Defeasible Inheritance-Based Description Logics

Abstract

Defeasible inheritance networks are a non-monotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach to non-monotonic reasoning. We will combine these two approaches and define a new non-monotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics (DLs), a family of logics well-suited to model structured information. In both cases we will provide a simple reasoning method that is built on top of the classical entailment relation and, thus, is amenable of an implementation based on existing reasoners. Eventually, we evaluate our approach on well-known landmark test examples.

Semantic characterization of rational closure: From propositional logic to description logics

“…On the contrary, once penguins are recognized as non-typical birds, no inheritance of typical properties is possible. In order to solve this problem, a strengthening of a rational closure-like algorithm with defeasible inheritance networks has been studied by [9].…”

“…The authors show that, for each order s, the consequence relation s is rational and can be computed in PSpace. In a subsequent work [9,11], the authors introduce an approach based on the combination of rational closure and Defeasible Inheritance Networks (INs). The authors first develop their approach at a propositional level, then they extend it to DLs, addressing both TBox and ABox reasoning.…”

OWL-POLAR: A framework for semantic policy representation and reasoning

“…Therefore, currently conflict detection between policies cannot be done using OWL-POLAR when it requires non-monotonic reasoning. However, this limitation would be relieved when nonmonotonic reasoning mechanisms becomes available in standard OWL-DL reasoners [6].…”

“…Then, it checks if P j is also active in this canonical state by finding all substitutions satisfying activation and role constraints of P j (line 3). Lastly, it checks if any of these substitutions satisfies the requirements listed above (lines [4][5][6][7][8]. The algorithm returns true if such a substitution exists (lines 5-7); otherwise it returns false (line 9).…”

A new semantics for overriding in description logics

“…In Section 6, we assume the reader to be familiar with the standard nonmonotonic semantics for DLs (Circumscription, Default logic, MKNF, Rational closure, etc.). Their syntax and semantics can be found in [3,4,21,10,18,29,19,40].…”