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词条 List of Boolean algebra topics
释义

  1. Articles with a wide scope and introductions

  2. Boolean functions and connectives

  3. Examples of Boolean algebras

  4. Extensions and generalizations

  5. Syntax

  6. Technical applications

  7. Theorems and specific laws

  8. People

  9. Philosophy

  10. Visualization

  11. Unclassified

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

Articles with a wide scope and introductions

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

Boolean functions and connectives

  • Ampheck
  • Boolean algebras canonically defined
  • 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
  • Peirce arrow
  • Sheffer stroke
  • Sole sufficient operator
  • Symmetric Boolean function
  • Symmetric difference
  • Zhegalkin polynomial

Examples of Boolean algebras

  • Boolean domain
  • Interior algebra
  • Lindenbaum–Tarski algebra
  • Two-element Boolean algebra

Extensions and generalizations

  • Complete Boolean algebra
  • Derivative algebra (abstract algebra)
  • First-order logic
  • Free Boolean algebra
  • De Morgan algebra
  • Heyting algebra
  • Monadic Boolean algebra
  • skew Boolean algebra

Syntax

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

Technical applications

  • And-inverter graph
  • Logic gate
  • Boolean analysis

Theorems and specific laws

  • 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

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

Philosophy

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

Visualization

  • Truth table
  • Karnaugh map
  • Venn diagram

Unclassified

  • 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
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