Abstract:
We study the complexity of the combination of the Description Logic ALCQI with a terminological formalism based on cardinality restrictions on concepts. This combination can naturally be embedded into C 2, the two variable fragment of predicate logic with counting quantiers, which yields a simple decidability result. We prove that with respect to worst-case complexity, this approach leads to an optimal solution, as ALCQI with cardinality restrictions has the same complexity as C
Citations
|
233
|
S.: Practical Reasoning for Expressive Description Logics
– Horrocks, Sattler, et al.
- 1999
|
|
225
|
The complexity of concept languages
– Donini, Lenzerini, et al.
- 1995
|
|
222
|
Reasoning in description logics
– Donini, Lenzerini, et al.
- 1996
|
|
185
|
The undecidability of the dominoe problem
– Berger
- 1966
|
|
177
|
On the decidability of query containment under constraints
– Calvanese, Giacomo, et al.
- 1998
|
|
176
|
The Classical Decision Problem
– Börger, Grädel, et al.
|
|
161
|
Attributive Concept Descriptions with Complements
– Schmidt-Schau, Smolka
- 1991
|
|
149
|
A Semantics and Complete Algorithm for Subsumption in the CLASSIC Description Logic
– Borgida, Patel-Schneider
- 1994
|
|
137
|
Description logic framework for information integration
– Calvanese, Giacomo, et al.
- 1998
|
|
111
|
Complexity of Modal Logics
– Spaan
- 1993
|
|
89
|
Hybrid languages
– Blackburn, Seligman
- 1995
|
|
88
|
TBox and ABox reasoning in expressive description logics
– Giacomo, Lenzerini
- 1996
|
|
71
|
A road-map on complexity for hybrid logics
– Areces, Blackburn, et al.
- 1999
|
|
56
|
Source integration in data warehousing
– Calvanese, Giacomo, et al.
- 1998
|
|
55
|
Decidability of Class-Based Knowledge Representation Formalisms
– Giacomo
- 1995
|
|
51
|
Combining deduction and model checking into tableaux and algorithms for Converse-PDL
– Giacomo, Massacci
|
|
50
|
Cardinality restrictions on concepts
– Baader, Buchheit, et al.
- 1996
|
|
20
|
Complexity of two-variable logic with counting
– Pacholski, Szwast, et al.
- 1997
|
|
20
|
Dominoes and the AEA case of the decision problem
– Wang
- 1962
|
|
17
|
Why is modal logic so robustly decidable?, in Descriptive Complexity and Finite
– Vardi
- 1997
|
|
16
|
A PSPACE algorithm for graded modal logic
– Tobies
- 1999
|
|
8
|
In so many possible worlds. Notre Dame
– Fine
- 1972
|
|
4
|
A NExpTime-complete description logic strictly contained
– Tobies
- 1999
|
|
2
|
On the relative expressiveness of description logics and order logics
– Borgida
- 1996
|
|
1
|
The Complexity of Cardinality Restrictions
– Gradel, Otto
- 1997
|
|
