User:Chalst/logic-watchlist

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

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

Logic in computer science

Logic for argument

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

Mathematical structures for logic and semantics

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

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

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