Relevant Closure: A New Form of Defeasible Reasoning for Description Logics

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

“…In conclusion, if we replace, in our definition of rational closure (Definition 20), the notion of exceptionality in Definition 19 (based on the entailment in ALC + T R ) with a different notion of exceptionality which exploits the materialization of the KB and entailment in ALC, inspired to the notions of exceptionality used in [8,7], the rational closure we obtain is different from the rational closure obtained based on exceptionality in Definition 19.…”

“…In [7] a semantic characterization of a variant of the notion of rational closure introduced in [8] has been presented, which is based on a generalization to ALC of our semantics in [22]. In [7], defeasible subsumption statements have the form C < D and typicality assertions are not allowed in the ABox, which is defined as a standard ALC ABox.…”

“…To conclude the session, we want to observe that our definition of exceptionality (Definition 19), which exploits preferential entailment, cannot be equivalently replaced with a notion of exceptionality which directly exploits entailment in ALC over the materialization of the KB, in the spirit of the other proposals of rational closure in [8,7]. In particular, consider a knowledge base K = (TBox, ABox) and let K S = {A ⊑ B | A ⊑ B ∈ TBox} be the set of strict inclusions in K and If we adopt the definition of exceptionality introduced just above, we get a different result.…”

Practical Reasoning for Defeasible Description Logics

“…In this section we present a class of reasoning procedures, called the Relevant Closures [48], that define a notion of relevance for axioms w.r.t. the exceptionality of the query antecedent.…”

Reasoning in the presence of inconsistency through Preferential ALC

“…On one hand, a notion of "typicality" has been proposed for which KBs are designed under the assumption that certain knowledge is typically true but admits "exceptions". Languages are augmented with defeasible implication and supported by some form of non-classical semantics [3,4,5,8,9,10,12,15,22]. On the other hand, inconsistency tolerant semantics have been proposed for KBs assumed to be designed for and used by classical reasoners [16,19,20,21,23,26].…”