Logic in Nonmonotonic Reasoning

We present a conceptual description of nonmonotonic formalisms as essentially two-layered reasoning systems consisting of a monotonic logical system, coupled with a mechanism of a reasoned choice of default assumptions. On this ‘surgery’, the main features of a nonmonotonic formalism are determined by the interplay between its logical basis and the nonmonotonic overhead. Furthermore, it allows us to see the majority of existing nonmonotonic systems as implementations of just two basic nonmonotonic mechanisms in various logical formalisms, giving raise to two principal paradigms of nonmonotonic reasoning, preferential and explanatory reasoning. In addition, we discuss the requirements and constraints this view imposes on nonmonotonic systems, as well as some of the main problems such systems should try to resolve. 1 Nonmonotonic Reasoning versus Logic: Pre-History of Relations Nonmonotonic reasoning is considered today an essential part of the logical approach to Artificial Intelligence. In fact, the birth of nonmonotonic reasoning can be loosely traced to the birth of Artificial Intelligence itself. This is due to the fact that John McCarthy, one of the fathers of AI, has suggested in [McCarthy, 1959] and consistently developed a research methodology that used logic to formalize the reasoning problems in AI. McCarthy’s objective was to formalize common sense reasoning about such problems. Despite this, the relationships between nonmonotonic reasoning and logic have always been controversial, part of a larger story of the relations between AI and logic in general (see [Thomason, 2003]). The origins of nonmonotonic reasoning proper lied in dissatisfaction with the traditional logical methods in representing and handling the problems posed by AI. Basically, the problem was that reasoning necessary for an intelligent behavior and decision making in realistic situations has turned out to be difficult, even impossible, to represent as deductive inferences in some logical system. The essence of this problem has been formulated by Marvin Minsky in his influential “frames paper” [1974], where he directly questioned the suitability of representing commonsense knowledge in a form of a deductive system: