Sentential Logic
Sentential logic is the branch of formal logic that takes whole declarative sentences as atomic units and combines them with truth-functional connectives. Also called propositional logic in CS contexts (see Propositional Logic).
Why stop at whole sentences?
Working at the sentence level (rather than predicates and quantifiers) is enough to capture a huge range of valid argument forms with minimal machinery.
Atomic sentences are symbolized P, Q, R… Each stands for a complete declarative claim (“It is raining,” “Boots is a cat”).
| Symbol | Name | English |
|---|---|---|
| ¬ | negation | not |
| ∧ | conjunction | and |
| ∨ | disjunction | or (inclusive) |
| → | conditional | if … then |
| ↔ | biconditional | if and only if |
Two assumptions
- Bivalence: every sentence is either true or false (no third value, no gaps)
- Truth-functional: the truth value of a complex sentence is fully determined by the truth values of its atomic parts
Five core valid forms: Modus Ponens, Modus Tollens, Disjunctive Syllogism, Hypothetical Syllogism, Constructive Dilemma. Classic invalid: Affirming the Consequent, denying the antecedent.