logic

Better Explained
Better Explained
Mathematical logic
1. Better Explained
  1. Propositional Equivalences
  2. Logical Equivalences
  3. material equivalence
2. General
  1. Theorem
    1. Well-formed formula
      1. Symbol (formal)
  2. Formal system/Logical calculus
    1. Better Explained
      1. Formal proof
      2. Formal semantics (logic)
      3. An interpretation of a formal language is (roughly) an assignment of meanings to its symbols and truth-conditions to its sentences
      4. Syntax (logic)
    2. Formal language
      1. Formal grammar
      2. Formation rule
      3. Formal definition
      4. The syntax of grammars
      5. G = (N,?,P,S)
      6. The semantics of grammars
      7. Chomsky hierarchy
      8. Type-0 grammars
      9. Recursively enumerable languages
      10. Type-1 grammars
      11. Context-sensitive languages
      12. Type-2 grammars
      13. Context-free languages
      14. Backus–Naur Form
      15. Type-3 grammars
      16. Regular languages
      17. Finite state automaton
      18. Analytic grammars
      19. Alphabet
      20. Well-formed formula
      21. Atomic formula
      22. Closed formulas
    3. Deductive system/Deductive apparatus
      1. Rule of inference
      2. Better Explained
      3. Admissible rule
      4. Summary
      5. Simplification
      6. Addition
      7. Conjunction
      8. Resolution
      9. Disjunctive syllogism
      10. Hypothetical syllogism
      11. Modus tollens
      12. Modus ponens
      13. Rules for classical sentential calculus
      14. Rules for negations
      15. Reductio ad absurdum (or Negation Introduction)
      16. Reductio ad absurdum (related to the law of excluded middle)
      17. Noncontradiction (or Negation Elimination)
      18. Double negation elimination
      19. Double negation introduction
      20. Rules for conditionals
      21. Deduction theorem (or Conditional Introduction)
      22. Modus ponens (or Conditional Elimination)
      23. Modus tollens
      24. Rules for conjunctions
      25. Adjunction (or Conjunction Introduction)
      26. Simplification (or Conjunction Elimination)
      27. Rules for disjunctions
      28. Addition (or Disjunction Introduction)
      29. Separation of Cases (or Disjunction Elimination)
      30. Disjunctive syllogism
      31. Rules for biconditionals
      32. Biconditional introduction
      33. Biconditional Elimination
      34. Rules of classical predicate calculus
      35. Universal Introduction (or Universal Generalization)
      36. Universal Elimination (or Universal Instantiation)
      37. Existential Introduction (or Existential Generalization)
      38. Existential Elimination (or Existential Instantiation)
      39. Axioms
      40. Logical axioms
      41. Non-logical axioms
      42. Axiom schema
  3. Axiomatic system
  4. Type theory
  5. Syntax (logic)
  6. Symbol (formal)
  7. Theory (mathematical logic)/formal theory
  8. Proof calculus
    1. Natural deduction
  9. Entailment
3. Traditional logic/Term logic
  1. Proposition
    1. Tautology (logic)
    2. Contradiction
  2. Inference
  3. Argument
    1. Validity
    2. Cogency
  4. Syllogism
  5. Square of opposition
  6. Venn diagram
4. Propositional logic & Boolean logic
  1. Better Explained
    1. Logical equivalence
      1. Identity laws
      2. Domination laws
      3. Idempotent laws
      4. Double negation law
      5. Commutative laws
      6. Associative laws
      7. Distributive laws
      8. De Morgan's laws
      9. Absorption laws
      10. Negation laws
  2. Boolean function
  3. Propositional formula
  4. Logical connective
    1. Better Explained
      1. Order of precedence
    2. Negation (not) (¬ or ~)
    3. Conjunction (and) (, &, or · )
    4. Disjunction (or) (?)
    5. Exclusive disjunction/Exclusive or/XOR ?
    6. Material implication (if...then) (?,? or ?)/Material conditional/Condition statement/??????????????
    7. Logical biconditional/Material biconditional/Biconditional (if and only if) (iff) (xnor) (bi-implication)(?,=,?)
      1. ? is not a logical connective
      2. p = q is not a compound proposition
    8. Contingency (philosophy)
  5. Truth table
5. Predicate logic
  1. Propositional function
