Chrysippus used a hunting dog at a three-way fork to illustrate the disjunctive syllogism (~230 BCE), an early figure of reasoning by elimination

Chrysippus of Soli (c. 279 – c. 206 BCE), the third head of the Stoa and the principal systematizer of Stoic propositional logic, is associated with a stock example of a hunting dog that reaches a fork of three roads: having sniffed and rejected two of the paths, it takes the third without sniffing — reasoning, in effect, that "the animal took either A or B or C, so if it did not take A or B it must have taken C." The move is the disjunctive syllogism (modus tollendo ponens): from a disjunction and the denial of all but one disjunct, the remaining disjunct is affirmed. It is inference by elimination — arriving at a conclusion not by confirming it directly but by ruling out the alternatives.

The example survives chiefly through the sceptic Sextus Empiricus, who cites the dog while debating whether animals reason; the Stoics themselves generally denied that animals possess logos, so the dog is best read as a vivid illustration of a logical form rather than a claim about canine rationality. What matters for the vault is the form: the disjunctive syllogism is one of the oldest explicit statements of reasoning-by-elimination, the same shape later mechanized in Jevons's Logic Piano, embodied in the goal-directed elimination of backward-chaining inference engines, and turned into an analytic discipline in Heuer's Analysis of Competing Hypotheses. It sits under the deductive branch of the three canonical forms of inference and is developed as a recurring mechanism in observation-reasoning-by-elimination-from-stoic-logic-to-symbolic-ai.