To integrate existing AI techniques into a consistent system, an intelligent core is needed, which is general and flexible, and can use the other techniques as tools to solve concrete problems. Such a system, NARS, is introduced. It is a general-purpose reasoning system developed to be adaptive and capable of working with insufficient knowledge and resources. Compared to traditional reasoning system, NARS is different in all major components (language, semantics, inference rules, memory structure, and control mechanism).
NARS is an intelligent reasoning system, whose interaction with its environment can be described as a stream of input sentences in a formally defined language and a stream of output sentences in the same language. These two streams are called the system's "experience" and "responses", respectively (Wang, 1994; Wang, 1995a; Wang, 1995b). Each sentence in the language represents an inheritance relation between two terms. By definition, a sentence "S C P" indicates that the subject term "S" is in the extension of the predicate term "P", and "P" is in the intension of "S". Because the relation "C" is defined to be reflexive and transitive, "S C P" also indicates that "S" inherits the intension of "P", and "P" inherits the extension of "S".
NARS (Non-Axiomatic Reasoning System) is an intelligent reasoning system. It answers questions according to the knowledge originally provided by its user. What makes it different from conventional reasoning systems is its ability to learn from its experience and to work with insufficient knowledge and resources. The NARS 4.1 demo is a Java applet. It comes with help information and simple examples to show how the system does deduction, induction, abduction, analogy, belief revision, membership evaluation, relational inference, backward inference, new concept formation, and so on, in a unified manner. The demo also allows its user to create new examples to test the system, as well as to see the internal structure and process when the system is running. The online help document contains links to relevant publications. A previous version of the system, NARS 3.0, is described in detail in (Wang, 1995), which, and other related publications, are available at the author's web page.
This paper introduces and discusses a new algebraic structure, the quasi-topologic structure. The idea of this structure comes from language analysis on the one hand and from analysis of some real situations of clustering on the other. From the cognitive point of view, it is related to the Logic of Determination of Objects (LDO) and to the Logic of Typical and Atypical Objects (LTA) which is particular case of LDO. From the mathematical point of view, it is related to topology. By introducing the notion of internal and external border, it extends the notion of border from classical topology.
The difference between typical instances and atypical instances in a natural categorization process has been introduced by E. Rosh and studied by cognitive psychology and AI. A lot of the knowledge representation systems are expressed in using fuzzy concepts but a degree of membership raises some problem for natural categorizations (especially to classification problems in anthropology, ethnology, archeology, linguistics but also in ontologies), but atypical instances of a concept cannot be apprehended adequately by different degrees from a prototype. Other formal approaches, as paraconsistent logics or non monotonic logics, conceptualize often atypical objects as exceptions. It had yet been developed an alternative way with the logics of determination of the objects (LDO). In this paper, we present the logics of typical and atypical (LTA) in order to give directly a logical approach of typicality / atypicality associated to a concept by a more common way than in LDO, in using only classes and not determination operators. It is introduced a distinction between predicative property and concept defined with its intension and its essence, a part of intension. A typical instance of a concept inherits all properties of intension; a typical instance inherits only properties of essence but it is a full member of the category associated to a concept and not a member with a weak degree of membership. In natural categorization, there are often instances (the exceptions) which do not inherit some properties of the essence; they cannot be considered as atypical instance and belong to the boundary of the category.