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Contents 1 Logic 1.1 Fundamental definitions 1.2 History of logic 1.3 Types of logic 1.4 Parts of logic 1.5 Mathematical logic 1.5.1 Proof theory 1.5.2 Model theory 1.5.3 Set theory 1.5.4 Algebraic logic 1.6 Philosophy of logic and Philosophical logic 1.7 Logic in computer science 1.7.1 Logic and Artificial intelligence 1.7.2 Type theory 1.7.3 Proof assistants 1.8 Logic for argument 2 The human side 2.1 Logicians 2.2 Institutions and movements 3 Logic categories 4 Related content 4.1 Categories 4.2 Articles

[edit] Logic

See User:Chalst/WikiProject Logic proposal

Note also the List of topics in logic.

[edit] Fundamental definitions

• Argument
  • Argument form
  • Informal logic
  • Logical argument
• Contradiction
• Inference
  • Fallacy, Validity
  • Abduction, Deduction, Induction
• Logical form, Proposition, Sentence
  • Assertion, Denial, Judgement, Propositional attitude
  • Formula, Schema, Symbolic logic, Well-formed formula
• Paradox
• Tautology, Theorem
• Truth

[edit] History of logic

• Boolean logic
• Begriffsschrift, Frege's propositional calculus
• Organon
• Nyaya
• Port-Royal Logic
• Principia Mathematica
• Principles of Theoretical Logic

[edit] Types of logic

• Classical logic: Bivalence and related laws, Peirce's law
• Intuitionistic logic: Intuitionistic type theory
• Substructural logic: Affine logic, Bunched logic, Linear logic, Relevance logic
• Modal logic and Temporal logic: Deontic logic, Description logic, Dynamic logic, Epistemic logic, Hybrid logic, Provability logic
• Predicate logic: First-order logic,Generalization (logic), Higher-order logic, Independence-friendly logic, Monadic logic, Second-order logic
• Propositional logic: Stoic logic
• Quantum logic
• Term logic: Aristotelian logic, Syllogism, Categorical syllogism, Disjunctive syllogism, Problem of multiple generality, Syllogistic fallacy, Square of opposition
• Combinatory logic

[edit] Parts of logic

• Logical connective
  • Negation
  • Logical conjunction
  • Logical disjunction
  • Logical conditional
  • Logical biconditional
  • Sheffer stroke (<- Logical nand, NAND)
  • Logical nor (<- Peirce arrow, NOR)
• Quantification (<- Quantifier)
  • Universal quantification
  • Existential quantification
  • Generalized quantifier
  • Uniqueness quantification
• Rule of inference
  • List of rules of inference
  • Modus ponens, Modus tollens, Hypothetical syllogism

[edit] Mathematical logic

• Arithmetic: Peano arithmetic, Robinson arithmetic, Second-order arithmetic
• Plural quantification
• Reverse mathematics

[edit] Proof theory

• Hilbert calculus: Consistency proof, Deduction theorem, Gödel's completeness theorem, Gödel's incompleteness theorem
• Natural deduction: Double negative elimination, Introduction rule, Elimination rule, Normal proof
• Proof net
• Sequent calculus: Cut-elimination, Takeuti conjecture
• Structural proof theory: Analytic proof, Bunched implication, Display logic, Calculus of structures

[edit] Model theory

• Categoricity
• Compactness theorem
• Completeness and Soundness
• Finite model property
• Löwenheim-Skolem theorem
• Maximal consistent set
• Skolem's paradox

[edit] Set theory

• Set theory: Axiomatic set theory
  • Zermelo set theory, Zermelo-Fraenkel set theory, von Neumann-Bernays-Gödel axioms
  • New Foundations
  • Morse-Kelley set theory
  • Kripke-Platek set theory
  • Fraenkel-Mostowski set theory
  • Positive set theory
  • Implementation of mathematics in set theory

[edit] Algebraic logic

• Boolean algebra
  • Monadic Boolean algebra
  • Boolean algebra with operators
• Categorical logic
  • Topos theory
  • Sheaf theory
• Stone duality
• Jònsson-Tarski theorem

[edit] Philosophy of logic and Philosophical logic

• Is logic empirical?
• Logic and pragmatics
  • Gricean maxim
• Multiple-valued logic
• Paraconsistent logic: Brazilian logic, Dialetheism
• Semantics of logic
  • Game semantics
  • Inferential role semantics
  • Kripke semantics
  • Model-theoretic semantics
  • Multiple-valued logic
  • Possible world semantics
  • Proof-theoretic semantics
  • Semantic theory of truth
  • Truth-conditional semantics

