Extended Caching, Backjumping and Merging for Expressive Description Logics

Steigmiller, Andreas; Liebig, Thorsten; Glimm, Birte

doi:10.1007/978-3-642-31365-3_40

Cited by 13 publications

(7 citation statements)

References 10 publications

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“…The complexity of reasoning in such logics is often the same as for the underlying classical DLs. Sometimes, highly-optimized reasoners [62,63] for classical reasoning problems can be reused after a suitable reduction.…”

Section: Discussionmentioning

confidence: 99%

The limits of decidability in fuzzy description logics with general concept inclusions

Borgwardt

Distel

Peñaloza

2015

Artificial Intelligence

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Fuzzy Description Logics (DLs) can be used to represent and reason with vague knowledge. This family of logical formalisms is very diverse, each member being characterized by a specific choice of constructors, axioms, and triangular norms, which are used to specify the semantics. Unfortunately, it has recently been shown that the consistency problem in many fuzzy DLs with general concept inclusion axioms is undecidable. In this paper, we present a proof framework that allows us to extend these results to cover large classes of fuzzy DLs. On the other hand, we also provide matching decidability results for most of the remaining logics. As a result, we obtain a near-universal classification of fuzzy DLs according to the decidability of their consistency problem.

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Section: Discussionmentioning

confidence: 99%

The limits of decidability in fuzzy description logics with general concept inclusions

Borgwardt

Distel

Peñaloza

2015

Artificial Intelligence

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“…We intend to extend -SHIN also for more description logics under more semantics. Besides, the presented dependency management allows for more informed backjumping, while also supporting the creation of precise cache unsatisfiability entries [29]. Among others, better heuristics are needed to guide the choices needed during tableau reasoning, and better use of cached information is expected to provide significant benefits.…”

Section: Discussionmentioning

confidence: 99%

Optimised ExpTime Tableaux for𝒮ℋℐ𝒩over Finite Residuated Lattices

Huang

Zhao

Gong

2014

Journal of Applied Mathematics

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This study proposes to adopt a novel tableau reasoning algorithm for the description logic SHIN with semantics based on a finite residuated De Morgan lattice. The syntax, semantics, and logical properties of this logic are given, and a sound, complete, and terminating tableaux algorithm for deciding fuzzy ABox consistency and concept satisfiability problem with respect to TBox is presented. Moreover, based on extended and/or completion-forest with a series of sound optimization technique for checking satisfiability with respect to a TBox in the logic, a new optimized ExpTime (complexity-optimal) tableau decision procedure is presented here. The experimental evaluation indicates that the optimization techniques we considered result in improved efficiency significantly.

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“…Moreover, Konclude uses a sophisticated dependency tracking mechanism that keeps track of how consequences have been derived. The tracked dependencies are then used to realise a precise unsatisfiability caching [14] and to cache required expansions for nodes in the completion graph, which allows for blocking nodes earlier in Konclude and works particularly well for mostly deterministic ontologies. Third, we have devised a range of new optimisations.…”

Section: Optimisationsmentioning

confidence: 99%

“…Moreover, the coupling with the saturation procedure is used to block earlier in tableau-based consistency checks and to extract interesting information such as obvious subsumptions and non-subsumptions. Finally, the developed poolbased merging [14] reduces the non-determinism when handling cardinality restrictions. Together with many low level optimisations such as the incremental completion graph building of (non-deterministic) branches and sophisticated processing queues, consistency checking in Konclude is usually unproblematic in practice even for ontologies with high expressivity (e.g., inverse roles, nominals, and cardinality restrictions).…”

Section: Optimisationsmentioning

confidence: 99%