In propositional logic, atomic formulas are propositions, i.e., assertions such as
A := “‘Aristotle is dead.”’
B := “‘Hildesheim is on the Rhine.”’
C := “‘Logic is fun.”
Atomic formulas are denoted by capital letters A, B, C, etc.
Each atomic formula is assigned a truth value: true (1) or false (0).
(In fuzzy logic truth values can be degrees between 0 and 1.)
“‘Propositional logic is not the study of truth, but of the relationship between the truth of one statement and that of another”’
There are several relationships between propositions that can be
expressed:
| word | symbol | example | terminus technicus |
| not | ¬ | not A ¬A | negation |
| and | ∧ | A and B A ∧ B | conjunction |
| or | ∨ | A or B A ∨ B | disjunction |
| implies | → | A implies B A → B | implication |
| if and only if | ↔ | A if and only if B A ↔ B | biconditional |
What is propositional logic ?
The natural language words may have slightly different meanings.
Example:
A ∧ B and B ∧ A should always have the same meaning.