This is a list of topics around Boolean algebra and propositional logic.
Articles with a wide scope and introductions
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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 ...
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Boolean algebra (structure)
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a gen ...
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Boolean algebra
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Field of sets
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Logical connective
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Propositional calculus
Boolean functions and connectives
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Ampheck
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Analysis of Boolean functions
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Balanced boolean function In mathematics and computer science, a balanced boolean function is a boolean function whose output yields as many 0s as 1s over its input set. This means that for a uniformly random input string of bits, the probability of getting a 1 is 1/2.
Exa ...
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Bent function
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Boolean algebras canonically defined
:''Boolean algebras are models of the equational theory of two values; this definition is equivalent to the lattice and ring definitions.''
Boolean algebra is a mathematically rich branch of abstract algebra. ''Stanford Encyclopaedia of Philosoph ...
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Boolean function
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Boolean matrix
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Boolean-valued function
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Conditioned disjunction
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Evasive Boolean function
In mathematics, an evasive Boolean function ''ƒ'' (of ''n'' variables) is a Boolean function for which every decision tree algorithm has running time of exactly ''n''. Consequently, every decision tree algorithm that represents the fun ...
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Exclusive or
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Functional completeness
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Logical biconditional
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Logical conjunction
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Logical disjunction
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Logical equality
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Logical implication
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Logical negation
In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P, \mathord P or \overline. It is interpreted intuitively as being true when P is false, and false ...
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Logical NOR
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Lupanov representation
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Majority function
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Material conditional
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Minimal axioms for Boolean algebra
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Peirce arrow
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Read-once function In mathematics, a read-once function is a special type of Boolean function that can be described by a Boolean expression in which each Variable (mathematics), variable appears only once.
More precisely, the expression is required to use only the op ...
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Sheffer stroke
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Sole sufficient operator
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Symmetric Boolean function In mathematics, a symmetric Boolean function is a Boolean function whose value does not depend on the order of its input bits, i.e., it depends only on the number of ones (or zeros) in the input.Ingo Wegener, "The Complexity of Symmetric Boolean F ...
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Symmetric difference
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Zhegalkin polynomial
Zhegalkin (also Žegalkin, Gégalkine or Shegalkin) polynomials (russian: полиномы Жегалкина), also known as algebraic normal form, are a representation of functions in Boolean algebra. Introduced by the Russian mathematician Iva ...
Examples of Boolean algebras
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Boolean domain
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Complete Boolean algebra
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Interior algebra In abstract algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are to topology and the modal logic S4 what Boolean algebras are to set theory and o ...
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Two-element Boolean algebra
Extensions of Boolean algebras
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Derivative algebra (abstract algebra) In abstract algebra, a derivative algebra is an algebraic structure of the signature
:
where
:
is a Boolean algebra and D is a unary operator, the derivative operator, satisfying the identities:
# 0D = 0
# ''x'' ...
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Free Boolean algebra In mathematics, a free Boolean algebra is a Boolean algebra with a distinguished set of elements, called ''generators'', such that:
#Each element of the Boolean algebra can be expressed as a finite combination of generators, using the Boolean opera ...
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Monadic Boolean algebra
Generalizations of Boolean algebras
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De Morgan algebra
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First-order logic
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Heyting algebra
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Lindenbaum–Tarski algebra
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Skew Boolean algebra
Syntax
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Algebraic normal form
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Boolean conjunctive query In the theory of relational databases, a Boolean conjunctive query is a conjunctive query without distinguished predicates, i.e., a query in the form R_1(t_1) \wedge \cdots \wedge R_n(t_n), where each R_i is a relation symbol and each t_i is a tupl ...
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Canonical form (Boolean algebra)
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Conjunctive normal form
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Disjunctive normal form
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Formal system
Technical applications
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And-inverter graph
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Logic gate
A logic gate is an idealized or physical device implementing a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, ...
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Boolean analysis
Theorems and specific laws
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Boolean prime ideal theorem
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Compactness theorem
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Consensus theorem
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De Morgan's laws
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Duality (order theory)
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Laws of classical logic
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Peirce's law
In logic, Peirce's law is named after the philosopher and logician Charles Sanders Peirce. It was taken as an axiom in his first axiomatisation of propositional logic. It can be thought of as the law of excluded middle written in a form tha ...
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Stone's representation theorem for Boolean algebras
In mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem is fundamental to the deeper understanding of Boolean algebra that emerged in the first hal ...
People
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Boole, George
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De Morgan, Augustus
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Jevons, William Stanley
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Peirce, Charles Sanders
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Stone, Marshall Harvey
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Venn, John
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Zhegalkin, Ivan Ivanovich
Philosophy
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Boole's syllogistic
Boolean logic is a system of syllogistic logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the "empty set", that is, a class of non-existent entities, such as round squares, without resorting to un ...
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Boolean implicant
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Entitative graph
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Existential graph
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Laws of Form''
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Logical graph
Visualization
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Truth table
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Karnaugh map
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Venn diagram
Unclassified
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Boolean function
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Boolean-valued function
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Boolean-valued model
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Boolean satisfiability problem
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Boolean differential calculus
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Indicator function
In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. That is, if is a subset of some set , one has \mathbf_(x)=1 if x\i ...
(also called the ''characteristic function'', but that term is used in probability theory for a different concept)
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Espresso heuristic logic minimizer
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Logical matrix
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Logical value
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Stone duality
In mathematics, there is an ample supply of categorical dualities between certain categories of topological spaces and categories of partially ordered sets. Today, these dualities are usually collected under the label Stone duality, since they fo ...
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Stone space
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Topological Boolean algebra
{{Order theory
Boolean algebra
Boolean algebra
Boolean algebra