User:Chalst/logic-watchlist

Core logic

See Wikipedia: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)#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

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

Mathematical logic

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

Logic in computer science

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

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).

Logic for argument

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

Mathematical structures for logic and semantics

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