### Table 5. An example ontology in Horn-SHIQ (top), and its translation into Horn-logic, consisting of the translated rules (middle) and auxiliary axioms (bottom).

2006

"... In PAGE 6: ... The implementation will warn you, if you have rules with multiple head atoms. For a concrete example of the transformation, consider the ontology given in Table5 (top). The according trans- 13http://owltools.... In PAGE 7: ...3. The rules at the bottom of Table5 define various aux- iliary predicates that are needed for the correctness of the translation. In order to restrict these definitions to a finite number of terms, we introduce a predicate O that speci- fies the individuals for which the program applies.... ..."

Cited by 5

### Table 5. An example ontology in Horn-SHIQ (top), and its translation into Horn-logic, consist- ing of the translated rules (middle) and auxiliary axioms (bottom).

"... In PAGE 10: ...3. The rules at the bottom of Table5 define various auxiliary predicates that are needed for the correctness of the translation. In order to restrict these definitions to a finite number of terms, we introduce a predicate O that specifies the individuals for which the program applies.... ..."

### Table 2: Denotational semantics for language de nition

"... In PAGE 3: ... This makes it a desirable target representation for our ontology. For describing our ontology in SHIQ we will use the notation explained in Table2 , that contains denota- tional semantics for our language translation. 4 Mikrokosmos mapping to SHIQ Once we have identi ed DL language we want to use SHIQ and we have described the Mikrokosmos ontology, we can proceed to map it.... ..."

### Table I. Translation of SHIQ into FOL

### Table 1: Semantics of SHIQ by Mapping to FOL

2005

"... In PAGE 3: ...from piy by simultaneously substituting x(i) for all y(i), respectively, and piy for pix. 2 Reducing SHIQ to Disjunctive Datalog Our reduction to disjunctive datalog is based on translating a SHIQ knowledge base KB into a first-order formula pi(KB), by the operator pi from Table1 . It is well-known that KB is satisfiable with respect to the standard direct model- theoretic semantics of SHIQ iff pi(KB) is satisfiable in first-order logic [2].... ..."

Cited by 4

### Table 1. Semantics of SHIQ by Mapping to FOL

2006

Cited by 17

### Table 3.1: Semantics of SHIQ by Mapping to FOL

2005

### Table 3.2: Direct Model-theoretic Semantics of SHIQ

2005