An Overview of Tableau Algorithms for Description Logics

@article{Baader2001AnOO,
  title={An Overview of Tableau Algorithms for Description Logics},
  author={Franz Baader and Ulrike Sattler},
  journal={Studia Logica},
  year={2001},
  volume={69},
  pages={5-40}
}
Description logics are a family of knowledge representation formalisms that are descended from semantic networks and frames via the system Kl-one. During the last decade, it has been shown that the important reasoning problems (like subsumption and satisfiability) in a great variety of description logics can be decided using tableau-like algorithms. This is not very surprising since description logics have turned out to be closely related to propositional modal logics and logics of programs… 
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References

SHOWING 1-10 OF 129 REFERENCES
Tableau Algorithms for Description Logics
  • F. Baader
  • Computer Science, Philosophy
    TABLEAUX
  • 2000
TLDR
This work focuses on description logics, a family of knowledge representation formalisms descended from semantic networks and frames via the system KL-ONE, which has turned out to be closely related to propositional modal logics and logics of programs (such as propositional dynamic logic).
Boosting the Correspondence between Description Logics and Propositional Dynamic Logics
TLDR
This paper derives decidability and complexity results for some of the most expressive logics appeared in the literature, and from the standpoint of PDLs, derives a general methodology for the representation of several forms of program determinism and for the specification of partial computations.
Practical Reasoning for Very Expressive Description Logics
TLDR
An algorithm is presented that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is well-suited for implementation.
On the Complexity of Terminological Reasoning
TLDR
This paper demonstrates that it is necessary to take TBoxes into account for complexity analyses for DLs and shows that reasoning with the description logic ALCRP(D) is NExpTime-complete regardless of whether T boxes are admitted or not.
Using an Expressive Description Logic: FaCT or Fiction?
TLDR
This paper describes a sound and complete tableaux subsumption testing algorithm for a relatively expressive Description Logic which, in spite of the logic’s worst case complexity, has been shown to perform well in realistic applications.
Exptime Tableaux for ALC
A Correspondence Theory for Terminological Logics: Preliminary Report
TLDR
It is proved that universal implications can be expressed within TSC, and it is shown that features correspond to deterministic programs in dynamic logic preserves decidability, although violates its finite model property.
Dynamic logic
TLDR
This book provides the first comprehensive introduction to Dynamic Logic, a system of remarkable unity that is theoretically rich as well as of practical value.
Reasoning in description logics
TLDR
Techniques for reasoning and computational complex problems in Description Logics are surveyed, including reasoning with plain concept expressions, reasoning with instances of concepts, and reasoning with axioms.
Practical Reasoning for Expressive Description Logics
TLDR
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.
...
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