Loop checking is a mechanism used to prune infinite SLD-derivations. Here we study two classes of loop checking mechanisms subsumption checks and context checks. We analyze their soundness, completeness relative strength and related concepts. We prove their soundness (no computed answer substitution to a goal is missed) and derr~nstrate their completeness (all resulting derivations are finite) ...

This paper explores the explanation of subsumption reasoning in Description Logics that are implemented using normalization methods, focusing on the perspective of knowledge en­ gineers. The notion of explanation is specified using a proof-theoretic framework for present­ ing the inferences supported in these systems. The problem of overly long explanations is ad­ dressed by decomposing them in...

Subsumption-based tabled logic programming promotes more aggressive reuse of answer tables over variant-based tabling. However resolving subgoals against answers in tabled logic programming may require accessing incomplete answer tables (i.e., more answers remain to be added). In subsumption-based tabling it is far more efficient to retrieve from completed tables. Scheduling strategies promote ...

We present a general preferential semantic framework for plausible subsumption in description logics, analogous to the KLM preferential semantics for propositional entailment. We introduce the notion of ordered interpretations for description logics, and use it to define two mutually dual non-deductive subsumption relations

We extend the description logic EL with reflexive roles and range restrictions, and show that subsumption remains tractable if a certain syntactic restriction is adopted. We also show that subsumption becomes PSpace-hard (resp. undecidable) if this restriction is weakened (resp. dropped). Additionally, we prove that tractability is lost when symmetric roles are added: in this case, subsumption ...

The inclusion-exclusion principle is a well-known mathematical principle used to count the number of elements in the union of a collection of sets in terms of intersections of sub-collections. We present an algorithm for counting the number of solutions of a given k-SAT formula using the inclusion-exclusion principle. The key contribution of our work consists of a novel subsumption pruning tech...

The pattern “Define Hybrid Class Resolving Disjointness due to Subsumption” is proposed as a Logical Ontology Design Pattern (Logical OP) solving a problem of disjointness inconsistency caused by a subsumption relation. Further away from solving design problems where the primitives of the representation language do not directly support certain logical constructs, this pattern helps resolving a ...