On Reasoning by Default

ON REASONING BY DEFAULT Raymond Reiter Department of Computer Science University of British Columbia Vancouver, B.C., Canada ABSTRACT This paper surveys a number of kinds of default reasoning in Artificial Intelligence, spec- ifically, default assignments to variables, the closed world assumption, the frame default for causal worlds, exceptions as defaults, and negation in Artificial Intelligence programming languages. Some of these defaults provide clear representa- tional and computational advantanges over their corresponding first order theories. Finally, the paper discusses various difficulties associated with default theories. If I don't know I don't know I think I know If I don't know I know I think I don't know R.D. Laing, Knots I. INTRODUCTION Default reasoning is commonly used in natural language understanding systems and in Artificial Intelligence in general. We use the term "default reasoning" to denote the process of arriving at conclusions based upon patterns of inference of the form "In the absence of any information to the contrary, assume..." In this paper, we take this pattern to have the more formal meaning "If certain information cannot be deduced from the given know- ledge base, then conclude..." Such reasoning rep- resents a form of plausible inference and is typically required whenever conclusions must be drawn despite the absence of total knowledge about a world. In order to fix some of these ideas, we begin by surveying a number of instances of default reasoning as they are commonly invoked in A.I. Specifically, we discuss default assignments to variables, the clo~ed world assumption, the frame default for causal worlds, exceptions as defaults, and negation in A.I. programming languages. We shall see that these may all be formalized by introducing a single default operator ~ where #W is taken to mean "W is not deducible from the given know- ledge base". In addition, we shall discover that the closed world and frame defaults provide clear representa- tional and computational advantages over their cor- responding first order theories. The former elim- inates the need for an explicit representation of negative knowledge about a world, while the latter eliminates the so-called frame axioms for dynamic worlds. Finally, we discuss various problems which arise as a result of augmenting first order logic with a default operator. 2. SOME INSTANCES OF DEFAULT REASONING IN A.I. The use of default reasoning in A.I. is far more widespread than is commonly realized. The purpose of this section is to point out a variety of seemingly different situations in which such reasoning arises, to accent common patterns which emerge when defaults are formalized, and to indi- cate certain representational and computational advantages of default reasoning. 2.1 Default Assignments to Variables A number of knowledge representation schemes, e.g. FRL [Roberts and Goldstein 1977], KRL [Bobrow and Winograd 1977], explicitly provide for the assignment of default values to variables (slots, terminals). For example, in KRL the unit for a person in an airline travel system has the form: 210 [Person UNIT Basic <hometown{(a City) PaloAlto; DEFAULT}> ] We can view this declaration as …

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