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Fundamental definitions
[edit]- Argument
- Contradiction: Absurdity, nonsense
- Inference
- Logical form, Proposition, Sentence
- Semantics of logic
- Paradox
- Tautology, Tautology (logic), Tautology (rhetoric), Theorem
- Rival conceptions of logic
- Truth
- Ancient logic
- Medieval logic
- Port-Royal Logic (Artaud)
- Laws of Thought (Boole)
- Begriffsschrift, Frege's propositional calculus
- Principia Mathematica
- Principles of Theoretical Logic (Hilbert & Ackermann)
Types of logic
[edit]- Classical logic: De Morgan duality, Peirce's law, principle of bivalence
- Diagrammatic reasoning: Carroll diagram, conceptual graph, entitative graph, Euler diagrams, existential graph, logical graph, Venn diagrams
- Intensional logic
- Intuitionistic logic and superintuitionistic logic:
- Modal logic:
- Predicate logic
- Propositional calculus: Stoic logic
- Substructural logic: Affine logic, Bunched logic, Connexive logic, Linear logic, Relevance logic
- Term logic: Aristotelian logic
- Rule of inference in modern logic
- List of rules of inference
- Case analysis
- Conditional proof
- Contraposition, Contraposition (traditional logic), Transposition (logic)
- Constructive dilemma, Destructive dilemma
- Conversion (logic), Dictum de omni et nullo
- Disjunctive syllogism
- Generalization (logic), Universal instantiation
- Hypothetical syllogism
- Modus ponendo tollens, Modus ponens, Modus tollendo ponens, Modus tollens
- Principle of contradiction, Reductio ad absurdum
- Proof by contradiction, Law of excluded middle, Proof by contrapositive
- Duality (logic)
- Natural deduction
Parts of logic
[edit]- Propositional connectives
- Negation
- Logical conjunction: simplification, conjunction introduction
- Logical disjunction: disjunction elimination, Disjunctive syllogism
- Logical conditional
- Logical biconditional: biconditional introduction, biconditional elimination (<- If and only if, Logical equality)
- Sheffer stroke (<- Logical nand, NAND)
- Logical nor (<- Peirce arrow, NOR)
- Exclusive disjunction
- Converse implication
- Material nonimplication
- Converse nonimplication
- Modal operator
- Quantification (<- Quantifier)
Subdisciplines of logic
[edit]Knowledge representation and reasoning
[edit]- Abduction --> Abductive reasoning
- Default logic
- Logic programming
- Inductive reasoning
- Model checking
- Boolean algebra (disambiguation)
- Categorical logic
- Heyting algebra
- Quantum logic
- Stone duality
- Jònsson-Tarski theorem
- Universal algebra
- Vector logic
- Compactness theorem, Lindström's theorem
- Completeness and Soundness
- Finite model theory
- Interpretation (model theory), type (model theory), signature (model theory)
- Kripke semantics, Neighborhood semantics
- Löwenheim-Skolem theorem
- Model constructions
- Properties of models
- Skolem's paradox
- Analytic proof
- Constructive proof: disjunction property, existence property
- Craig interpolation, Herbrand's theorem
- Hilbert system: consistency proof, deduction theorem
- Natural deduction
- Proof net
- Sequent calculus: cut-elimination, midsequent, Takeuti conjecture
- Structural proof theory: analytic proof, bunched implication
Theories
[edit]- Theory (mathematical logic)
- Arithmetic: Peano arithmetic, Robinson arithmetic, Second-order arithmetic
Applications of logic in mathematical
[edit]- Applied model theory
- Classical recursive mathematics
- Constructivism_(mathematics)
- Intuitionism, Preintuitionism
- Brouwer–Heyting–Kolmogorov interpretation
- Existence proof
- (constructive): Smale's paradox, fan theorem, bar induction
- (violates PEM): Strategy-stealing argument
- Non-constructive principles:
- Proof mining
- Combinatory logic
- Typed lambda calculus
- Logical framework
- LF (logical framework) (rename to Edinburgh Logical Framework)
- Calculus of constructions, calculus of inductive constructions
- Type inference
Proof assistants
[edit]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 | ||
|
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 | ||
|
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).
Logic for argument
[edit]Mathematical structures for logic and semantics
[edit]Topology and order theory
[edit]- Domain theory
- Equilogical space
- Stone duality, Stone's representation theorem for Boolean algebras
- Specialization (pre)order
- Sober space
- Spectral space
- Alexandrov topology
- Upper topology
- Lawson topology
Untyped lambda calculus
[edit]- Is logic empirical?
- Logic and pragmatics
- Paraconsistent logic: Brazilian logic, dialetheism
- Tense logic^
- Approaches to semantics of logic
- Sense and reference, Sinn, Bedeutung
- Truth value, truth function
The human side
[edit]Logicians
[edit]- Pierre Abélard, Wilhelm Ackermann, Aristotle
- Johan van Benthem (logician), Corrado Böhm, Anicius Manlius Severinus Boethius, George Boole, Franz Brentano, Luitzen Egbertus Jan Brouwer
- Georg Cantor, Rudolf Carnap, Lewis Carroll, Alonzo Church, Paul Cohen, Newton da Costa, William Craig (logician), Haskell Curry
- Richard Dedekind, Augustus De Morgan, Michael A. E. Dummett, J. Michael Dunn
- Solomon Feferman, Abraham Fraenkel, Gottlob Frege
- Robin Gandy, Gerhard Gentzen, Kurt Gödel, Anil Gupta
- Susan Haack, Leon Henkin, Jacques Herbrand, Arend Heyting, David Hilbert, Jaakko Hintikka, Alfred Horn, William Alvin Howard
- William Stanley Jevons
- Stephen Cole Kleene, Saul Kripke, Georg Kreisel
- Christine Ladd-Franklin, Francis William Lawvere, Gottfried Wilhelm Leibniz, John Lemmon, Clarence Irving Lewis, David Kellogg Lewis, Adolf Lindenbaum, Paul Lorenzen, Leopold Löwenheim, Jan Lukasiewicz
- William of Ockham
- Hugh MacColl, Saunders MacLane, Anatoly Maltsev, Ruth Barcan Marcus, Richard Montague, Andrzej Mostowski
- John von Neumann
- Charles Sanders 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, Czesław Ryll-Nardzewski
- Ernst Schröder, Dana Scott, Duns Scotus, William of Sherwood, Thoralf Skolem
- William W. Tait, Alfred Tarski, Anne Sjerp Troelstra, Alan Turing, Kazimierz Twardowski
- Alfred North Whitehead
- Ernst Zermelo
Institutions and movements
[edit]Logic categories
[edit]- 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:Logic puzzles
- Category:Logical fallacies
- Category:Logicians
- Category:Mathematical logic
- Category:Modal logic
- Category:Paradoxes
- Category:Philosophical logic
- Category:Rules of inference
Related content
[edit]Categories
[edit]- Category:Cognition
- Category:Evidence
- Category:Formal languages
- Category:Proofs
- Category:Rhetoric
- Category:Lemmas
- Category:Theorems
Lists and tables
[edit]- Index of logic articles (R:List of topics in logic)
- List of logicians
- List of mathematical logic topics
Articles
[edit]- Category of being
- Concept
- Formal science
- Foundations of mathematics
- Philosophy of science
- Reasoning
- Thought, Idea
False friends
[edit]- Laws of thought: unfocussed article, not to be confused with article on Boole's Laws of Thought