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We introduce and investigate the expressivWe introduce and investigate the expressive description logic (DL) ALCSCC++, in which the global and local cardinality constraints introduced in previous papers can be mixed. On the one hand, we prove that this does not increase the complexity of satisfiability checking and other standard inference problems. On the other hand, the satisfiability problem becomes undecidable if inverse roles are added to the languages. In addition, even without inverse roles, conjunctive query entailment in this DL turns out to be undecidable. We prove that decidability of querying can be regained if global and local constraints are not mixed and the global constraints are appropriately restricted. The latter result is based on a locally-acyclic model construction, and it reduces query entailment to ABox consistency in the restricted setting, i.e., to ABox consistency w.r.t. restricted cardinality constraints in ALCSCC, for which we can show an ExpTime upper bound. which we can show an ExpTime upper bound.  +
@techreport{BBR2019,
  author      = {Franz Baader and Bartosz Bednarczyk and Sebastian Rudolph},
  title       = {Satisfiability Checking and Conjunctive Query Answering in
                 Description Logics with Global and Local Cardinality
                 Constraints},
  institution = {Computational Logic Group},
  year        = {2019}
}
Techreport  +
BaaderBednarczykRudolphECAI2020Report.pdf  +
Computational Logic Group  +
Franz Baader, Bartosz Bednarczyk, SebastiaFranz Baader, Bartosz Bednarczyk, Sebastian Rudolph<br /> '''[[Techreport3041|Satisfiability Checking and Conjunctive Query Answering in Description Logics with Global and Local Cardinality Constraints]]''' <br />__NOTOC__Technical Report, ''Computational Logic Group'', 2019<br/><span class="fas fa-chevron-right" style="font-size: 85%;" ></span> [[Techreport3041|Details]] <span class="fas fa-chevron-right" style="font-size: 85%; margin-left: 2ex; "></span> [[Media:BaaderBednarczykRudolphECAI2020Report.pdf|Download]]dia:BaaderBednarczykRudolphECAI2020Report.pdf|Download]]  +
Franz Baader, Bartosz Bednarczyk, SebastiaFranz Baader, Bartosz Bednarczyk, Sebastian Rudolph<br /> '''[[Techreport3041/en|Satisfiability Checking and Conjunctive Query Answering in Description Logics with Global and Local Cardinality Constraints]]''' <br />__NOTOC__Technical Report, ''Computational Logic Group'', 2019<br/><span class="fas fa-chevron-right" style="font-size: 85%;" ></span> [[Techreport3041|Details]] <span class="fas fa-chevron-right" style="font-size: 85%; margin-left: 2ex;" ></span> [[Media:BaaderBednarczykRudolphECAI2020Report.pdf|Download]]dia:BaaderBednarczykRudolphECAI2020Report.pdf|Download]]  +
Satisfiability Checking and Conjunctive Query Answering in Description Logics with Global and Local Cardinality Constraints  +
techreport  +
2019  +
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Satisfiability Checking and Conjunctive Query Answering in Description Logics with Global and Local Cardinality Constraints  +
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2. November 2021, 12:32:45  +