• Source: Outline of logic

Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct (or valid) and incorrect (or fallacious) inferences. Logicians study the criteria for the evaluation of arguments.




Foundations of logic


Philosophy of logic

Analytic-synthetic distinction
Antinomy
A priori and a posteriori
Definition
Description
Entailment
Identity (philosophy)
Inference
Logical form
Logical implication
Logical truth
Logical consequence
Name
Necessity
Material conditional
Meaning (linguistic)
Meaning (non-linguistic)
Paradox (list)
Possible world
Presupposition
Probability
Quantification
Reason
Reasoning
Reference
Semantics
Strict conditional
Syntax (logic)
Truth
Truth value
Validity




Branches of logic


Affine logic
Alethic logic
Aristotelian logic
Boolean logic
Buddhist logic
Bunched logic
Categorical logic
Classical logic
Computability logic
Deontic logic
Dependence logic
Description logic
Deviant logic
Doxastic logic
Epistemic logic
First-order logic
Formal logic
Free logic
Fuzzy logic
Higher-order logic
Infinitary logic
Informal logic
Intensional logic
Intermediate logic
Interpretability logic
Intuitionistic logic
Linear logic
Many-valued logic
Mathematical logic
Metalogic
Minimal logic
Modal logic
Non-Aristotelian logic
Non-classical logic
Noncommutative logic
Non-monotonic logic
Ordered logic
Paraconsistent logic
Philosophical logic
Predicate logic
Propositional logic
Provability logic
Quantum logic
Relevance logic
Sequential logic
Strict logic
Substructural logic
Syllogistic logic
Symbolic logic
Temporal logic
Term logic
Topical logic
Traditional logic
Zeroth-order logic




Philosophical logic






= Informal logic and critical thinking

=
Informal logic
Critical thinking
Argumentation theory

Argument
Argument map
Accuracy and precision
Ad hoc hypothesis
Ambiguity
Analysis
Attacking Faulty Reasoning
Belief
Belief bias
Bias
Cognitive bias
Confirmation bias
Credibility
Critical reading
Critical thinking
Decidophobia
Decision making
Dispositional and occurrent belief
Emotional reasoning
Evidence
Expert
Explanation
Explanatory power
Fact
Fallacy
Higher-order thinking
Inquiry
Interpretive discussion
Occam's razor
Opinion
Practical syllogism
Precision questioning
Propaganda
Propaganda techniques
Problem Solving
Prudence
Pseudophilosophy
Reasoning
Relevance
Rhetoric
Rigour
Socratic questioning
Source credibility
Source criticism
Theory of justification
Topical logic
Vagueness




= Deductive reasoning

=



Theories of deduction

Anti-psychologism
Conceptualism
Constructivism
Conventionalism
Counterpart theory
Deflationary theory of truth
Dialetheism
Fictionalism
Formalism (philosophy)
Game theory
Illuminationist philosophy
Logical atomism
Logical holism
Logicism
Modal fictionalism
Nominalism
Polylogism
Pragmatism
Preintuitionism
Proof theory
Psychologism
Ramism
Semantic theory of truth
Sophism
Trivialism
Ultrafinitism




= Fallacies

=
Fallacy (list) – incorrect argumentation in reasoning resulting in a misconception or presumption. By accident or design, fallacies may exploit emotional triggers in the listener or interlocutor (appeal to emotion), or take advantage of social relationships between people (e.g. argument from authority). Fallacious arguments are often structured using rhetorical patterns that obscure any logical argument. Fallacies can be used to win arguments regardless of the merits. There are dozens of types of fallacies.




Formal logic


Formal logic – Mathematical logic, symbolic logic and formal logic are largely, if not completely synonymous. The essential feature of this field is the use of formal languages to express the ideas whose logical validity is being studied.
List of mathematical logic topics




= Symbols and strings of symbols

=



Logical symbols


Logical variables
Propositional variable
Predicate variable
Literal
Metavariable
Logical constants
Logical connective
Quantifier
Identity
Brackets



= Logical connectives
=
Logical connective

Converse implication
Converse nonimplication
Exclusive or
Logical NOR
Logical biconditional
Logical conjunction
Logical disjunction
Material implication
Material nonimplication
Negation
Sheffer stroke



