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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An experience-grounded semantics is introduced for an intelligent reasoning system, which is adaptive, and works with insufficient knowledge and resources. According to this semantics, truth and meaning are defined with respect to the experience of the system — the truth value of a statement indicates the amount of available evidence, and the meaning of a term indicates its experienced relations with other terms. The major difference between experience-grounded semantics and modeltheoretic semantics is that the former does not assume the sufficiency of knowledge and resources. This approach provides new ideas to the solution of some important problems in cognitive science.

First-order predicate logic meets many problems when used to explain or reproduce cognition and intelligence. These problems have a common nature, that is, they all exist outside mathematics, the domain for which mathematical logic was designed. Cognitive logic and mathematical logic are fundamentally different, and the former cannot be obtained by partially revising or extending the latter. A reasoning system using a cognitive logic is briefly introduced, which provides solutions to many problems in a unified manner. 1 Mathematical logic and cognition An automatic reasoning system usually consists of the following major components: 1. a formal language that represents knowledge, 2. a semantics that defines meaning and truth value in the language, 3. a set of inference rules that derives new knowledge, 4. a memory that stores knowledge, 5. a control mechanism that chooses premises and rules in each step. The first three components are usually referred to as a logic, or the logical part of the reasoning system, and the last two as an implementation of the logic, or the control part of the system. At the present time, the most influential theory for the logic part of reasoning systems is mathematical logic, especially, first-order predicate logic. For the control part, it is the theory of computability and computational complexity. Though these theories have been very successful in many domains, their application in cognitive science and artificial intelligence shows fundamental differences from human reasoning in similar situations.

This paper discusses the problem of resources-limited information processing. After a review of relevant approaches in several fields, a new approach, controlled concurrency, is described and analyzed. This method is proposed for adaptive systems working under insufficient knowledge and resources. According to this method, a problemsolving activity consists of a sequence of steps which behaves like an anytime algorithm --- it is interruptible, and the quality of the result is improved incrementally. The system carries out many such activities in parallel, distributes its resources among the them in a time-sharing manner, and dynamically adjusts the distribution according to the feedback of each step. The step sequence for a given problem is formed at run time, according to the system's knowledge structure, which is also dynamically formed and adjusted. Finally, this approach is compared with other approaches, and several of its properties and implications are discussed. In a computer ...