Mathematical logic and foundations Propositional logic Concept
Propositional logic
Builds on PropositionNegationConjunctionDisjunctionImplicationBiconditional
Summary
Propositional logic is the part of logic that studies propositions and the connectives that join them. Its formulas are made from propositional variables with connectives such as , , , and . It does not look inside a proposition, so it has no variables for objects and no quantifiers.
Remarks
Other names are sentential logic and propositional calculus. In classical propositional logic, the value of a formula depends only on the values of its variables. A truth table computes it. Predicate logic extends propositional logic with predicates and quantifiers.
Reading path
To understand this page from the ground up, read these 7 pages in order. The foundations come first.
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- no evidence level
- Proposition concept
- Conjunction definition
- Disjunction definition
- Implication definition
- Negation definition
- Biconditional definition
- Propositional logic concept
Where this leads
94 pages build on this one.
- Cantor set is closed
- Closure is closed
- Contrapositive
- Logical equivalence
- Predicate logic
- De Morgan's laws
- Intersection of closed sets is closed
- Proof by contrapositive
- Tautology
- A set is closed iff it equals its closure
- Zermelo–Fraenkel set theory
- Russell's paradox
- Proof by contradiction
- Double negation law
- Closure is the smallest closed superset
- De Morgan's laws for sets
- Proof complexity
- Model theory
- Proof complexity
- Brouwer–Heyting–Kolmogorov interpretation
- Forcing
- Transfer principle
- Von Neumann universe
- Type theory
- Second-order logic
- Realizability
- Intuitionistic logic
- Woodin cardinal
- Naive set theory
- Many-valued logic
- Skolem's paradox
- Axiom of regularity
- Constructible universe
- Brouwer–Heyting–Kolmogorov interpretation
- Kunen's inconsistency theorem
- Interior algebra
- Borel determinacy theorem
- Singular cardinals hypothesis
- Axiom schema of replacement
- Internal set theory
- Constructive analysis
- Curry–Howard correspondence
- Cut-elimination theorem
- Ordinal analysis
- Algebraic logic
- Logical connective
- Burali-Forti paradox
- Axiom schema of replacement
- Realizability
- Cohen's independence of CH
- Homotopy type theory
- Intuitionistic type theory
- Hilbert system
- Paraconsistent logic
- Whitehead problem
- Constructivism
- Infinitary logic
- Lindström's theorem
- Theory
- Nonstandard analysis
- Modal logic
- Constructivism
- Linear logic
- Zero sharp
- Constructive analysis
- Homotopy type theory
- Set theory
- Von Neumann–Bernays–Gödel set theory
- Satisfiability
- Higher-order logic
- Intuitionistic type theory
- Logical consequence
- Lindenbaum–Tarski algebra
- Proof theory
- Axiom of regularity
- Natural deduction
- Signature
- Sequent calculus
- Axiom of constructibility
- Foundations of mathematics
- Type theory
- Gödel's consistency of CH and AC
- Jensen's covering theorem
- Set theory
- Proof theory
- Logicism
- Von Neumann–Bernays–Gödel set theory
- Church's theorem on undecidability of first-order logic
- Class
- Sequent calculus
- Axiom of determinacy
- Inner model
- Naive set theory
- Class
Further reading
- Web https://en.wikipedia.org/wiki/Propositional_logic, lead section
About this page
| Tag | 09K9MWD2QQ |
|---|---|
| URI | m2://09K9MWD2QQ |
| Aliases | sentential-logic, propositional-calculus |
| Kind | concept |
| Writing | W1 stated |
| MSC | 03B05 |
| Uses | Proposition, Negation, Conjunction, Disjunction, Implication, Biconditional |
| Same as |
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What this page needs for W2
- edge defines in: at least one definition (0 of 1)
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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