    1. Predicate (mathematical logic)
  2. Quantification
    1. Existential quantification
    2. Universal quantification
  3. First-order logic
  4. Second-order logic
  5. Monadic predicate calculus
6. Classical logic/standard logic
  1. First-order logic
  2. Syllogism
  3. Boolean logic
7. Set theory
  1. Class (set theory)
    1. Set (mathematics)
      1. Finitary relation
      2. Entailment
      3. Finite set
      4. Infinite set
      5. Cardinality
      6. Uncountable set
      7. Countable set
      8. Recursive set
      9. Disjoint sets
      10. Membership
      11. Element (mathematics)
      12. Subset
      13. ? ? A.
      14. A ? A.
      15. A = B if and only if A ? B and B ? A
      16. Power set
      17. Basic operations
      18. Union (set theory)
      19. Intersection (set theory)
      20. Complement (set theory)
      21. Cartesian product
      22. n-ary product
      23. Special sets
      24. Describing sets
      25. Intensional definition/??? (???)
      26. {x|P(x)}
      27. Enumeration
      28. Venn diagram
    2. Better Explained
      1. Set Identities.
      2. Identity laws
      3. Domination laws
      4. Idempotent laws
      5. Complementation law
      6. Commutative laws
      7. Associative laws
      8. Distributive laws
      9. De Morgan's laws
      10. AnB=AUB
      11. Absorption laws
      12. Complement laws
  2. Extensionality
  3. Function (mathematics)
    1. Definition
      1. Notation
      2. Domain of a function
      3. Range (mathematics)
      4. Ordered pair
    2. Function composition
      1. Functional powers
      2. Transformation monoid
      3. Composition operator
    3. Inverse function
    4. Function spaces
    5. bijection, injection and surjection
    6. Floor and ceiling functions
    7. convex, monotonic, unimodal
      1. Convex function
      2. Monotonic function
    8. odd or even
    9. holomorphic, meromorphic, entire
    10. vector-valued
    11. computable
    12. differentiable, integrable
    13. linear, polynomial, rational
    14. algebraic, transcendental
    15. trigonometric
    16. fractal
    17. continuous
    18. Order theory
    19. Graph of a function
    20. Sequence
      1. Better Explained
      2. A function defined on an interval of the integers is usually called a sequence.
      3. Series (mathematics)
      4. Basic properties
      5. Potential confusion
      6. Convergent series
      7. Properties of series
      8. Non-negative terms
      9. Absolute convergence
      10. Conditional convergence
      11. Function series
      12. Power series
      13. Laurent series
      14. Dirichlet series
      15. Trigonometric series
      16. Fourier series
      17. Summation
      18. Sequences and automata
      19. Types of sequences
      20. ±1-sequence
      21. Arithmetic progression
      22. Cauchy sequence
      23. Farey sequence
      24. Fibonacci sequence
      25. Geometric progression
      26. Look-and-say sequence
      27. Thue–Morse sequence
  4. Axiomatic set theory
8. Model theory
  1. Structure (mathematical logic)
  2. Interpretation (logic)
  3. Finite model theory
  4. Non-standard model
  5. Truth value
9. Proof theory
  1. Formal proof
  2. Deductive system
  3. Formal system
  4. Theorem
  5. Entailment
  6. Rule of inference
    1. Modus ponens
    2. Modustollens
    3. Hypothetical syllogism
    4. Disjunctive syllogism
    5. Addition
    6. Simplification
    7. Conjunction
    8. Resolution
    9. Fallacy
  7. Syntax (logic)
  8. Mathematical proof
    1. Direct proof
    2. Mathematical induction
    3. Transposition (logic)
    4. Proof by contradiction
    5. Constructive proof
    6. Proof by exhaustion
    7. Combinatorial proof
    8. Probabilistic proof
    9. Nonconstructive proof
    10. Visual proof
    11. Elementary proof
    12. Two-column proof
    13. Better Explained
      1. Existence Proofs
      2. Uniqueness Proofs
10. Computability theory
  1. Recursion
  2. Recursive set
  3. Recursively enumerable set
  4. Decision problem
  5. Church–Turing thesis
  6. Computable function
  7. Primitive recursive function
Philosophical logic
Metalogic and Metamathematics
Non-classical logic