Hypertableau Reasoning for Description Logics

Abstract

We present a novel reasoning calculus for the description logic SHOIQ^+---a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableau-based reasoning calculi used in state-of-the-art reasoners. In order to reduce nondeterminism, we base our calculus on hypertableau and hyperresolution calculi, which we extend with a blocking condition to ensure termination. In order to reduce the size of the constructed models, we introduce anywhere pairwise blocking. We also present an improved nominal introduction rule that ensures termination in the presence of nominals, inverse roles, and number restrictions---a combination of DL constructs that has proven notoriously difficult to handle. Our implementation shows significant performance improvements over state-of-the-art reasoners on several well-known ontologies

Optimising Ontology Classification

“…The only case where HermiT 1.3 performs more tests is on GALEN, which is due to the fact that, on deterministic ontologies, HermiT 1.2.2a uses satisfiability tests and the pre-model reading technique [8] which identifies all subsumers of the tested class. In contrast, our method does not test the satisfiability of each class, so after the first phase there are unknown possible subsumers that need to be checked in the second phase.…”

“…Note, however, that C is tested for satisfiability only if P [C] = ∅ (line 5), which avoids the test if a pre-model for C has been generated previously. The pre-model for C is used to update K[C]: if D was added to L(s 0 ) deterministically (which can easily be checked in reasoners that use dependency-directed backtracking), then D is guaranteed to be a subsumer of C [8], so C, D is added to K. The pre-model for C is also used to update (7), the reasoner relates s 0 with some fresh s 1 by property op2 such that D ∈ L(s 1 ). Let us assume, however, that to satisfy axiom (6), the reasoner now adds F to…”

Intelligent Tableau Algorithm for DL Reasoning

“…As for more complicated CNF test cases, these reasoners easily become intractable based on our test results. Modified versions of tableau algorithms such as hypertableaux [14], which uses hyper-resolution instead of simple tableau branching, are developed and applied in reasoners such as HermiT. Even though the performance in dealing with disjunctions is improved, based on our test results, HermiT is normally performing worse than others in situations where a big amount of nodes needs to be constructed in the underlying pre-model (see Section 5).…”

Uniform Evaluation of Nonmonotonic DL-Programs

“…We compared DReW with the DL reasoners HermiT 1.3.5 [42] and Pellet 2.3.0 [47]. We differentiate two DReW benchmark run settings: (i) DReW[clingo] and (ii) DReW[DLV] (in brackets the employed model builder is given).…”