Formalized nonmonotonic reasoning emerged in relation to the study of artificial intelligence. The paper discusses some uses of nonmonotonic reasoning that has become a mathematical subject, observations regarding AI, and the problems logical AI encountered before it can reach human level intelligence.

article Share on Problems and projections in CS for the next 49 years Author: John McCarthy Stanford University, Stanford, California Stanford University, Stanford, CaliforniaView Profile Authors Info & Claims Journal of the ACMVolume 50Issue 1January 2003 pp 73–79https://doi.org/10.1145/602382.602405Published:01 January 2003Publication History 5citation2,392DownloadsMetricsTotal Citations5Total Downloads2,392Last 12 Months10Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

Phenomenal data mining finds relations between the data and the phenomena that give rise to data rather than just relations among the data..Science and common sense both tell us that the facts about the world are not directly observable but can be inferred from observations about the effects of actions. What people infer about the world is not just relations among observations but relations among entities that are much more stable than observations. For example, 3-dimensional objects are more stable than the image on a person's retina, the information directly obtained from feeling an object or on an image scanned into a computer..This talk concerns what can be inferred by programs about phenomena from data and what facts are relevant to doing this. In order to infer phenomena from data, facts about their relations must be supplied. Sometimes these facts can be implicit in the programs that look for the phenomena, but more generality is achieved if the facts are represented as sentences of logic in a knowledge base used by the programs..Creating knowledge bases containing both common sense knowledge and knowledge of the domain of the data will be a lot of work. This is unavoidable..The result of phenomenal data-mining can include an extended database with additional fields on existing relations and new relations. Thus the relations describing supermarket baskets can be extended with a customer field, and new relations about customers and their properties can be introduced..

Human free will is a product of evolution and contributes to the success of the human animal. Useful robots will also require free will of a similar kind, and we will have to design it into them. Free will is not an all-or-nothing thing. Some agents have more free will, or free will of different kinds, than others, and we will try to analyse this phenomenon. Our objectives are primarily technological, i.e. to study what aspects of free will can make robots more useful, and we will not try to console those who find determinism distressing. We distinguish between having choices and being conscious of these choices; both are important, even for robots, and consciousness of choices requires more structure in the agent than just having choices and is important for robots. Consciousness of free will is therefore not just an epiphenomenon of structure serving other purposes. Free will does not require a very complex system. Young children and rather simple computer systems can represent internally ‘I can, but I won't’ and behave accordingly. Naturally I hope this detailed design stance will help understand human free will. It takes the compatibilist philosophical position. There may be some readers interested in what the paper says about human free will and who are put off by logical formulas. The formulas are not important for the arguments about human free will; they are present for people contemplating AI systems using mathematical logic. They can skip the formulas, but the coherence of what remains is not absolutely guaranteed.

Progress in logic-based AI Hubert Dreyfus claims that "symbolic AI" is a "degenerating research program", i.e. is not making progress.It's hard to see how he would know, since he makes no claim to have read much of the recent literature.In defending "symbolic AI", I shall concentrate on just one part of symbolic AI-the logic-based approach.It was first proposed in [7], attracted only intermittent following at first, but has had an increasing number of workers since 1970.'I think other approaches to AI will also eventually succeed, perhaps even connectio'nism.To contradict an earlier Dreyfus metaphor "AI at the Crossroads Again", it isn't a crossroads but a race including logic-based AI, SOAR, connectionism and several other contenders.How goes the logic-based runner?In fits and starts, as problems are identified and progress made.Within logic-based AI, I shall emphasize one development-formalized nonmonotonic reasoning, because it illustrates intermittent but definite progress.It was first proposed in [8], gained momentum with the 1980 special issue of Artificial Intelligence, and summarized in the collection [3].It has continued to develop, see e.g.[6].Minsky [ll] mentioned the need for something like nonmonotonic reasoning, but used this fact as evidence for the inadequacy of logic-based approaches to AI and the need for approaches not based on logic.This isn't how things have gone.Nonmonotonic reasoning has developed as a branch of mathematical logic, using * (MIT Press, Cambridge, MA, 1992); liii + 354 pages, $13.95.

We present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in (McCarthy 1980) and some applications to formalizing common sense knowledge. The applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities. Included are nonmonotonic treatments of is-a hierarchies, the unique names hypothesis, and the frame problem. The new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription. A still more general formalism called prioritized circumscription is briefly explored.

First Order Programming Logic is a simple, yet powerful formal system for reasoning about recursive programs. In its simplest form, it has one major limitation: it cannot establish any property of the least fixed point of a recursive program which is false for some other fixed point. To rectify this weakness, we present two intuitively distinct approaches to strengthening First Order Programming Logic and prove that either extension makes the logic relatively complete. In the process, we prove that the two approaches are formally equivalent. The relative completeness of the extended logic is significant because it suggests it can establish all "ordinary" properties (obviously we cannot escape the Godelian incompleteness inherent in any programming logic) of recursive programs including those which compute partial functions.The second contribution of this paper is to establish that First Order Programming Logic is applicable to iterative programs as well. In particular, we show that the intermittent assertions method--an informal proof method for iterative programs which has not been formalized--is conveniently formalized simply as sugared First Order Programming Logic applied to the recursive translations of iterative programs.

The report gives a complete defining description of the international algorithmic language ALGOL 60. This is a language suitable for expressing a large class of numerical processes in a form sufficiently concise for direct automatic translation into the language of programmed automatic computers. The introduction contains an account of the preparatory work leading up to the final conference, where the language was defined. In addition the notions reference language, publication language, and hardware representations are explained. In the first chapter a survey of the basic constituents and features of the language is given, and the formal notation, by which the syntactic structure is defined, is explained. The second chapter lists all the basic symbols, and the syntactic units know as identifiers, numbers, and strings are defined. Further, some important notions such as quantity and value are defined. The third chapter explains the rules for forming expressions, and the means of these expressions. Three different types of expressions exist: arithmetic, Boolean (logical), and designational. The fourth chapter describes the operational units of the language, known and statements. The basic statements are: assignment statements (evaluation of a formula), go to statements (explicit break of the sequence of execution of statements), dummy statements, and procedure statements (call for execution of a closed process, defined by a procedure declaration). The formation of more complex structures, having statement character, is explained. Thes include: conditional statements, for statements, compound statements, and blocks. In the fifth chapter the units known as declarations, serving for defining permanent properties of the units entering into a process described in the language, are defined. The report ends with two detailed examples of the use of the language, and an alphabetic index of definitions.