See Wikipedia:WikiProject Logic, User:Chalst/WikiProject Logic proposal, Portal:Logic

• Argument
  • Argument form
  • Informal logic
  • Logical argument
• Contradiction: Absurdity, nonsense
• Inference
  • Fallacy, Validity
  • Logical consequence
  • Logical reasoning: Abductive reasoning, Deductive reasoning, Inductive reasoning
• Logical form, Proposition, Sentence
  • Assertion, Denial, Judgement, Propositional attitude
  • Formula, Schema, Symbolic logic, Well-formed formula (d:WFF)
  • Hypothesis, Assumption, Premise
• Semantics of logic
• Paradox
• Tautology, Tautology (logic), Tautology (rhetoric), Theorem
• Rival conceptions of logic
• Truth

• Ancient logic
  • Aristotelian logic, Organon, Term logic
  • Stoic logic
  • Nyaya
• Medieval logic
• Port-Royal Logic (Artaud)
• Laws of Thought (Boole)
• Begriffsschrift, Frege's propositional calculus
• Principia Mathematica
• Principles of Theoretical Logic (Hilbert & Ackermann)

• 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:
  • Intuitionistic type theory
  • Modal companion
• Modal logic:
  • Temporal logic
  • Deontic logic, Description logic, Dynamic logic, Epistemic logic, Hybrid logic, Provability logic
  • Classical modal logic, Intuitionistic modal logic
• Predicate logic
  • First-order logic
  • Independence-friendly logic, Monadic logic
  • Second-order logic, Higher-order 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)
  • De Morgan's laws
  • Duality (mathematics)#Duality in logic and set theory
  • Square of opposition
• Natural deduction
  • elimination rule
  • introduction rule, conjunction introduction

• Syllogism, Categorical syllogism, Problem of multiple generality, Syllogistic fallacy

See Logical connective

• Propositional connectives
  • Negation
    • Contradiction
    • Contrary (logic)
    • Negation (rhetoric)
    • Not!
  • 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
  • Alethic modality, axiology, common knowledge (logic), deontic logic, doxastic logic, epistemic logic, temporal logic
• Quantification (<- Quantifier)
  • Universal quantification: vacuous truth
  • Epsilon calculus
  • Existential quantification
  • Generalized quantifier
  • Plural quantification
  • Uniqueness quantification

• 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
• Model checking

• Boolean algebra (disambiguation)
  • Boolean algebra (logic), Boolean algebra (structure), Boolean algebra (introduction), Boolean logic
  • Monadic Boolean algebra
  • Boolean algebra with operators
  • Boolean algebras canonically defined
• Categorical logic
  • Topos theory
  • Sheaf theory
• Heyting algebra
• Quantum logic
• Stone duality
• Jònsson-Tarski theorem
• Universal algebra
  • Basis (universal algebra), clone (algebra), variety (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
  • Herbrand universe, Herbrand interpretation
  • Maximal consistent set
• Properties of models
  • Finite model property
  • Model-completeness, Tarski–Vaught test
  • Categoricity, Ryll-Nardzewski theorem, Morley's categoricity theorem
• Skolem's paradox

• Analytic proof
• Constructive proof: disjunction property, existence property
• Craig interpolation, Herbrand's theorem
• Hilbert system: consistency proof, deduction theorem
  • Disjunctive normal form, conjunctive normal form
  • Gödel's completeness theorem
  • Gödel's incompleteness theorem: 1-consistency, omega-consistency, self-verifying systems
  • Hilbert-Ackermann system^
  • Hilbert-Lewis system
• Natural deduction
  • double negative elimination, Glivenko's theorem, Gödel–Gentzen negative translation, Friedman translation
  • normal proof, subformula property
  • Fitch-style calculus
• Proof net
• Sequent calculus: cut-elimination, midsequent, Takeuti conjecture
• Structural proof theory: analytic proof, bunched implication
  • Display logic, Calculus of structures

• Theory (mathematical logic)
  • Structure (mathematical logic), signature (mathematical logic)
  • Pseudoelementary class, elementary class, reduct
• Arithmetic: Peano arithmetic, Robinson arithmetic, Second-order arithmetic

• Applied model theory
• Classical recursive mathematics
  • Markov's principle: Specker sequence, Strategy-stealing argument
• 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:
  • König's lemma
  • Non-measurable set: Banach–Tarski paradox, Hausdorff paradox, Vitali set
• Proof mining

• Algebraic semantics
• Denotational semantics
  • Full abstraction, full completeness
• Operational semantics

• Combinatory logic
  • Applicative structure
  • B,C,K,W system, SKI combinator calculus
  • Fixed point combinator
• Typed lambda calculus
  • Curry–Howard correspondence
  • Dependent type, Pure type system
  • Simply typed lambda calculus, system F
  • Lambda-mu calculus
• Logical framework
  • LF (logical framework) (rename to Edinburgh Logical Framework)
  • Calculus of constructions, calculus of inductive constructions
• Type inference

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

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

• Domain theory
  • Scott continuity
  • Synthetic 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

• Complexity theory

• Set theory: Axiomatic set theory
  • Zermelo set theory, Zermelo–Fraenkel set theory, Von Neumann–Bernays–Gödel set theory
  • Urelement
  • New Foundations
  • Morse–Kelley set theory
  • Kripke–Platek set theory, Kripke–Platek set theory with urelements
  • Fraenkel-Mostowski set theory
  • Positive set theory
  • Implementation of mathematics in set theory

• Böhm's theorem
• delta reduction

• Is logic empirical?
• Logic and pragmatics
  • Gricean maxim
• Paraconsistent logic: Brazilian logic, dialetheism
• Tense logic^
  • Accidental necessity, Compossibility, Principle of sufficient reason
  • Problem of future contingents

• Approaches to semantics of logic
  • Game semantics
  • Inferential role semantics
  • Model-theoretic semantics
  • Multiple-valued logic
  • Possible world semantics
  • Proof-theoretic semantics
  • Semantic theory of truth
  • Truth-conditional semantics
• Sense and reference, Sinn, Bedeutung
  • Definite description, rigid designator, non-rigid designator
  • Causal theory of reference, direct reference theory, theory of descriptions, theory of reference^
• Truth value, truth function

• 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

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

• 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

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

• Index of logic articles (R:List of topics in logic)
  • Outline of logic (R:List of basic topics in logic)
• List of logicians
• List of mathematical logic topics
  • List of basic discrete mathematics topics
  • List of rules of inference

• Table of mathematical symbols

• Category of being
• Concept
• Formal science
• Foundations of mathematics
  • Reverse mathematics
• Philosophy of science
• Reasoning
  • Analogy
• Thought, Idea
  • Law of thought

• Laws of thought: unfocussed article, not to be confused with article on Boole's Laws of Thought