Functional completeness and Boolean expression
Boolean function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually, or). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Functional completeness and Boolean function are boolean algebra.
See Functional completeness and Boolean function
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge.
See Functional completeness and Cambridge University Press
Charles Sanders Peirce
Charles Sanders Peirce (September 10, 1839 – April 19, 1914) was an American scientist, mathematician, logician, and philosopher who is sometimes known as "the father of pragmatism".
See Functional completeness and Charles Sanders Peirce
Clone (algebra)
In universal algebra, a clone is a set C of finitary operations on a set A such that.
See Functional completeness and Clone (algebra)
De Morgan's laws
In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. Functional completeness and De Morgan's laws are boolean algebra.
See Functional completeness and De Morgan's laws
Digital electronics
Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them.
See Functional completeness and Digital electronics
Disjunctive normal form
In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or in philosophical logic a cluster concept.
See Functional completeness and Disjunctive normal form
Emil Leon Post
Emil Leon Post (February 11, 1897 – April 21, 1954) was an American mathematician and logician.
See Functional completeness and Emil Leon Post
Fredkin gate
The Fredkin gate (also controlled-SWAP gate and conservative logic gate) is a computational circuit suitable for reversible computing, invented by Edward Fredkin.
See Functional completeness and Fredkin gate
Hadamard transform
The Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an example of a generalized class of Fourier transforms.
See Functional completeness and Hadamard transform
Henry M. Sheffer
Henry Maurice Sheffer (1 September 1882 – 17 March 1964) was an American logician.
See Functional completeness and Henry M. Sheffer
Isomorphism
In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping.
See Functional completeness and Isomorphism
Lattice (order)
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.
See Functional completeness and Lattice (order)
Logic gate
A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Functional completeness and logic gate are Charles Sanders Peirce.
See Functional completeness and Logic gate
Logical biconditional
In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used to conjoin two statements P and Q to form the statement "P if and only if Q" (often abbreviated as "P iff Q"), where P is known as the antecedent, and Q the consequent.
See Functional completeness and Logical biconditional
Logical conjunction
In logic, mathematics and linguistics, and (\wedge) is the truth-functional operator of conjunction or logical conjunction.
See Functional completeness and Logical conjunction
Logical connective
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant.
See Functional completeness and Logical connective
Logical disjunction
In logic, disjunction, also known as logical disjunction or logical or or logical addition or inclusive disjunction, is a logical connective typically notated as \lor and read aloud as "or".
See Functional completeness and Logical disjunction
Logical NOR
In Boolean logic, logical NOR, non-disjunction, or joint denial is a truth-functional operator which produces a result that is the negation of logical or. Functional completeness and logical NOR are Charles Sanders Peirce.
See Functional completeness and Logical NOR
Majority function
In Boolean logic, the majority function (also called the median operator) is the Boolean function that evaluates to false when half or more arguments are false and true otherwise, i.e. the value of the function equals the value of the majority of the inputs. Functional completeness and majority function are boolean algebra.
See Functional completeness and Majority function
Material conditional
The material conditional (also known as material implication) is an operation commonly used in logic.
See Functional completeness and Material conditional
Mathematical logic
Mathematical logic is the study of formal logic within mathematics.
See Functional completeness and Mathematical logic
McGraw Hill Education
McGraw Hill is an American publishing company for educational content, software, and services for pre-K through postgraduate education.
See Functional completeness and McGraw Hill Education
Monotonic function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.
See Functional completeness and Monotonic function
NAND gate
In digital electronics, a NAND gate (NOT-AND) is a logic gate which produces an output which is false only if all its inputs are true; thus its output is complement to that of an AND gate.
See Functional completeness and NAND gate
Negation
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P to another proposition "not P", standing for "P is not true", written \neg P, \mathord P or \overline.
See Functional completeness and Negation
NOR gate
The NOR gate is a digital logic gate that implements logical NOR - it behaves according to the truth table to the right.
See Functional completeness and NOR gate
Post's lattice
In logic and universal algebra, Post's lattice denotes the lattice of all clones on a two-element set, ordered by inclusion.
See Functional completeness and Post's lattice
Propositional calculus
The propositional calculus is a branch of logic. Functional completeness and propositional calculus are boolean algebra.
See Functional completeness and Propositional calculus
Quantum computing
A quantum computer is a computer that exploits quantum mechanical phenomena.
See Functional completeness and Quantum computing
Reversible computing
Reversible computing is any model of computation where the computational process, to some extent, is time-reversible.
See Functional completeness and Reversible computing
Russell's paradox
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician Bertrand Russell in 1901.
See Functional completeness and Russell's paradox
Set (mathematics)
In mathematics, a set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
See Functional completeness and Set (mathematics)
Sheffer stroke
In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both".
See Functional completeness and Sheffer stroke
Singleton (mathematics)
In mathematics, a singleton (also known as a unit set or one-point set) is a set with exactly one element.
See Functional completeness and Singleton (mathematics)
Subset
In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment).
See Functional completeness and Subset
Toffoli gate
In logic circuits, the Toffoli gate, also known as the CCNOT gate (“controlled-controlled-not”), invented by Tommaso Toffoli, is a CNOT gate with two control qubits and one target qubit.
See Functional completeness and Toffoli gate
Truth table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. Functional completeness and truth table are boolean algebra and propositional calculus.
See Functional completeness and Truth table
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, which in classical logic has only two possible values (true or false).
See Functional completeness and Truth value
Unary operation
In mathematics, a unary operation is an operation with only one operand, i.e. a single input.
See Functional completeness and Unary operation
Universal set
In set theory, a universal set is a set which contains all objects, including itself.
See Functional completeness and Universal set
See also
Propositional calculus
- Clause (logic)
- Deductive closure
- DiVincenzo's criteria
- Formation rule
- Frege system
- Frege's propositional calculus
- Functional completeness
- Implicational propositional calculus
- Intermediate logic
- List of axiomatic systems in logic
- Literal (mathematical logic)
- Logical connectives
- Logical consequence
- Minimal axioms for Boolean algebra
- Negation introduction
- Negation normal form
- Nicod's axiom
- Predicate (mathematical logic)
- Predicate logic
- Principle of distributivity
- Proposition
- Propositional attitudes
- Propositional calculus
- Propositional formula
- Propositional proof system
- Propositional variable
- Propositions
- Resolution (logic)
- Rule of inference
- Rule of replacement
- Rules of inference
- Second-order propositional logic
- Stoic logic
- Substitution (logic)
- Suppes–Lemmon notation
- Tautology (logic)
- Truth table
- Unsatisfiable core
- Wholistic reference
References
Also known as Adequacy (logic), Complete set of Boolean operators, Expressive adequacy, Functionally complete, Post's criterion, Post's functional completeness theorem, Sole sufficient operator, Sufficiently connected.