From inheritance relation to nonaxiomatic logic

Abstract A nonaxiomatic reasoning system is an adaptive system that works with insufficient knowledge and resources. At the beginning of the paper, three binary term logics are defined. The first is based only on an inheritance relation. The second and the third suggest a novel way to process extension and intension, and they also have interesting relations with Aristotle's syllogistic logic. Based on the three simple systems, a nonaxiomatic logic is defined. It has a term-oriented language and an experience-grounded semantics. It can uniformly represent and process randomness, fuzziness, and ignorance. It can also uniformly carry out deduction, abduction, induction, and revision.

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