logical-reasoninglisted

# Logical Reasoning Logic is the study of what follows from what. A valid logical argument has a form that preserves truth — if the premises are true, the conclusion cannot be false. This skill covers the core machinery of deductive and inductive reasoning: the rules of inference, the standard argument forms, the common errors, and the boundary between the two styles of reasoning. **Agent affinity:** paul (chair-level framing), elder (inference-pattern drills), tversky (inductive strength) **Concept IDs:** crit-deductive-reasoning, crit-inductive-reasoning, crit-argument-structure ## The Reasoning Toolbox at a Glance | # | Pattern | Form | Type | |---|---|---|---| | 1 | Modus ponens | If P then Q; P; therefore Q | Deductive, valid | | 2 | Modus tollens | If P then Q; not Q; therefore not P | Deductive, valid | | 3 | Hypothetical syllogism | If P then Q; if Q then R; therefore if P then R | Deductive, valid | | 4 | Disjunctive syllogism | P or Q; not P; therefore Q | Deductive, valid | | 5 | Constructive dilemma | (P or Q); (if P then R); (if Q then S); therefore (R or S) | Deductive, valid | | 6 | Universal instantiation | All A are B; x is an A; therefore x is a B | Deductive, valid | | 7 | Existential generalization | a has property P; therefore something has property P | Deductive, valid | | 8 | Affirming the consequent | If P then Q; Q; therefore P | Deductive, INVALID | | 9 | Denying the antecedent | If P then Q; not P; therefore not Q | Deductive, INVALID | | 10 |