Semantical Considerations On Nonmonotonic Logic

Abstract

Commonsense reasoning is “nonmonotonic” in the sense that we often draw, on the basis of partial information, conclusions that we later retract when we are given more complete information. Some of the most interesting products of recent attempts to formalize nonmonotonic reasoning are the nonmonotonic logics of McDermott and Doyle [McDermott and Doyle, 1980; McDermott, 1982]. These logics, however, all have peculiarities that suggest they do not quite succeed in capturing the intuitions that prompted their development. In this paper we reconstruct nonmonotonic logic as a model of an ideally rational agent’s reasoning about his own beliefs. For the resulting system, called autoepistemic logic, we define an intuitively based semantics for which we can show autoepistemic logic to be both sound and complete. We then compare autoepistemic logic with the approach of McDermott and Doyle, showing how it avoids the peculiarities of their nonmonotonic logic.