[edit] Logic in computer science

• Recursion theory
• Domain theory
• Finite model theory
  • Model checking

[edit] Logic and Artificial intelligence

• Abduction --> Abductive reasoning
  • Abductive validation, Circumscription
• Default logic
• Logic programming
  • Answer set programming, negation as failure
  • Horn clause, Unification, First-order resolution
  • Prolog
  • Uniform proof
• Inductive reasoning
  • Fluent calculus, Frame problem, Situation calculus

[edit] Type theory

• Typed lambda calculus
  • Curry-Howard
  • Dependent type, Pure type system
• Logical framework
  • LF (logical framework) (rename to Edinburgh Logical Framework)
  • Calculus of constructions

[edit] Proof assistants

Basis for modelling	Proof assistants and Automated theorem provers
Systems based on logical frameworks
LF (logical framework)	LCF theorem prover, Twelf
Hereditary Harrop formulae	Isabelle, Lambda-PROLOG
Calculus of constructions and extensions	Coq, LEGO theorem prover
Intuitionistic type theory	NuPRL, MetaPRL, ALF theorem prover
Linear logic	Forum meta-logic
Systems based on direct symbolic representations
Hilbert calculus	Metamath
First-order logic	Mizar, Vampire theorem prover
Church's simple theory of types and extensions	HOL theorem prover, Prototype Verification System, ProofPower
Equational logic	Gabbay's deductive system, OBJ3
Rewriting logic	Maude system, ELAN

To incorporate: Automath, NQTHM, MinLog, ACL2, Otter (software).

[edit] Logic for argument

• Argumentation theory
  • Common sense
  • Dialectic, Rhetoric
  • Burden of proof
• College logic
  • Critical thinking

[edit] The human side

[edit] Logicians

• Pierre Abélard, Wilhelm Ackermann, Aristotle
• Boethius, George Boole, Franz Brentano, Luitzen Egbertus Jan Brouwer
• Rudolf Carnap, Lewis Carroll, Alonzo Church, Newton da Costa, Haskell Curry
• Augustus de Morgan, Michael A. E. Dummett, J. Michael Dunn
• Solomon Feferman, Gottlob Frege
• Gerhard Gentzen, Kurt Gödel, Anil Gupta
• Susan Haack, Leon Henkin, Jacques Herbrand, Arend Heyting, David Hilbert, Jaakko Hintikka
• Stephen Cole Kleene, Saul Kripke
• Francis William Lawvere, Gottfried Wilhelm Leibniz, Clarence Irving Lewis, David Kellogg Lewis, Adolf Lindenbaum,Leopold Löwenheim, Jan Lukasiewicz
• William of Ockham
• Saunders MacLane, Ruth Barcan Marcus, Richard Montague, Andrzej Mostowski
• John von Neumann
• Charles Pierce, Giuseppe Peano, Gilbert de la Porrée, Emil Leon Post, Dag Prawitz, Arthur Prior
• Willard Van Orman Quine
• Frank Plumpton Ramsey, Abraham Robinson, J. Barkley Rosser, Bertrand Russell
• Duns Scotus
• Alfred Tarski, Anne Sjerp Troelstra, Alan Turing, Kazimierz Twardowski

[edit] Institutions and movements

• Scholasticism, Scotism
• Lwów-Warsaw School of Logic
• School of Brentano

[edit] Logic categories

• Category:Logic
  • Category:Mathematical logic
  • Category:Fuzzy logic
  • Category:History of logic
  • Category:Latin logical phrases
  • Category:Laws of thought
  • Category:Logic in computer science
    • Category:Type theory
    • Category:Theorem provers
  • Category:Logic puzzles
  • Category:Logical fallacies
  • Category:Logicians
  • Category:Mathematical logic
    • Category:Boolean algebra
    • Category:Categorical logic
    • Category:Model theory
    • Category:Proof theory
    • Category:Set theory
      • Category:Cardinal numbers
  • Category:Modal logic
  • Category:Paradoxes
  • Category:Philosophical logic
• Category:Rules of inference

[edit] Related content

[edit] Categories

• Category:Cognition
• Category:Evidence
• Category:Formal languages
• Category:Proofs
• Category:Rhetoric

[edit] Articles

• Category of being
• Concept
• Formal science
• Foundations of mathematics
  • Reverse mathematics
• Thought, Idea