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.

Abstract not found

In a probability-based reasoning system, Bayes’ theorem and its variations are often used to revise the system’s beliefs. However, if the explicit conditions and the implicit conditions of probability assignments are properly distinguished,it follows that Bayes ’ theorem is not a generally applicable revision rule. Upon properly distinguishing belief revision from belief updating, we see that Jeffrey’s rule and its variations are not revision rules, either. Without these distinctions, the limitation of the Bayesian approach is often ignored or underestimated. Revision, in its general form, cannot be done in the Bayesian approach, because a probability distribution function alone does not contain the information needed by the operation. 1

. Problems for strict and convex Bayesianism are discussed. A set-based Bayesianism generalizing convex Bayesianism and intervalism is proposed. This approach abandons not only the strict Bayesian requirement of a unique real-valued probability function in any decision-making context but also the requirement of convexity for a set-based representation of uncertainty. Levi's E-admissibility decision criterion is retained and is shown to be applicable in the non-convex case. Keywords: Uncertainty, decision-making, maximum entropy, Bayesian methods. 1. Introduction. The reigning philosophy of uncertainty representation is strict Bayesianism. One of its central principles is that an agent must adopt a single, real-valued probability function over the events recognized as relevant to a given problem. Prescriptions for defining such a function for a given agent in a given situation range from the extreme personalism of deFinetti (1964, 1974) and Savage (1972) to the objective Bayesianism of...

Non-Axiomatic Reasoning System (NARS) is an intelligent reasoning system, where intelligence means working and adapting with insu cient knowledge and resources. NARS uses a new form of term logic, or an extended syllogism, in which several types of uncertainties can be represented and processed, and in which deduction, induction, abduction, and revision are carried out in a uni ed format. The system works in an asynchronously parallel way. The memory of the system is dynamically organized, and can also be interpreted as a network. After present the major components of the system, its implementation is brie y described. An example is used to show howthe system works. The limitations of the system are also discussed. 1

The paper studies the extension of one of the basic issues of classical statistics to interval probability. It is concerned with the Generalized Neyman-Pearson problem, i.e. an alternative testing problem where both hypotheses are described by interval probability. First the Huber-Strassen theorem and the literature based on it is reviewed. Then some results are presented indicating that the restrictive assumption of C-probability (two-monotonicity) underlying all that work can be overcome in favor of considering general interval probability in the sense of Weichselberger (1999A). So the full expressive power, which is provided by interval probability, can also be utilized in testing hypotheses. AMS classification: primary 62A20; secondary 60A05; 62F35 Keywords: Interval probability, F-probability, capacities, NeymanPearson testing, Huber-Strassen theorem, generalized neighborhood models, least favorable pseudo-capacities Thomas Augustin, Department of Statistics, Ludwig-M...

"Uncertainty in artificial intelligence" is an active research field, where several approaches have been suggested and studied for dealing with various types of uncertainty. However, it's hard to rank the approaches in general, because each of them is usually aimed at a special application environment. This paper begins by defining such an environment, then show why some existing approaches cannot be used in such a situation. Then a new approach, Non-Axiomatic Reasoning System, is introduced to work in the environment. The system is designed under the assumption that the system's knowledge and resources are usually insufficient to handle the tasks imposed by its environment. The system can consistently represent several types of uncertainty, and can carry out multiple operations on these uncertainties. Finally, the new approach is compared with the previous approaches in terms of uncertainty representation and interpretation. 1 The Problem The central issue of this paper is uncertaint...

this paper is to show that fuzzy logic is a suitable tool to manage several types of probability-like functionals. Namely, we show that the superadditive functions, the necessities, the upper and lower probabilities, and the envelopes can be considered theories of suitable fuzzy logics. Some general results about the compactness in fuzzy logic are also obtained. Q 1997 Academic Press 1.

Abstract not found

A complete description of intelligent or cognitive systems always requires a model of reasoning. In real world situations reasoning is never sharp. Therefore an interval statistical formalism is presented for reasoning under conditions of uncertainty on different levels. After a short outline of the theoretical foundations, the possibilities for a representation of psychological insights are discussed. Although substantial new aspects on the relationship between logic and statistics are provided the final example and the discussion of other theories are largely tutorial. I. INTRODUCTION A. Uncertainty The formal semantical interpretation of a proposition may be considered as the assignment of a truth value. In case of vagueness or unfulfilled presupposition of reference, the meaning of a proposition might become indeterminate, i.e. it can neither said to be true nor false. Thus, when assigning truth values to propositions there are three possibilities: the proposition is true, false ...