To preference via entrenchment
Preferential models represent an important step in knowledge representation theory, and the preferential entailment on models whose preferential relation satisfies additional second-order properties of smoothness or stopperedness can be characterized by a system P fulfilling the following eight axioms: Supraclassicality, Left logical equivalence, Right weakening, And, Cut Cautious monotonicity, Or, and Weak transitivity. The aim of this paper is to introduce a binary relation among sentences, called partial entrenchment, that represents a simple generalization of Gärdenfors and Makinson's epistemic entrenchment, and has the features of being monotonic and expressing extensions. Several of the obtained results have to be mentioned: (1) Any class of sentences satisfying the system P can be generated as the intersection of partial entrenchment extensions. (2) The subclass of partial entrenchments consisting of total preorders is Gärdenfors and Makinson's expectation orderings which characterize previous notions of expectation inference and rational inference. (3) Restricting the class of expectation orderings with properties parameterized by theories, one gets epistemic entrenchment, a well-known class of linear preorders of sentences characterizing the AGM (Alchourrón-Gärdenfors-Makinson) postulates for belief revision. (4) A further generalization of partial entrenchment can lead to a uniform characterization of all nonmonotonic inference relations. The paper is organized as follows: Section 2 introduces partial entrenchment, explains its role, and compares its features to other approaches. Section 3 defines a monotonic consequence relation based on partial entrenchment, called maxiconsistent inference, and proves some of its properties. The maxiconsistent consequence is proved to satisfy the properties of the axiom system P. The final Section 4 shows that every preferential consequence relation can be expressed as a maxiconsistent inference of a partial entrenchment, while the maxiconsistent inference expresses sceptical nonmonotonic consequence by an intersection of possible extensions.
scientific article; zbMATH DE number 1308107
scientific article