Ground Nonmonotonic Modal Logics

J. of Logic and Computation

In this paper we discuss ground logics, a family of nonmonotonic modal logics, with the goal of using them in knowledge representation. Ground logics are based on the idea of minimizing the knowledge expressed by non-modal formulae. The nonmonotonic character of the logics can be described either by a fix-point equation that introduces assumptions on the non-modal part of the theory, or by means of a preference relation on possible-worlds models. We address both the epistemological and the computational properties of ground logics. We discuss the representational features by providing a thorough comparison between them and McDermott and Doyle logics. We find that there are a number of interesting notions that are nicely captured by ground logics. Particularly interesting is the ground logic for S5. We show that reasoning in ground logics is p3-hard. Moreover we prove that p3 is also an upper bound for reasoning in the major ground logics. Moreover, we identify some special cases of practical interest where the complexity of reasoning in ground logics is lower than in the general case.

@article{DoNR97,
  title =        "Ground Nonmonotonic Modal Logics",
  year =          "1997",
  author =       "Donini, Francesco M. and Nardi, Daniele and Rosati,
Riccardo",
  journal =      "J. of Logic and Computation",
  pages =        "523-548",
  number =       "4",
  volume =       "7",
}