Nonmonotonic Logic II

Abstract

Tradmonal logics suffer from the "monotomclty problem"' new axioms never mvahdate old theorems One way to get nd of this problem ts to extend traditional modal logic in the following way The operator M (usually read "possible") is extended so that Mp is true whenever p is consistent with the theory Then any theorem of this form may be mvahdated if ~p ~s added as an axiom This extension results m nonmonotomc versions of the systems T, $4, and $5 These systems are complete in that a theorem is provable in a theory based on one of them just if it is true m all "noncommittal" models of that theory, where a noncommittal model ts one m which as many thmgs are possible as possible Nonmonotomc $4 is probably the most interesting of the three, since it is stronger than ordinary $4 but has all the usual inferential machinery of $4 There is a straightforward proof procedure for the sententlal subset of nonmonotomc $4. This approach to nonmonotonlc logic may be applied to several problems in knowledge representation for arUficml mtelhgence Its main advantages over competmg approaches are that tt factors out problems of resource hmltattons and allows the symbol M to appear m any context, since M is a meaningful part of the language