User:Gregbard/logic cats
Please be advised that the concepts in this category may be also expressed in terms of arguments, theorems, or rules of inference. Very often the same concept is in more than one of these categories, expressed a different way and sometimes with a different name.
See also[edit]
- Category:Arguments
- Category:Argument forms
- Category:Rules of inference
- Category:Theorems
- Category:Theorems
- Category:Axioms of modal logic
- Category:Syllogistic logic (traditional, Aristotelian, term)
- Category:Syllogisms
- Category:Truth functions
Theorems of propositional logic[edit]
- Modus ponens
- Modus tollens
- Law of identity
- Law of the excluded middle, Tertium non datur
- Law of noncontradiction
- Hypothetical syllogism, Transitivity of implication, Chain argument, Chain rule
- Disjunctive syllogism
- Constructive dilemma
- Destructive dilemma
- Simplification
- Addition (logic), Disjunction introduction
- Conjunction introduction, Conjunction (logic)
- De Morgan's laws, Negation of conjunction, Negation of disjunction
- Double negation
- Transposition
- Material implication (rule of inference)
- Material equivalence
- Exportation (logic)
- Importation (logic)
- Export-import law, Import-export law
- Absorption (logic), Adjunction (logic)
- Absorption law
- Peirce's law
- Rule of concretion
- Compactness theorem
- A recto ad obliquum
- Ex falso quodlibet
- Henkin's theorem
- Wolfram axiom
- Nicod's axiom
- Case analysis
- Golden rule (propositional logic)
- Meridith's astonishing single axiom
- Frege's theorem
- Praeclarum theorema
- Consensus theorem
- Conditionalization
- Law of Duns Scotus, Law of denial of antecedent
- Contraposition
- Consequentia mirabilis, Law of Clavius
- Biconditional
- Proof by contradiction
- Resolution (logic)
- Reductio ad absurdum
- Law of permutation
- Affirming the consequent
- Composition (logic)
- Law of triple negation
- Laws of development
- Replacement (logic)
- Shunting (logic)
- Goodman's theorem
- Merging of implication
- Strengthened implication
- Weakened implication
- Drop an always true factor
- Drop an always false term
- Indirect reduction of syllogism
- Weak law of excluded middle
- Identity of equivalence
- Associative property, Associativity
- Associativity of disjunction
- Associativity of conjunction
- Associativity of implication
- Associativity of equivalence
- Commutative property, Commutativity
- Commutativity of implication
- Commutativity of conjunction
- Commutativity of disjunction
- Commutativity of equivalence, equivalence of negations, negation of equivalents, Complete commutative law of equivalence
- Distributive property, *Distributivity, Principle of distributivityDistribution of implication
- Distribution of implication over equivalence
- Distribution of conjunction over conjunction
- Distribution of conjunction over disjunction
- Distribution of disjunction over disjunction
- Distribution of disjunction over conjunction
- Distribution of disjunction over equivalence
- Distribution of negation over equivalence
- Double distribution
- Self distributive law of implication
- Idempotency, Tautologousness
- Tautology (rule of inference)
- Idempotency of entailment
- Idempotency of conjunction
- Idempotency of conjunction of identity
- Idempotency of disjunction
- Idempotency of disjunction of identity, Principle of tautology for disjunction,
- Principle of tautology for conjunction, idempotency of conjunction of identity
- Monotonic property, Monotonicity
- Monotonicity of conjunction
- Monotonicity of disjunction
- Monotonicity of entailment
- Law of conflation (monotonicity)
Valid syllogistic forms[edit]
First figure
Second figure
Third figure
Fourth figure
other[edit]
- Categorical proposition
- Subject term
- Predicate term
- Quantifier
- Copula
- Universal proposition
- Particular proposition
- Universal affirmative
- Particular affirmative
- Universal negative
- Particular negative
- Standard form
- Major term
- Minor term
- Middle term
- Figure
- Mood
- Undistributed middle
- Illicit major
- Illicit minor
- Exclusive premises
- Affirmative conclusion from a negative premise
- Negative conclusion from affirmative premises
- Existential fallacy
- Enthymeme
- Superalternation, Superaltern
- Subalternation, Subaltern
- Contrary, Contraries, Law of contraries
- Subcontrary, Subcontraries,
- Contradictory, Contradiction
- Converse (logic), Conversion
- Obverse (logic), Obversion
- Inverse (logic), Inversion
- Contraposition (traditional logic), Contrapositive
- Transposition (logic), Transpositive