List of Boolean algebra topics

This is a list of topics around Boolean algebra and propositional logic.

## Articles with a wide scope and introductions

[edit]

* Algebra of sets
* Boolean algebra (structure)
* Boolean algebra
* Field of sets
* Logical connective
* Propositional calculus

## Boolean functions and connectives

[edit]

* Ampheck
* Analysis of Boolean functions
* Balanced Boolean function
* Bent function
* Boolean algebras canonically defined
* Boolean function
* Boolean matrix
* Boolean-valued function
* Conditioned disjunction
* Evasive Boolean function
* Exclusive or
* Functional completeness
* Logical biconditional
* Logical conjunction
* Logical disjunction
* Logical equality
* Logical implication
* Logical negation
* Logical NOR
* Lupanov representation
* Majority function
* Material conditional
* Minimal axioms for Boolean algebra
* Peirce arrow
* Read-once function
* Sheffer stroke
* Sole sufficient operator
* Symmetric Boolean function
* Symmetric difference
* Zhegalkin polynomial

## Examples of Boolean algebras

[edit]

* Boolean domain
* Complete Boolean algebra
* Interior algebra
* Two-element Boolean algebra

## Extensions of Boolean algebras

[edit]

* Derivative algebra (abstract algebra)
* Free Boolean algebra
* Monadic Boolean algebra

## Generalizations of Boolean algebras

[edit]

* De Morgan algebra
* First-order logic
* Heyting algebra
* Lindenbaum–Tarski algebra
* Skew Boolean algebra

## Syntax

[edit]

* Algebraic normal form
* Boolean conjunctive query
* Canonical form (Boolean algebra)
* Conjunctive normal form
* Disjunctive normal form
* Formal system

## Technical applications

[edit]

* And-inverter graph
* Logic gate
* Boolean analysis

## Theorems and specific laws

[edit]

* Boolean prime ideal theorem
* Compactness theorem
* Consensus theorem
* De Morgan's laws
* Duality (order theory)
* Laws of classical logic
* Peirce's law
* Stone's representation theorem for Boolean algebras

## People

[edit]

* Boole, George
* De Morgan, Augustus
* Jevons, William Stanley
* Peirce, Charles Sanders
* Stone, Marshall Harvey
* Venn, John
* Zhegalkin, Ivan Ivanovich

## Philosophy

[edit]

* Boole's syllogistic
* Boolean implicant
* Entitative graph
* Existential graph
* Laws of Form
* Logical graph

## Visualization

[edit]

* Truth table
* Karnaugh map
* Venn diagram

## Unclassified

[edit]

* Boolean function
* Boolean-valued function
* Boolean-valued model
* Boolean satisfiability problem
* Boolean differential calculus
* Indicator function (also called the characteristic function, but that term is used in probability theory for a different concept)
* Espresso heuristic logic minimizer
* Logical matrix
* Logical value
* Stone duality
* Stone space
* Topological Boolean algebra

* v
* t
* e

Logic

* History

Major fields|

* Computer science
* Formal semantics (natural language)
* Inference
* Philosophy of logic
* Proof
* Semantics of logic
* Syntax

| Logics|

* Classical
* Informal
* Critical thinking
* Reason
* Mathematical
* Non-classical
* Philosophical

|

Theories|

* Argumentation
* Metalogic
* Metamathematics
* Set

Foundations|

* Abduction
* Analytic and synthetic propositions
* Antecedent
* Consequent
* Contradiction
* Paradox
* Antinomy
* Deduction
* Deductive closure
* Definition
* Description
* Dichotomy
* Entailment
* Linguistic
* Form
* Induction
* Logical truth
* Name
* Necessity and sufficiency
* Premise
* Probability
* Proposition
* Reference
* Statement
* Substitution
* Truth
* Validity

Lists|

| Topics|

* Mathematical logic
* Boolean algebra
* Set theory

|

Other|

* Logicians
* Rules of inference
* Paradoxes
* Fallacies
* Logic symbols

* Category
* Outline
* Portal
* WikiProject
* changes

* v
* t
* e

Order theory

* Topics
* Glossary
* Category

Key concepts|

* Binary relation
* Boolean algebra
* Cyclic order
* Lattice
* Partial order
* Preorder
* Total order
* Weak ordering

Results|

* Boolean prime ideal theorem
* Cantor–Bernstein theorem
* Cantor's isomorphism theorem
* Dilworth's theorem
* Dushnik–Miller theorem
* Hausdorff maximal principle
* Knaster–Tarski theorem
* Kruskal's tree theorem
* Laver's theorem
* Mirsky's theorem
* Szpilrajn extension theorem
* Zorn's lemma

Properties & Types (list)|

* Antisymmetric
* Asymmetric
* Boolean algebra
* topics
* Completeness
* Connected
* Covering
* Dense
* Directed
* (Partial) Equivalence
* Foundational
* Heyting algebra
* Homogeneous
* Idempotent
* Lattice
* Bounded
* Complemented
* Complete
* Distributive
* Join and meet
* Reflexive
* Partial order
* Chain-complete
* Graded
* Eulerian
* Strict
* Prefix order
* Preorder
* Total
* Semilattice
* Semiorder
* Symmetric
* Total
* Tolerance
* Transitive
* Well-founded
* Well-quasi-ordering (Better)
* (Pre) Well-order

Constructions|

* Composition
* Converse/Transpose
* Lexicographic order
* Linear extension
* Product order
* Reflexive closure
* Series-parallel partial order
* Star product
* Symmetric closure
* Transitive closure

Topology & Orders|

* Alexandrov topology & Specialization preorder
* Ordered topological vector space
* Normal cone
* Order topology
* Order topology
* Topological vector lattice
* Banach
* Fréchet
* Locally convex
* Normed

Related|

* Antichain
* Cofinal
* Cofinality
* Comparability
* Graph
* Duality
* Filter
* Hasse diagram
* Ideal
* Net
* Subnet
* Order morphism
* Embedding
* Isomorphism
* Order type
* Ordered field
* Positive cone of an ordered field
* Ordered vector space
* Partially ordered
* Positive cone of an ordered vector space
* Riesz space
* Partially ordered group
* Positive cone of a partially ordered group
* Upper set
* Young's lattice

*[v]: View this template
*[t]: Discuss this template
*[e]: Edit this template