Unification in a Description Logic with Transitive Closure of Roles

@inproceedings{Baader2001UnificationIA,
  title={Unification in a Description Logic with Transitive Closure of Roles},
  author={Franz Baader and Ralf K{\"u}sters},
  booktitle={LPAR},
  year={2001}
}
Unification of concept descriptions was introduced by Baader and Narendran as a tool for detecting redundancies in knowledge bases. It was shown that unification in the small description logic FL₀, which allows for conjunction, value restriction, and the top concept only, is already ExpTime-complete. The present paper shows that the complexity does not increase if one additionally allows for composition, union, and transitive closure of roles. It also shows that matching (which is polynomial in… 
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References

SHOWING 1-10 OF 19 REFERENCES
Augmenting Concept Languages by Transitive Closure of Roles: An Alternative to Terminological Cycles
TLDR
A way of retaining, in an extended language, the pleasant features of gfp-semantics for FLQ with cyclic definitions without running into the troubles caused by cycles in larger languages is proposed.
Matching in Description Logics
TLDR
A new approach to performing matching is proposed, based on a ‘concept-centred’ normal form, rather than the more standard ‘structural subsumption’normal form for concepts, so that matching can be performed using arbitrary concept patterns of the description language, thus removing restrictions from previous work.
Matching in Description Logics with Existential Restrictions
TLDR
This work presents sound and complete decision algorithms for the solvability of matching problems and for computing sets of matchers for matching problems in description logics with existential restrictions.
Unification of Concept Terms in Description Logics
TLDR
This work shows that this inference problem for description logics is of interest for applications, and presents first decidability and complexity results for a small concept description language.
Explaining reasoning in description logics
TLDR
Four major issues in explaining the conclusions of procedurally implemented deductive systems are explored and a meta-language for describing interesting aspects of complicated objects is used to limit the amount of information that should be presented or explained.
Automata on Infinite Objects
  • W. Thomas
  • Computer Science
    Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics
  • 1990
Asking Queries about Frames
TLDR
This paper investigates the algorithms required when answers are deduced by matching queries against a "structural normal form" of descriptions, and introduces a useful refinement of the notion of structural subsumption.
On the state complexity of intersection of regular languages
TLDR
A more general result is shown that given an arbitrary integer k > 0 and k nonnegative integers there exist k regular languages L 1 , L k such that L 1 is accepted by an n 1 -state DFA and any DFA accepting nl<i<k L i needs at least n l . . . nk states.
The Complexity of Set Constraints
TLDR
This work presents several results on the computational complexity of solving systems of set constraints, which form a natural complexity hierarchy depending on the form of the constraint language.
...
...