• Corpus ID: 1609661

# Complexity results and practical algorithms for logics in knowledge representation

@inproceedings{Tobies2001ComplexityRA,
title={Complexity results and practical algorithms for logics in knowledge representation},
author={Stephan Tobies},
booktitle={ArXiv},
year={2001}
}
• S. Tobies
• Published in ArXiv 13 June 2001
• Computer Science
Description Logics (DLs) are used in knowledge-based systems to represent and reason about terminological knowledge of the application domain in a semantically well-defined manner. In this thesis, we establish a number of novel complexity results and give practical algorithms for expressive DLs that provide different forms of counting quantifiers. We show that, in many cases, adding local counting in the form of qualifying number restrictions to DLs does not increase the complexity of the…
416 Citations

## Figures from this paper

Reasoning for Description Logics aroundSHIQ in a Resolution Framework
• Computer Science
• 2004
The proposed algorithms provide alternative mechanisms for reasoning in the Semantic Web by reducing SHIQ(D) knowledge bases to disjunctive datalog programs and show that so-called DL-safe rules can be combined withdisjunctive programs obtained by the transformation to increase the expressivity of the logic, without affecting decidability.
Consequence-Based Reasoning for Description Logics with Disjunctions and Number Restrictions
• Computer Science
J. Artif. Intell. Res.
• 2018
The calculus and techniques presented provide an important addition to the repertoire of practical implementation techniques for description logic reasoning and are implemented in a new reasoner called Sequoia.
Tableau-based reasoning for description logics with inverse roles and number restrictions
This thesis is able to show an elimination of inverse roles for a sub-family of DLs, and provides three sub-tableaux caching techniques that are sound and global (but with different power in caching functionality).
The Combined Complexity of Reasoning with Closed Predicates in Description Logics
• Computer Science
Description Logics
• 2015
It is proved that conjunctive query answering in (plain) ALCO is hard for coNEXPTIME in combined complexity, which singles out nominals as a previously unidentified source of additional complexity when answering queries over expressive DLs.
Data Complexity of Instance Checking in The EL Family of Description Logics
CoNP-hardness is established (and even coNP-completeness) results regarding data complexity of instance checking w.r.t. combined complexity are investigated and an extension of EL is identified, called ELI, for which data complexityOf instance checking in ELI w.R.T. sets of GCIs is tractable.
On the Complexity and Expressiveness of Description Logics with Counting
• Computer Science
• 2019
This paper investigates the expressive power of the DLs obtained in this way, using appropriate bisimulation characterizations and 0–1 laws as tools to differentiate between the expressiveness of different logics.
Closed Predicates in Description Logics: Results on Combined Complexity
• Computer Science
AMW
• 2016
The results show that consistency testing and instance query answering in the presence of closed predicates is NP-complete even for rich dialects of the DL-Lite family, and imply 2EXPTIME-hardness of query Answer in ALCO for the standard open-world setting.
On Expressive Description Logics with Composition of Roles in Number Restrictions
It is shown that ALCN(o) extended with inverse roles both in number and in value restrictions becomes undecidable, whereas it can be safely extended with qualified number restrictions without losing decidability of reasoning.
Complexities of Horn Description Logics
• Computer Science
TOCL
• 2013
It is found that Horn-ALC already has the same worst-case complexity as ALC, that is, ExpTime, but it is also identified various DLs for which reasoning is PSpace-complete, and simplified syntactic definitions of Horn DLs are derived for which suitable normal form transformations are exploited.
On Decidability of Expressive Description Logics with Composition of Roles in Number Restrictions
It is shown that ALCN(o) extended with inverse roles both in number and in value restrictions becomes undecidable, whereas it can be safely extended with qualified number restrictions without losing decidability.

## References

SHOWING 1-10 OF 181 REFERENCES
Exptime Tableaux for ALC
• Computer Science
Description Logics
• 1996
Decidable Reasoning in Terminological Knowledge Representation Systems
• Computer Science
IJCAI
• 1993
The decidability of a number of desirable TKRS-deduction services are proved through a sound, complete and terminating calculus for reasoning in ALCNR-knowledge bases, and the result that inclusion statements in A LCNR can be simulated by terminological cycles, if descriptive semantics is adopted.
Practical Reasoning for Expressive Description Logics
• Computer Science
LPAR
• 1999
An algorithm is presented that decides satisfiability of the DL ACC extended with transitive eind inverse roles, role hierarchies, and quaJifying number restrictions, and early experiments indicate that this algorithm is well-suited for implementation.
An Overview of Tableau Algorithms for Description Logics
• Computer Science, Philosophy
Stud Logica
• 2001
This article focuses on three features that play an important rôle in description logics (number restrictions, terminological axioms, and role constructors), and shows how they can be taken into account by tableau algorithms.
Optimising Tableaux Decision Procedures For Description Logics
This thesis suggests that, while subsumption reasoning in such languages is known to be intractable in the worst case, a suitably optimised algorithm can provide acceptable performance with a realistic knowledge base and demonstrates that the optimisation techniques improve FaCT's performance by at least three orders of magnitude.
The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics
• S. Tobies
• Philosophy
J. Artif. Intell. Res.
• 2000
This work reduces the complexity of reasoning with cardinality restrictions to reasoning with the (in general weaker) terminological formalism of general axioms for ALCQ extended with nominals, and shows that pure concept satisfiability for A LCQI with Nominals is NExpTime-complete.
A Suggestion for an n-ary Description Logic
• Computer Science
Description Logics
• 1999
A restriction most Description Logics (DLs) have in common with most Modal Logics is their restriction to unary and binary predicates. To our knowledge, the only DLs that overcome these restrictions
Complexity of Terminological Reasoning Revisited
This paper demonstrates that it is necessary to take acyclic TBoxes into account for complexity cinalyses, and shows that there exist logics for which the complexity of reasoning remains in PSPACE if acyClic T boxes are added and alsoLogics forWhich the complexity increases.
PSPACE Reasoning for Graded Modal Logics
A PSPACE algorithm that decides satisfiability of the graded modal lo gic Gr(KR), a natural extension of propositional modal logic KR by counting expressions, is presented, which is the first known algorithm which meets the lower bound for the complexity of the problem.
Reasoning with Individuals for the Description Logic SHIQ
• Computer Science
An algorithm for combined Tbox and Abox reasoning in the $$\mathcal{SHIQ}$$ description logic is presented, of particular interest as it can be used to decide the problem of (database) conjunctive query containment w.r.t. a schema.