User:Chalst/logic-watchlist

=Core logic=
 * See WikiProject Logic, User:Chalst/WikiProject Logic proposal, Portal:Logic

Fundamental definitions

 * 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

History of logic

 * 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)

Types of logic

 * 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

Inference

 * 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)
 * Square of opposition
 * Natural deduction
 * elimination rule
 * introduction rule, conjunction introduction


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

Parts of logic
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

=Subdisciplines of logic=

Knowledge representation and reasoning

 * 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

Algebraic logic

 * 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

Model theory

 * 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

Proof theory

 * 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

Theories

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

Applications of logic in mathematical

 * 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

Semantics of programming languages

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

Type theory

 * 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

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

Logic for argument

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

Topology and order theory

 * 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

Recursion theory

 * Complexity theory

Set 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

Untyped lambda calculus

 * Böhm's theorem
 * delta reduction

Philosophy of logic and Philosophical logic

 * 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

Semantics of logic

 * 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

=The human side=

Logicians

 * 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

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

=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

=Related content=

Categories

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

Lists and tables

 * 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

Articles

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

False friends

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