Classical Logic
| T true | ·∧· | ||
| ¬ | ↕ | ↕ | |
| ⊥ false | ·∨· | ||
| Negation permutes truth with false and conjunction with disjunction |
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In classical logic, with its intended semantics, the truth values are true (1 or T) and false (0 or ⊥); that is, classical logic is a two-valued logic. This set of two values is also called the Boolean domain. Corresponding semantics of logical connectives are truth functions, whose values are expressed in the form of truth tables. Logical biconditional becomes the equality binary relation, and negation becomes a bijection which permutes true and false. Conjunction and disjunction are dual with respect to negation, which is expressed by De Morgan's laws:
- ¬(p∧q) ⇔ ¬p ∨ ¬q
- ¬(p∨q) ⇔ ¬p ∧ ¬q
Propositional variables become variables in the Boolean domain. Assigning values for propositional variables is referred to as valuation.
Read more about this topic: True And False
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