Uniied Inference in Extended Syllogism 1. Term Logic vs. Predicate Logic

There are two major traditions in formal logic: term logic and propo-sitional/predicate logic, exempliied respectively by the Syllogism of Aristotle and the First-Order Predicate Logic founded by Frege, Rus-sell, and Whitehead. Term logic is diierent from predicate logic in both its knowledge representation language and its inference rules. Term logic represents knowledge in subject{predicate statements. In the simplest form, such a statement contains two terms, linked together by an inheritance relation: S P where S is the subject term of the statement, and P is the predicate term. Intuitively, this statement says that S is a specialization (instan-tiation) of P, and P is a generalization (abstraction) of S. This roughly corresponds to \S is a kind of P" in English. Term logic uses syllogistic inference rules, in each of which two statements sharing a common term generate a new statement linking the two unshared terms. In Aristotle's syllogism (Aristotle, 1989), all statements are binary (that is, either true or false), and all valid inference rules are deduction, therefore when both premises are true, the conclusion is guaranteed to be true. When Aristotle introduced the deduction/induction distinction , he presented it in term logic, and so did Peirce when he added abduction into the picture (Peirce, 1931). According to Peirce, the de-duction/abduction/induction triad is deened formally in terms of the position of the shared term: c 1998 Kluwer Academic Publishers. Printed in the Netherlands.