# 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 29 subcategories, out of 29 total.

### B

- Bottom (empty)

### C

### D

### E

### F

- Functional Completeness (15 P)

### H

- Hilbert Proof System Instance 2 (16 P)

### I

### L

- Law of Identity (14 P)

### M

### N

### P

- Precisely One Function (1 P)

### R

- Rule of Sequent Introduction (1 P)
- Rule of Substitution (1 P)
- Rule of Theorem Introduction (1 P)

### T

- Top (empty)
- Truth Table Proofs (100 P)

## Pages in category "Propositional Logic"

The following 37 pages are in this category, out of 37 total.

### E

- Equivalence of Definitions of Consistent Proof System
- Equivalence of Definitions of Consistent Set of Formulas
- Equivalence of Logical Implication and Conditional
- Equivalence of Semantic Consequence and Logical Implication
- Existence of Conjunctive Normal Form of Statement
- Existence of Disjunctive Normal Form of Statement
- Existence of Negation Normal Form of Statement

### L

### N

### P

### S

- 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 Tableaus
- Soundness and Completeness of Semantic Tableaus/Corollary 1
- Soundness and Completeness of Semantic Tableaus/Corollary 2
- Soundness Theorem for Semantic Tableaus
- Substitution for Equivalent Subformula is Equivalent