Category:Propositional Logic
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This category contains results about Propositional Logic.
Definitions specific to this category can be found in Definitions/Propositional Logic.
Propositional logic is a sub-branch of symbolic logic in which the truth values of propositional formulas are investigated and analysed.
The atoms of propositional logic are simple statements.
There are various systems of propositional logic for determining the truth values of propositional formulas, for example:
- Natural deduction is a technique for deducing valid sequents from other valid sequents by applying precisely defined proof rules, each of which themselves are either "self-evident" axioms or themselves derived from other valid sequents.
- The Method of Truth Tables, which consists of the construction of one or more truth tables which exhaustively list all the possible truth values of all the statement variables with a view to determining the required answer by inspection.
Subcategories
This category has the following 36 subcategories, out of 36 total.
A
- Atoms of Propositional Logic (empty)
B
- Bottom (empty)
C
D
- De Morgan's Laws (Logic) (50 P)
- Deduction Theorem (2 P)
E
F
- Functional Completeness (15 P)
H
- Hilbert Proof System Instance 2 (18 P)
L
- Law of Identity (14 P)
M
N
P
- Precisely One Function (1 P)
- Proof by Contraposition (5 P)
R
- Rule of Sequent Introduction (1 P)
- Rule of Substitution (1 P)
- Rule of Theorem Introduction (1 P)
S
- Statement Variables (empty)
T
- Top (empty)
- Truth Table Proofs (103 P)
Ł
Pages in category "Propositional Logic"
The following 35 pages are in this category, out of 35 total.
E
N
P
- Proof by Contraposition
- Proof of Theorem by Truth Table
- Propositional Calculus is Decidable
- Provable by Gentzen Proof System iff Negation has Closed Tableau
- Provable by Gentzen Proof System iff Negation has Closed Tableau/Formula
- Provable by Gentzen Proof System iff Negation has Closed Tableau/Set of Formulas
S
- Semantic Consequence Union Negation
- Semantic Tableau Algorithm
- Semantic Tableau Algorithm is Decision Procedure for Tautologies
- Semantic Tableau Algorithm Terminates
- Semantic Tableau Algorithm/Heuristics
- Set of Literals Satisfiable iff No Complementary Pairs
- Soundness and Completeness of Gentzen Proof System
- Soundness and Completeness of Semantic Tableaux
- Soundness and Completeness of Semantic Tableaux/Corollary 1
- Soundness and Completeness of Semantic Tableaux/Corollary 2
- Soundness Theorem for Semantic Tableaux
- Substitution for Equivalent Subformula is Equivalent