- See User:Chalst/WikiProject Logic proposal
Note also the List of topics in logic.
Fundamental definitions
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:
- Quantum logic
- Term logic: Aristotelian logic, Syllogism, Categorical syllogism, Disjunctive syllogism, Problem of multiple generality, Syllogistic fallacy, Square of opposition
- Combinatory logic
Parts of logic
- : Consistency proof, Deduction theorem, Gödel's completeness theorem, Gödel's incompleteness theorem
- Natural deduction: Double negative elimination, Introduction rule, Elimination rule,
- Proof net
- Sequent calculus: Cut-elimination, Takeuti conjecture
- Structural proof theory: Analytic proof, Bunched implication, , Calculus of structures
Proof assistants
Basis for modelling |
and Automated theorem provers |
Systems based on logical frameworks |
LF (logical framework) |
LCF theorem prover, Twelf |
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Isabelle, |
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Coq, |
Intuitionistic type theory |
, , |
Linear logic |
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Systems based on direct symbolic representations |
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First-order logic |
Mizar, Vampire theorem prover |
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HOL theorem prover, Prototype Verification System, |
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Gabbay's deductive system, OBJ3 |
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Maude system, |
To incorporate: , , , ACL2, Otter (software).
Logic for argument
The human side
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,
- 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
Institutions and movements
Logic categories
Related content
Categories
Articles