Non-Axiomatic Reasoning System is an adaptive system that works with insu cient knowledge and resources. At the beginning of the paper, three binary term logics are de ned. The rst 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 Non-Axiomatic Logic is de ned. It has a term-oriented language and an experience-grounded semantics. It can uniformly represents and processes randomness, fuzziness, and ignorance. It can also uniformly carries out deduction, abduction, induction, and revision.

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Psychological evidence shows that probability theoryisnotaproper descriptive model of intuitive human judgment. Instead, some heuristics have been proposed as such a descriptive model. This paper argues that probability theory has limitations even as a normative model. A new normative model of judgment under uncertainty is designed under the assumption that the system's knowledge and resources are insu cient with respect to the questions that the system needs to answer. The proposed heuristics in human reasoning can also be observed inthis new model, and can be justi ed according to the assumption.