User:Matthew Kastor/Books/Logical


Logical

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Logical[edit]

Articles with a wide scope and introductions: Algebra of sets; Boolean algebra (structure); Boolean algebra; Field of sets; List of logic symbols; Logical connective; Necessity and sufficiency; Propositional calculus; Truth function
General Information and Vocabulary: 2-valued morphism; Bitwise operation; Boolean data type; Boolean expression; Boolean satisfiability problem; Boolean-valued model; Booleo; Chaff algorithm; Correlation immunity; Davis–Putnam algorithm; DPLL algorithm; Formula game; Join (sigma algebra); Logic alphabet; Logic redundancy; Logical matrix; Logical value; Modal algebra; Petrick's method; Product term; Propositional formula; Stone duality; Stone functor; True quantified Boolean formula; Truth value; Vector logic
Visualization: Binary decision diagram; Implication graph; Karnaugh map; Propositional directed acyclic graph; Quine–McCluskey algorithm; Reed–Muller expansion; Truth table; Venn diagram
Logical Connectives and functions: Ampheck; Balanced boolean function; Bent function; Boolean algebras canonically defined; Boolean function; Boolean-valued function; Conditioned disjunction; Converse implication; Converse nonimplication; Evasive Boolean function; Exclusive or; False (logic); Functional completeness; If and only if; Inclusion (Boolean algebra); Indicative conditional; Indicator function; Logical NOR; Logical biconditional; Logical conjunction; Logical disjunction; Logical equality; Logical implication; Logical negation; Lupanov representation; Majority function; Material conditional; Material equivalence; Material nonimplication; Modal operator; Negation; Parity function; Peirce arrow; Sheffer stroke; Sole sufficient operator; Statement (logic); Strict conditional; Symmetric Boolean function; Symmetric difference; Tautology (logic); Zhegalkin polynomial
Syntax: Algebraic normal form; Boolean conjunctive query; Canonical form (Boolean algebra); Conjunctive normal form; Disjunctive normal form; Formal system
Normal Forms: Blake canonical form; Canonical normal form; Herbrand normal form; Herbrandization; Horn clause; Negation normal form; Prenex normal form; Skolem normal form
Theorems and specific laws: Absorption law; Boole's expansion theorem; Boolean prime ideal theorem; Compactness theorem; Consensus theorem; De Morgan's laws; Duality (order theory); Laws of classical logic; Peirce's law; Poretsky's law of forms; Stone's representation theorem for Boolean algebras
Philosophy: Boole's syllogistic; Entitative graph; Existential graph; Implicant; Laws of Form; Logical graph
Examples of Boolean algebras: Boolean domain; Boolean ring; Goodman–Nguyen–van Fraassen algebra; Interior algebra; Lindenbaum–Tarski algebra; Relation algebra; Residuated Boolean algebra; Robbins algebra; Sigma-algebra; Topological Boolean algebra; Two-element Boolean algebra
Extensions and generalizations: Complete Boolean algebra; Derivative algebra (abstract algebra); First-order logic; Free Boolean algebra; Heyting algebra; Monadic Boolean algebra; Skew lattice
Technical applications: And-inverter graph; Boolean analysis; Boolean operations in computer-aided design; Circuit minimization; Espresso heuristic logic minimizer; Logic gate
People: Augustus De Morgan; Charles Sanders Peirce; George Boole; Ivan Ivanovich Zhegalkin; John Venn; Marshall Harvey Stone; William Stanley Jevons
Propositional Calculus: Clause (logic); Contradiction; Deductive closure; Formation rule; Frege system; Frege's propositional calculus; Implicational propositional calculus; Intermediate logic; List of logic systems; Literal (mathematical logic); Logical consequence; Nicod's axiom; Open sentence; Predicate (mathematical logic); Principle of distributivity; Proof by contrapositive; Proposition; Propositional proof system; Propositional variable; Rule of inference; Rule of replacement; Second-order propositional logic; Substitution (logic); Syncategorematic term; System L; Unsatisfiable core; Zeroth-order logic
Propositional Fallacies: Affirming a disjunct; Affirming the consequent; Denying the antecedent
Rules of Inference: List of rules of inference; Absorption (logic); Admissible rule; Associative property; Biconditional elimination; Biconditional introduction; Commutative property; Commutativity of conjunction; Conjunction introduction; Constructive dilemma; Contraposition (traditional logic); Destructive dilemma; Disjunction elimination; Disjunction introduction; Disjunctive syllogism; Distributive property; Double negative elimination; Existential generalization; Existential instantiation; Exportation (logic); Hypothetical syllogism; List of valid argument forms; Material implication (rule of inference); Modus non excipiens; Modus ponendo tollens; Modus ponens; Modus tollens; Negation as failure; Resolution (logic); SLD resolution; Simplification; Structural rule; Tautology (rule of inference); Transposition (logic); Universal generalization; Universal instantiation
Theorems in Propositional Logic: Case analysis; Consequentia mirabilis; Contraposition; Double negation; Frege's theorem; Idempotency of entailment; Law of excluded middle; Law of identity; Law of noncontradiction; Monotonicity of entailment; Principle of explosion; Proof by contradiction; Reductio ad absurdum