Nonmonotonic inconsistency. (English) Zbl 1082.03508
Summary: Nonmonotonic consequence is the subject of a vast literature, but the idea of a nonmonotonic counterpart of logical inconsistency – the idea of a defeasible property representing internal conflict of an inductive or evidential nature – has been entirely neglected. After considering and dismissing two possible analyses relating nonmonotonic consequence and a nonmonotonic counterpart of logical inconsistency, this paper offers a set of postulates for nonmonotonic inconsistency, an analysis of nonmonotonic inconsistency in terms of nonmonotonic consequence, and a series of results showing that nonmonotonic inconsistency conforms to these postulates given the analysis of nonmonotonic inconsistency presented here and certain postulates for nonmonotonic consequence.
The results presented here establish the interest of certain previously undiscussed postulates of nonmonotonic consequence. These results also show that nonmonotonicity, which has never seemed useful in the formulation of general principles governing nonmonotonic reasoning, is relevant to the positive characterization of nonmonotonic inference after all.
The results presented here establish the interest of certain previously undiscussed postulates of nonmonotonic consequence. These results also show that nonmonotonicity, which has never seemed useful in the formulation of general principles governing nonmonotonic reasoning, is relevant to the positive characterization of nonmonotonic inference after all.
Keywords:
Nonmonotonic reasoning; Inconsistency; Inductive inference; Conflicting evidence; Cumulativity; Default logic; Preferential entailment; Poole systems; Multiple inheritance with exceptionsReferences:
| [1] | Cross, C., Belief revision, nonmonotonic reasoning, and the Ramsey test, (Kyburg, H.; Loui, R.; Carlson, G., Knowledge Representation and Defeasible Reasoning (1990), Kluwer: Kluwer Boston, MA), 223-244 |
| [2] | D. Gabbay, Theoretical foundations for nonmonotonic reasoning in expert systems, in: K. Apt (Ed.), Logics and Models of Concurrent Systems, Springer, Berlin, pp. 439-457; D. Gabbay, Theoretical foundations for nonmonotonic reasoning in expert systems, in: K. Apt (Ed.), Logics and Models of Concurrent Systems, Springer, Berlin, pp. 439-457 · Zbl 0581.68068 |
| [3] | Horty, J.; Thomason, R.; Touretzky, D., A skeptical theory of inheritance in nonmonotonic semantic networks, Artificial Intelligence, 42, 2-3, 311-348 (1990) · Zbl 0717.68085 |
| [4] | Kraus, S.; Lehmann, D.; Magidor, M., Nonmonotonic reasoning, preferential models, and cumulative logics, Artificial Intelligence, 44, 1-2, 167-207 (1990) · Zbl 0782.03012 |
| [5] | Makinson, D., General theory of cumulative inference, (Reinfrank, M.; de Kleer, J.; Ginsberg, M. L.; Sandewall, E., Nonmonotonic Reasoning. Nonmonotonic Reasoning, Lecture Notes in Artificial Intelligence, 346 (1989), Springer: Springer Berlin), 1-18 · Zbl 0675.03007 |
| [6] | Makinson, D., General patterns in nonmonotonic reasoning, (Gabbay, D. M.; Hogger, C. J.; Robinson, J. A., Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 3: Nonmonotonic Reasoning and Uncertain Reasoning (1994), Oxford University Press: Oxford University Press Oxford), 35-110 · Zbl 0804.03017 |
| [7] | Poole, D., A logical framework for default reasoning, Artificial Intelligence, 36, 1, 27-47 (1988) · Zbl 0647.68094 |
| [8] | Reiter, R., A logic for default reasoning, Artificial Intelligence, 13, 1-2, 81-132 (1980) · Zbl 0435.68069 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
