Optimizing Terminological Reasoning for Expressive Description Logics

Abstract

Tableau algorithms are currently the most widely used and empirically the fastest algorithms for reasoning in expressive description logics, including the important description logics SHIQ and SHOIQ. Achieving a high level of performance on terminological reasoning in expressive description logics when using tableaubased algorithms requires the incorporation of a wide variety of optimizations. The description logic system FaCT++ implements a wide variety of such optimizations, some present in other reasoners and some novel or refined in FaCT++.

Everything you always wanted to know about blank nodes

“…Conversely, reasoners that implement OWL's Direct Semantics -such as FaCT++ [68], HermiT [53], RacerPro [32], Pellet [63], etc. -often support existential semantics and anonymous individuals.…”

Knowledge acquisition: Past, present and future

“…Such knowledge representation schemes were initially called terminological logics, then term subsumption languages (Patel-Schneider, Owsnicki-Klewe, Kobsa, Guarino, MacGregor, Mark, McGuinness, Nebel, Schmiedel and Yen, 1990) and eventually came to be called by their current name, description logics (Baader et al, 2003). It was realized that the representation primitives available in CLASSIC were too weak for many purposes and research focused on the computational complexity of algorithms for inference with a variety of combinations of more comprehensive representation primitives, and on the implementation of algorithms to provide tools that were as computationally effective as was possible (Haarslev and Moller, 2001;Tsarkov, Horrocks and Patel-Schneider, 2007). Skuce, Shenkang and Beauvillé (1989) presented and demonstrated a term subsumption workbench written in Smalltalk at the 4 th KAW.…”

MORe: Modular Combination of OWL Reasoners for Ontology Classification

“…The optimisations employed by these reasoners aim not only to improve performance on individual subsumption tests, but also to reduce the number of tests performed when classifying a given ontology-most OWL 2 reasoners use variants of the well-known Enhanced Traversal Algorithm to incrementally construct a compact representation of the subsumption relation, along with the told subsumptions optimisation, which provides an inexpensive way of identifying "obvious" subsumption relationships that hold in the input ontology [2,11]. Identifying obvious non-subsumptions is also important, as most possible subsumption relationships do not hold, and has been addressed by optimisations such as completely defined concepts, which identifies a fragment of the ontology for which told subsumptions provide complete information, model-merging, and other related techniques that exploit the computations performed during individual class satisfiability tests [23,11,9,8].…”