証明力を拡張した適切さの論理ER

抄録

The formalization of human deductive reasoning is a main issue in artificial intelligence. Although classical logic (CL) is one of the most useful ways for the formalization, the implication of CL has some fallacies. For example, in CL, A ⟶ B can be inferred from B for an arbitrary formula A. This inference is not relevant from the viewpoint of the meaning of implication which human has. In human reasoning, when A ⟶ B is inferred, A and B should be related. Relevant logic has been studied for removal of the implication fallacies of CL. For the relevance of A ⟶ B, several principles are introduced. One of the most important principles is Variable-sharing, where, if A ⟶ B is a theorem, then A and B share an atomic proposition. Relevant logical system should satisfy this principle. Another principle is that the truth values of A and B do not decide A ⟶ B. Classification of the fallacies of implication is also introduced. Fallacies are classified into those of relevance, validity, or necessity. Since the fallacies of relevance and validity are strong fallacies, they are removed from almost all relevant logical systems. Relevant logic, however, is a weaker logical system than CL. In this paper, we propose the relevant logic ER. Then we prove that Variable-sharing holds in ER, that fallacies of relevance and validity are removed from ER. We also prove that ER is not weaker than R. Respecially, disjunctive syllogism holds in ER but does not hold in R. In this sense, ER is a natural formalization of human reasoning.