Reasoning with Generics and Induction

Based on the results of reasoning with generics, this paper attempts to clarify the relationship between generic reasoning and inductive reasoning. First, to capture reasoning with generics, logics for obtaining intermediate conclusions are provided; then, the priority order of the subsets of the premise set are introduced to eliminate the contradictions or incompatibility generated by intermediate conclusions. Through these filters, the final conclusions are obtained. There are different priority rules on subsets of a premise set corresponding to three kinds of generic reasoning: reasoning with factual sentences (from generic sentences), reasoning by deduction and reasoning by induction. If these three kinds of reasoning are combined, together they can characterise inductive reasoning. After reviewing how scholars’ have previously interpreted inductive reasoning, this paper concludes that there is another way to interpret inductive reasoning with generic reasoning, parallel to the probability method. 1 Reasoning with generics Generic sentences, for instance, ‘birds fly ’ or ‘ducks lay eggs’, express rules or laws. Unlike universal sentences, generic sentences tolerate exceptions. Even when there is no positive example in the real world (for example, ‘unicorns have one horn’), we sometimes accept a generic sentence, which makes generic sentences intensional. Because reasoning with generics tolerates exceptions, it is non-monotonic. 1.1 Interpretation of generic sentences This paper restricts its scope to i-generics1 and employs the semantics from Mao and Zhou (2003) for generics: The canonical form of a generic sentence with subject-predicate (SP) structure is ‘(normal S) (normally P)’. The duty of ‘normal’ is to choose a set of (normal) objects (the term’s extension) for every possible world based on both a subject sense and predicate sense. ‘Normally’ is used to choose the normal situation. The sense of the term ‘S’ can be expressed as λxS by λ-expression. From a semantic aspect, a sense is a function expressed as s, and ‘normal’ is a binary function N (s1, s2) called the normal function. s1, s2 respectively ∗ This work was supported by “the Fundamental Research Funds for the Central Universities”. Copyright c ⃝ by the paper’s authors. Copying permitted for private and academic purposes. In: T. Ågotnes, B. Liao, Y.N. Wang (eds.): Proceedings of the first Chinese Conference on Logic and Argumentation (CLAR 2016), Hangzhou, China, 2-3 April 2016, published at http://ceur-ws.org 1Krifka et al. (1995) distinguish between d-generic and i-generic sentences. ‘Dinosaurs are extinct’ is an example of d-generic sentence, since a type of animal can be extinct but individual members of that type can only be dead. ‘Birds fly’ is a famous example of an i-generic sentence.