Non-Axiomatic Reasoning System (Version 4.1)

Pei Wang Research Division, Intelligenesis Corporation and Center for Research on Concepts and Cognition, Indiana University

http://www.cogsci.indiana.edu/farg/pwang.html

Ë = È Ë È Introduction ¯ “ ” means that “ and are similar to each other”.

NARS (Non-Axiomatic Reasoning System) is an intelligent f “ ” is the truth value of the sentence, where is reasoning system. It answers questions according to the the “frequency”, a real number in [0, 1], indicating the ratio knowledge originally provided by its user. What makes it of positive evidence among all evidence of the relation, and different from conventional reasoning systems is its ability c is the “conﬁdence”, a real number in (0, 1), indicating the to learn from its experience and to work with insufﬁcient amount of evidence the system has on the relation. knowledge and resources. Each question that can be asked to the system has the form The NARS 4.1 demo is a Java applet. It comes with help ËÖÈ . A question looks just like a piece of knowledge, ex-

information and simple examples to show how the system È cept that there is no truth value, and that Ë or (but not does deduction, induction, abduction, analogy, belief revi- both) can be a special symbol “?”. A question without “?” sion, membership evaluation, relational inference, backward is like a “yes/no” question — the system is asked to evaluate inference, new concept formation, and so on, in a unified the truth value of the given relation. A question with “?” is manner. like a “what” question — the system is asked to find a term The demo also allows its user to create new examples to that have more positive evidence and less negative evidence test the system, as well as to see the internal structure and for the given relation. process when the system is running. The on-line help docu- Since the confidence of a piece of knowledge cannot reach ment contains links to relevant publications. 1.0, no answer is absolutely sure. Instead, the system needs A previous version of the system, NARS 3.0, is described to compare the available candidates to choose a “best an- in detail in (Wang, 1995), which, and other related publica- swer”, which may be overturned by new knowledge or fur- tions, are available at the author’s web page. ther consideration.

The System Inference Rules NARS is based on the conjecture that what we call “intelli- The following basic rules are involved in this demo. Each gence” can be built into a computer system by making it to of them in NARS takes two pieces of existing knowledge as adapt to its experience, that is, to answer questions accord- premises, and derive a piece of new knowledge as conclu- ing to available knowledge and resources. sion. The premises must share at least one common term. Concretely, it means that the system should open to new

knowledge and questions in real time, and answer questions Revision Deduction

Ë È Ë Å

½ ½ ½

according to its available knowledge when the knowledge ½

Ë È Å È

¾ ¾ ¾ and resources are insufﬁcient to provide a perfect answer. ¾

——————— ———————

È Ë È Knowledge Representation Ë NARS does not use ﬁrst-order predicate logic. Instead, each

Abduction Induction

piece of knowledge in NARS has the form “ ËÖÈ ”.

Ë Å Å Ë

½ ½ ½ ½ È

Here Ë is the subject term, and is the predicate term. In

È Å Å È

¾ ¾ ¾ ¾

the simplest situation, both of them are words. Ö is an in-

heritance relation. In this demo, three types of inheritance ——————— ———————

È Ë È

relations can be used: Ë

Ë È Ë È

¯ “ ” means that “ is a special type of ”; Analogy Comparison

Ë Å Ë Å

½ ½ ½ ½

Ë ¾ È Ë È

¯ “ ” means that “ is an instance of ”;

Å = È È Å

¾ ¾ ¾ ¾

¾ È fË gÈ

Since by deﬁnition Ë is identical to ,rules User Interface on the “¾” relation can be derived from those on the “ ” The user interface of NARS 4.1 allows the user to provide relation. knowledge and questions to the system in a text ﬁeld. The

In each rule, there is a truth value function that calculate system will return answers to the questions in another win-

f; c >

the strength and conﬁdence of the conclusion (< ) dow. Since the timing of input inﬂuences the system’s pro-

< f ;c > < f ;c >

½ ¾ ¾ from those of the premises ( ½ and ). cessing, the user can also specify the number of inference Different rule use different function. steps allowed between input events.

According to how the confidence c is calculated, the The user can let the system to work step by step, or to run above rules can be put into three categories: continuously. The user can open several display windows 1. In Deduction and Analogy, the confidence of the conclu- to watch the internal inference process, as well as the con- sion can be very close to the confidence of a premise, so tent and priority distribution of the task pool and knowledge these types of inference can produce relatively sure an- base. swers. There are several system parameters the user can adjust to change the system’s behavior, such as the forgetting rate of 2. In Abduction, Induction, and Comparison, the confidence the knowledge base, and so on. of the conclusion is always much lower than that of the There is an on-line User’s Guide that explains how the premises, so these types of inference are more tentative. demo can be used. 3. Revision is the only rule where the confidence of the conclusion is higher than that of the promises, because this Examples rule merges the evidence of the premises into that of the The NARS 4.1 demo has a set of examples attached, and conclusion. each of which shows a basic function or property of the system. By observing how the examples are processed in the

Besides these basic rules, NARS 4.1 also has compound- system, the user can get direct experience on how the sys-

term composition and decomposition rules, such as “ Ë tem works.

Ë È ½ Ë È ¾ È ½ \ È ¾µ ´ if and only if and ”. Another The examples include: input and output, context sen- type of rule is backward inference rule that derive question sitivity, deduction, induction, abduction, mixed inference,

from question and knowledge, such as from available knowl- conﬁdence processing, backward inference, contradiction

Å ? ¾ Å

edge “Ë ” and question “ ” to derive a new ques- handling, similarity evaluation, compound term formation,

¾ Ë tion “ ? ”, whose answer and the knowledge can derive Hempel’s paradox, relation operators, and fuzzy concept for- an answer to the original question. This kind of rule allows mation. the system to work in a goal-directed manner. In the on-line documentation, each example comes with a simple explanation about the system’s processing and the Control Mechanism result, as well as links to related publications. Because of the assumption of real time input, NARS cannot All of these examples can be given to the system by work on a task at a time, but must allow multiple tasks to copy/paste. When a user becomes familiar enough to the be under processing at the same time. Because of the as- system, he or she can create new examples to test the sys- sumption of insufﬁcient knowledge and resources, it cannot tem, as long as they can be expressed in the formal language assume that all tasks will be processed to their “logical end”, of NARS. or to be solved by considering all relevant knowledge in the These examples show that NARS is different from other system. reasoning systems in terms of the knowledge representation Instead, the system processes multiple inference tasks by language, the semantics of the language, the inference rules, time-sharing. Each task is given a priority value, which indi- the knowledge base structure, the control mechanism, and cates the frequency for it to be processed for a time slice. Af- the relation with users. NARS provides a uniﬁed solution to ter a task is selected for processing, a piece of knowledge is many problems that are traditionally handled in isolation to also selected according to a priority distribution, then the de- one another. rived task and knowledge are put back into the task pool and knowledge base, and the priority of the involved task and References knowledge is adjusted according to the feedback obtained in Wang, P. 1995. Non-Axiomatic Reasoning System: Explor- this inference step. ing the essence of intelligence. Ph.D. diss., Dept. of Com- When an answer is found for a user question, it is re- puter Science and Program of Cognitive Science, Indiana ported, then the system continue to look for a better one, Univ. if the task still have a high enough priority.

The Demonstration NARS has been implemented several times. The current version, 4.1, is a Java applet which is available at the author’s web page. There is also a ﬁle for download, which contains both the code and the documentation.