Strings of symbols


Atomic formula
Open sentence



Types of propositions

Proposition

Analytic proposition
Axiom
Atomic sentence
Clause (logic)
Contingent proposition
Contradiction
Logical truth
Propositional formula
Rule of inference
Sentence (mathematical logic)
Sequent
Statement (logic)
Subalternation
Tautology
Theorem



= Rules of inference
=
Rule of inference (list)

Biconditional elimination
Biconditional introduction
Case analysis
Commutativity of conjunction
Conjunction introduction
Constructive dilemma
Contraposition (traditional logic)
Conversion (logic)
De Morgan's laws
Destructive dilemma
Disjunction elimination
Disjunction introduction
Disjunctive syllogism
Double negation elimination
Generalization (logic)
Hypothetical syllogism
Law of excluded middle
Law of identity
Modus ponendo tollens
Modus ponens
Modus tollens
Obversion
Principle of contradiction
Resolution (logic)
Simplification
Transposition (logic)



Formal theories


Formal proof
List of first-order theories



Expressions in a metalanguage

Metalanguage

Metalinguistic variable
Deductive system
Metatheorem
Metatheory
Interpretation




= Propositional and boolean logic

=



Propositional logic

Propositional logic

Absorption law
Clause (logic)
Deductive closure
Distributive property
Entailment
Formation rule
Functional completeness
Intermediate logic
Literal (mathematical logic)
Logical connective
Logical consequence
Negation normal form
Open sentence
Propositional calculus
Propositional formula
Propositional variable
Rule of inference
Strict conditional
Substitution instance
Truth table
Zeroth-order logic



Boolean logic

Boolean algebra (list)
Boolean logic
Boolean algebra (structure)
Boolean algebras canonically defined
Introduction to Boolean algebra
Complete Boolean algebra
Free Boolean algebra
Monadic Boolean algebra
Residuated Boolean algebra
Two-element Boolean algebra
Modal algebra
Derivative algebra (abstract algebra)
Relation algebra
Absorption law
Laws of Form
De Morgan's laws
Algebraic normal form
Canonical form (Boolean algebra)
Boolean conjunctive query
Boolean-valued model
Boolean domain
Boolean expression
Boolean ring
Boolean function
Boolean-valued function
Parity function
Symmetric Boolean function
Conditioned disjunction
Field of sets
Functional completeness
Implicant
Logic alphabet
Logic redundancy
Logical connective
Logical matrix
Product term
True quantified Boolean formula
Truth table




= Predicate logic and relations

=



Predicate logic

Predicate logic

Atomic formula
Atomic sentence
Domain of discourse
Empty domain
Extension (predicate logic)
First-order logic
First-order predicate
Formation rule
Free variables and bound variables
Generalization (logic)
Monadic predicate calculus
Predicate (mathematical logic)
Predicate logic
Predicate variable
Quantification
Second-order predicate
Sentence (mathematical logic)
Universal instantiation



Relations

Mathematical relation

Finitary relation
Antisymmetric relation
Asymmetric relation
Bijection
Bijection, injection and surjection
Binary relation
Composition of relations
Congruence relation
Connected relation
Converse relation
Coreflexive relation
Covering relation
Cyclic order
Dense relation
Dependence relation
Dependency relation
Directed set
Equivalence relation
Euclidean relation
Homogeneous relation
Idempotence
Intransitivity
Involutive relation
Partial equivalence relation
Partial function
Partially ordered set
Preorder
Prewellordering
Propositional function
Quasitransitive relation
Reflexive relation
Serial relation
Surjective function
Symmetric relation
Ternary relation
Transitive relation
Trichotomy (mathematics)
Well-founded relation




Mathematical logic


Mathematical logic




= Set theory

=
Set theory (list)

