Complex Role Inclusions with Role Chains on the Right are Expressible in SROIQ

Complex Role Inclusions with Role Chains on the Right are Expressible in SROIQ

Michael Compton (CSIRO, Cygnet, Australia)
Copyright: © 2015 |Pages: 18
DOI: 10.4018/IJSWIS.2015010103

Abstract

The syntax of both SROIQ and OWL 2 allow complex role inclusion axioms where the role composition occurs on the left of the subsumption relation, but not where the role composition occurs on the right. This paper proves that, despite the lack of syntax, SROIQ, and consequently OWL 2, can already express such complex role inclusions. This is shown by proving that complex role inclusion axioms where the role composition occurs on the right of the subsumption relation can already be expressed in terms of complex role inclusions on the left. The resulting syntactic restrictions are similar to those already present in SROIQ and OWL 2.
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Introduction

The Description Logic IJSWIS.2015010103.m01 has syntax for role subsumptions of the form:

IJSWIS.2015010103.m02
(1) but not of the form:

IJSWIS.2015010103.m03
(2)

Such axioms, called complex role inclusion axioms, show a subsumption relation between role IJSWIS.2015010103.m04 and the role composition, or chain, IJSWIS.2015010103.m05.

Given an interpretation IJSWIS.2015010103.m06, role compositions have the standard meaning:

IJSWIS.2015010103.m07
and thus (1) has the semantics:

In general, such axioms result in undecidablity, but, decidability can be regained by enforcing restrictions on the relationships between roles. IJSWIS.2015010103.m11, for example, requires a strict partial ordering of roles. Recently, complex role inclusions with role chains on the left have been studied in IJSWIS.2015010103.m12, IJSWIS.2015010103.m13, IJSWIS.2015010103.m14 and IJSWIS.2015010103.m15.

Excepting a part solution for IJSWIS.2015010103.m16 (Mosurivić & Krdzăvac, 2011), no description logics that allow role chains on the right of the subsumption relation have been published.

Contribution

This paper shows that complex role inclusions on the right, that is, of the form of (2), with semantics:

IJSWIS.2015010103.m17
IJSWIS.2015010103.m18
IJSWIS.2015010103.m19
are definable in terms of complex role inclusions on the left, and thus, despite not being directly permitted in the syntax, can already be expressed in IJSWIS.2015010103.m20, IJSWIS.2015010103.m21 and, consequently, OWL 2.1

Both soundness and completeness are proved for the method. Soundness showing that the definitions given imply the desired role compositions, and completeness demonstrating that all models with the intended semantics are admitted: i.e., the definitions do not imply `hidden' restrictions on satisfying models.

A set of syntactic restrictions constrain the valid complex role inclusion axioms in IJSWIS.2015010103.m22. The definitions given here result in syntactic restrictions for complex role inclusions on the right; these restrictions are a consequence of the construction in terms of role chains on the left and do not add any further restrictions to the logic.

The restrictions are similar to the existing IJSWIS.2015010103.m23 restrictions:

  • Roles on the right of the subsumption in a complex role inclusion are not ‘simple’, IJSWIS.2015010103.m24 in (2); and

  • The global partial ordering on roles requires either IJSWIS.2015010103.m25 or IJSWIS.2015010103.m26.

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