Why nonmonotonic logic?

Abstract The motivation for nonmonotonic logic is to produce a machine representation for default reasoning, broadly construed. In this paper we argue that all nonmonotonic logics have (by definition) inference rules that fail to preserve truth, and this fact leads to several undesirable features. In response to these problems, but recognizing the importance of the original motivation for nonmonotonic logic, we propose an alternative to nonmonotonic logic, which achieves nonmonotonicity of reasoning without abandoning in any way truth preserving inferences. This approach is based on a possible worlds framework, which we illustrate with a small Prolog program. Motivating this approach is an important distinction, which we believe the advocates of nonmonotonic logic to be ignoring: that between inferencing and making decisions, or equivalently that between inferencing and theory construction.

[1]  Marianne Winslett,et al.  Is Belief Revision Harder Than You Thought? , 1986, AAAI.

[2]  David Lewis.  Counterpart Theory and Quantified Modal Logic , 1968 .

[3]  Brian F. Chellas.  Modal Logic: Normal systems of modal logic , 1980 .

[4]  R. Loui,et al.  Change in View , 1987, Artif. Intell..

[5]  Max J. Cresswell,et al.  A New Introduction to Modal Logic , 1998 .

[6]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[7]  Marvin Belzer,et al.  A conditional logic for defeasible beliefs , 1988, Decis. Support Syst..

[8]  Johan de Kleer,et al.  Problem Solving with the ATMS , 1986, Artif. Intell..

[9]  Graeme Forbes,et al.  The metaphysics of modality , 1985 .

[10]  Drew McDermott,et al.  Nonmonotonic Logic and Temporal Projection , 1987, Artif. Intell..

[11]  J. Dekleer.  An assumption-based TMS , 1986 .

[12]  Johan de Kleer,et al.  Extending the ATMS , 1986, Artif. Intell..

[13]  Ian Hacking,et al.  What is logic , 1979 .

[14]  Stephen Cole Kleene.  Mathematical Logic , 1967 .

[15]  Johan de Kleer,et al.  An Assumption-Based TMS , 1987, Artif. Intell..

[16]  McDermottDrew.  Nonmonotonic Logic II , 1982 .

[17]  I. Good,et al.  Chance, Cause, Reason. , 1979 .

[18]  R. Bradley,et al.  Possible worlds: An introduction to logic and its philosophy , 1979 .

[19]  John McCarthy,et al.  Circumscription - A Form of Non-Monotonic Reasoning , 1980, Artif. Intell..

[20]  Alvin Plantinga,et al.  The Nature of Necessity. , 1975 .

[21]  Marek J. Sergot,et al.  The British Nationality Act as a logic program , 1986, CACM.

[22]  Marvin Minsky,et al.  A framework for representing knowledge , 1974 .

[23]  James E. Tomberlin,et al.  On the Plurality of Worlds. , 1989 .

[24]  Van Fraassen,et al.  Formal semantics and logic , 1971 .