Aleph null
Bijection, injection and surjection
Binary set
Cantor's diagonal argument
Cantor's first uncountability proof
Cantor's theorem
Cardinality of the continuum
Cardinal number
Codomain
Complement (set theory)
Constructible universe
Continuum hypothesis
Countable set
Decidable set
Denumerable set
Disjoint sets
Disjoint union
Domain of a function
Effective enumeration
Element (mathematics)
Empty function
Empty set
Enumeration
Extensionality
Finite set
Forcing (mathematics)
Function (set theory)
Function composition
Generalized continuum hypothesis
Index set
Infinite set
Intension
Intersection (set theory)
Inverse function
Large cardinal
Löwenheim–Skolem theorem
Map (mathematics)
Multiset
Morse–Kelley set theory
Naïve set theory
One-to-one correspondence
Ordered pair
Partition of a set
Pointed set
Power set
Projection (set theory)
Proper subset
Proper superset
Range of a function
Russell's paradox
Sequence (mathematics)
Set (mathematics)
Set of all sets
Simple theorems in the algebra of sets
Singleton (mathematics)
Skolem paradox
Subset
Superset
Tuple
Uncountable set
Union (set theory)
Von Neumann–Bernays–Gödel set theory
Zermelo set theory
Zermelo–Fraenkel set theory




= Metalogic

=
Metalogic – The study of the metatheory of logic.

Completeness (logic)
Syntax (logic)
Consistency
Decidability (logic)
Deductive system
Interpretation (logic)
Cantor's theorem
Church's theorem
Church's thesis
Effective method
Formal system
Gödel's completeness theorem
Gödel's first incompleteness theorem
Gödel's second incompleteness theorem
Independence (mathematical logic)
Logical consequence
Löwenheim–Skolem theorem
Metalanguage
Metasyntactic variable
Metatheorem
Object language – see metalanguage
Symbol (formal)
Type–token distinction
Use–mention distinction
Well-formed formula



Proof theory

Proof theory – The study of deductive apparatus.

Axiom
Deductive system
Formal proof
Formal system
Formal theorem
Syntactic consequence
Syntax (logic)
Transformation rules



Model theory

Model theory – The study of interpretation of formal systems.

Interpretation (logic)
Logical validity
Non-standard model
Normal model
Model
Semantic consequence
Truth value




= Computability theory

=
Computability theory – branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability and definability. The basic questions addressed by recursion theory are "What does it mean for a function from the natural numbers to themselves to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?". The answers to these questions have led to a rich theory that is still being actively researched.

Alpha recursion theory
Arithmetical set
Church–Turing thesis
Computability logic
Computable function
Computation
Decision problem
Effective method
Entscheidungsproblem
Enumeration
Forcing (computability)
Halting problem
History of the Church–Turing thesis
Lambda calculus
List of undecidable problems
Post correspondence problem
Post's theorem
Primitive recursive function
Recursion (computer science)
Recursive language
Recursive set
Recursively enumerable language
Recursively enumerable set
Reduction (recursion theory)
Turing machine




Semantics of natural language


Formal semantics (natural language)

Formal systems
Alternative semantics
Categorial grammar
Combinatory categorial grammar
Discourse representation theory
Dynamic semantics
Inquisitive semantics
Montague grammar
Situation semantics
Concepts
Compositionality
Counterfactuals
Generalized quantifier
Logic translation
Mereology
Modality (natural language)
Opaque context
Presupposition
Propositional attitudes
Scope (formal semantics)
Type shifter
Vagueness




Classical logic


Classical logic

Properties of classical logics:
Law of the excluded middle
Double negation elimination
Law of noncontradiction
Principle of explosion
Monotonicity of entailment
Idempotency of entailment
Commutativity of conjunction
De Morgan duality – every logical operator is dual to another
Term logic
General concepts in classical logic
Baralipton
Baroco
Bivalence
Boolean logic
Boolean-valued function
Categorical proposition
Distribution of terms
End term
Enthymeme
Immediate inference
Law of contraries
Logical connective
Logical cube
Logical gyroelongated square bipyramid
Logical hexagon
Logical icosahedron
Logical octahedron
Logical pentagon
Logical pentagonal bipyramid
Logical snub dishenoid
Logical triaugmented triangular prism
Logical triangular bipyramid
Logical tetrahedron
Major term
Middle term
Minor term
Octagon of Prophecies
Organon
Polysyllogism
Port-Royal Logic
Premise
Prior Analytics
Relative term
Sorites paradox
Square of opposition
Triangle of opposition
Sum of Logic
Syllogism
Tetralemma
Truth function




= Modal logic

=
Modal logic

Alethic logic
Deontic logic
Doxastic logic
Epistemic logic
Temporal logic




Non-classical logic


Non-classical logic

Affine logic
Bunched logic
Computability logic
Decision theory
Description logic
Deviant logic
Free logic
Fuzzy logic
Game theory
Intensional logic
Intuitionistic logic
Linear logic
Many-valued logic
Minimal logic
Non-monotonic logic
Noncommutative logic
Paraconsistent logic
Probability theory
Quantum logic
Relevance logic
Strict logic
Substructural logic




Concepts of logic


Deductive reasoning
Inductive reasoning
Abductive reasoning
Mathematical logic

Proof theory
Set theory
Formal system
Predicate logic
Predicate
Higher-order logic
Propositional calculus
Proposition
Boolean algebra
Boolean logic
Truth value
Venn diagram
Peirce's law
Aristotelian logic
Non-Aristotelian logic
Informal logic
Fuzzy logic
Infinitary logic
Infinity
Categorical logic
Linear logic
Metalogic
Order
Ordered logic
Temporal logic
Linear temporal logic
Linear temporal logic to Büchi automaton
Sequential logic
Provability logic
Interpretability logic
Interpretability
Quantum logic
Relevant logic
Consequent
Affirming the consequent
Antecedent
Denying the antecedent
Theorem
Axiom
Axiomatic system
Axiomatization
Conditional proof
Invalid proof
Degree of truth
Truth
Truth condition
Truth function
Double negation
Double negation elimination
Fallacy
Existential fallacy
Logical fallacy
Syllogistic fallacy
Type theory
Game theory
Game semantics
Rule of inference
Inference procedure
Inference rule
Introduction rule
Law of excluded middle
Law of non-contradiction
Logical constant
Logical connective
Quantifier
Logic gate
Boolean Function
Quantum logic gate
Tautology
Logical assertion
Logical conditional
Logical biconditional
Logical equivalence
Logical AND
Negation
Logical OR
Logical NAND
Logical NOR
Contradiction
Subalternation
Logicism
Polysyllogism
Syllogism
Hypothetical syllogism
Major premise
Minor premise
Term
Singular term
Major term
Middle term
Quantification
Plural quantification
Logical argument
Validity
Soundness
Inverse (logic)
Non sequitur
Tolerance
Satisfiability
Logical language
Paradox
Polish notation
Principia Mathematica
Quod erat demonstrandum
Reductio ad absurdum
Rhetoric
Self-reference
Necessary and sufficient
Sufficient condition
Nonfirstorderizability
Occam's Razor
Socratic dialogue
Socratic method
Argument form
Logic programming
Unification




History of logic


History of logic




Literature about logic






= Journals

=
Journal of Logic, Language and Information
Journal of Philosophical Logic
Linguistics and Philosophy




= Books

=
A System of Logic
Attacking Faulty Reasoning
Begriffsschrift
Categories (Aristotle)
Charles Sanders Peirce bibliography
De Interpretatione
Gödel, Escher, Bach
Introduction to Mathematical Philosophy
Language, Truth, and Logic
Laws of Form
Novum Organum
On Formally Undecidable Propositions of Principia Mathematica and Related Systems
Organon
Philosophy of Arithmetic
Polish Logic
Port-Royal Logic
Posterior Analytics
Principia Mathematica
Principles of Mathematical Logic
Prior Analytics
Rhetoric (Aristotle)
Sophistical Refutations
Sum of Logic
The Art of Being Right
The Foundations of Arithmetic
Topics (Aristotle)
Tractatus Logico-Philosophicus




Logic organizations


Association for Symbolic Logic




Logicians


List of logicians
List of philosophers of language




See also



Index of logic articles
Mathematics
List of basic mathematics topics
List of mathematics articles
Philosophy
List of basic philosophy topics
List of philosophy topics
Outline of discrete mathematics – for introductory set theory and other supporting material




References






External links



Taxonomy of Logical Fallacies
forall x: an introduction to formal logic, by P.D. Magnus, covers sentential and quantified logic
Translation Tips, by Peter Suber, for translating from English into logical notation
Math & Logic: The history of formal mathematical, logical, linguistic and methodological ideas. In The Dictionary of the History of Ideas.
Logic test Test your logic skills
Logic Self-Taught: A Workbook (originally prepared for on-line logic instruction)

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