# A Goal-Oriented Algorithm for Unification in ELH_R^+ w.r.t. Cycle-Restricted Ontologies

From International Center for Computational Logic

# A Goal-Oriented Algorithm for Unification in ELH_R^+ w.r.t. Cycle-Restricted Ontologies

##### Franz BaaderFranz Baader, Stefan BorgwardtStefan Borgwardt, Barbara MorawskaBarbara Morawska

Franz Baader, Stefan Borgwardt, Barbara Morawska

Technical Report,

**A Goal-Oriented Algorithm for Unification in ELH_R^+ w.r.t. Cycle-Restricted Ontologies**Technical Report,

*Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universität Dresden*, volume 12-05, 2012.*LTCS-Report***Kurzfassung****Abstract**

Unification in Description Logics (DLs) has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. For the DL EL, which is used to define several large biomedical ontologies, unification is NP-complete. A goal-oriented NP unification algorithm for EL that uses nondeterministic rules to transform a given unification problem into solved form has recently been presented. In this report, we extend this goal-oriented algorithm in two directions: on the one hand, we add general concept inclusion axioms (GCIs), and on the other hand, we add role hierarchies (H) and transitive roles (R+). For the algorithm to be complete, however, the ontology consisting of the GCIs and role axioms needs to satisfy a certain cycle restriction.**Bemerkung:****Note:**See http://lat.inf.tu-dresden.de/research/reports.html.**Forschungsgruppe:****Research Group:**Automatentheorie

```
@techreport{ BaBM-LTCS-12-05,
address = {Dresden, Germany},
author = {Franz {Baader} and Stefan {Borgwardt} and Barbara {Morawska}},
institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
note = {See http://lat.inf.tu-dresden.de/research/reports.html.},
number = {12-05},
title = {A Goal-Oriented Algorithm for Unification in {$\mathcal{ELH}_{R^+}$} w.r.t. Cycle-Restricted Ontologies},
type = {LTCS-Report},
year = {2012},
}
```