=Paper=
{{Paper
|id=Vol-3637/paper49
|storemode=property
|title=Automated Reasoning Support for Standpoint-OWL 2
|pdfUrl=https://ceur-ws.org/Vol-3637/paper49.pdf
|volume=Vol-3637
|authors=Florian Emmrich,Lucía Gómez Álvarez,Hannes Strass
|dblpUrl=https://dblp.org/rec/conf/jowo/EmmrichAS23
}}
==Automated Reasoning Support for Standpoint-OWL 2==
https://ceur-ws.org/Vol-3637/paper49.pdf
Automated Reasoning Support for Standpoint-OWL 2
Florian Emmrich1,∗ , Lucía Gómez Álvarez1 and Hannes Strass1
1
Technische Universität Dresden, Germany
Abstract
We present a tool for modelling and reasoning with knowledge from various diverse (and possibly con-
flicting) viewpoints. The theoretical underpinnings are provided by enhancing base logics by standpoints
according to a recently introduced formalism that we also recall. The tool works by translating the
standpoint-enhanced version of the description logic SROIQ to its plain (i.e. classical) version. Existing
reasoners can then be directly used to provide automated support for reasoning about diverse standpoints.
Keywords
Standpoint Logic, OWL 2 DL, Reasoning
1. Introduction
The Semantic Web has democratised the production of knowledge sources by providing a set of
standards for the specification of vocabularies, rules, and data stores. The standard for authoring
ontologies and knowledge bases is the Web Ontology Language OWL 2 [1], a language based
on description logic (DL) [2]. Beyond the publication of independently developed sources, a
fundamental goal of the Semantic Web is to support the integration and combination of the
knowledge embedded within them. However, the interoperability between ontologies is often
hindered by semantic heterogeneity, differences in perspectives and other contextual factors.
A recent proposal aiming to address these challenges is Standpoint Logic (SL) [3], a framework
for multi-perspective reasoning. SL is a multi-modal logic conceived to support the coexistence
of multiple standpoints and the establishment of alignments between them. The language
supports expressions of the form □s [𝜙] and ♦s [𝜙], which express information relative to the
standpoint s and read, respectively: “according to s, it is unequivocal/conceivable that 𝜙”. In the
semantics, standpoints are represented by sets of precisifications,1 such that □s [𝜙] and ♦s [𝜙]
hold if 𝜙 is true in all/some of the precisifications in s. For the sake of illustration, let us revisit
a condensed version of the example provided by Gómez Álvarez et al. [4].
Example 1. A range of conceptualisations for the notion of forest have been specified for different
purposes, giving rise to diverging or even contradictory statements regarding forest distributions.
Consider a knowledge integration scenario involving two sources adopting a land cover (LC) and
a land use (LU) perspective on forestry. LC characterises a forest as a “forest ecosystem” with a
Ontology Showcase and Demonstrations Track, 9th Joint Ontology Workshops (JOWO 2023), co-located with FOIS 2023,
19-20 July, 2023, Sherbrooke, Québec, Canada.
∗
Corresponding author.
Envelope-Open florian.emmrich1@tu-dresden.de (F. Emmrich)
© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
CEUR Workshop Proceedings (CEUR-WS.org)
Proceedings
http://ceur-ws.org
ISSN 1613-0073
1
Precisifications are analogous to the worlds of modal-logic frameworks with possible-worlds semantics.
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
minimum area (F1) where a forest ecosystem is specified as an ecosystem with a certain ratio of
tree canopy cover (F2). LU defines a forest with regard to the purpose for which an area of land is
put to use by humans, i.e. a forest is a maximally connected area with “forest use” (F3).2 Sources
LC and LU agree that forests subsume broadleaf, needleleaf and tropical forests (F4), and they both
adhere to some upper-level ontology ULO that formalises general terms, stipulating for instance
that land and ecosystem are disjoint categories (F5). Using standard DL notation and providing
“perspective annotations” by means of correspondingly labelled multi-modal logic box operators,
the example can be formalised in a standpoint-enhanced description logic as follows:
(F1) □LC [Forest ≡ ForestEcosystem ⊓ ∃hasLand .Area ≥0 .5 ha ]
(F2) □LC [ForestEcosystem ≡ Ecosystem ⊓ TreeCanopy ≥20 % ]
(F3) □LU [Forest ≡ ForestlandUse ⊓ MCON ] ∧ □∗ [ForestlandUse ⊑ Land ]
(F4) □LC∪LU [(BroadleafForest ⊔ NeedleleafForest ⊔ TropicalForest ) ⊑ Forest ]
(F5) (LC ⪯ ULO) ∧ (LU ⪯ ULO) ∧ □ULO [Land ⊓ Ecosystem ⊑ ⊥]
Here we use the sharper operator ⪯ to establish hierarchies of standpoints. Notice that ecosystem
and land are disjoint categories according to the overarching ULO (F5), yet forests are defined
as ecosystems according to LC (F1) and as lands according to LU (F3). As discussed in [3], these
kinds of disagreements result in well-reported challenges in the area of Ontology Integration
[5, 6] and make ontology merging a non-trivial task. Standpoint logic overcomes the usual
tradeoffs by supporting standpoint-dependent knowledge specifications, which allows the
statements (F1)–(F5) to be jointly represented.
In recent work, Gómez Álvarez et al. [4] introduced First-Order Standpoint Logic (FOSL)
and showed favourable complexity results for its sentential fragments, which disallow modal
operators being applied to formulas with free variables. Specifically, adding sentential stand-
points does not increase the complexity for fragments that are NP-hard, which is shown by
means of a polytime equisatisfiable translation. These results apply to the sentential standpoint
variants of the expressive SROIQ family of description logics, logical basis of OWL 2 DL [1]. In
a nutshell, given a knowledge base in sentential Standpoint-SROIQ𝑏𝑠 3 , the provided polytime
translation outputs an equisatisfiable knowledge base in plain SROIQ𝑏𝑠 . Beyond establishing
tight complexity bounds, this presented us with a way to leverage existing highly optimised
OWL reasoners to provide reasoning support for ontology languages extended by standpoint
modelling. In this work, we adjust this translation to plain SROIQ,4 and we present an imple-
mentation thereof, which effectively constitutes the first tool supporting automated reasoning
on Standpoint-OWL 2 DL in combination with existing off-the-shelf reasoners.
The paper is structured as follows. We first introduce the syntax and semantics of sentential
Standpoint-SROIQ and describe briefly how SROIQ relates to OWL 2 (Section 2.1). We then
explain how to encode sentential Standpoint-SROIQ axioms in an OWL 2 DL ontology, and how
our implementation translates them in such a way that they can be processed by an OWL 2 DL
reasoner (Section 3). We proceed to detail the usage of the command-line tool (Section 4) and
we conclude the paper with a discussion of the contributions and future work.
2
“Forest use” areas may qualify for logging concessions and be classified into, e.g. agricultural or recreational use.
3
Notice that the published translation [4] is for the mildly stronger SROIQ𝑏𝑠 instead of the more mainstream SROIQ.
4
To the best of our knowledge current reasoners do not support SROIQ𝑏𝑠 .
Table 1
“Plain” SROIQ role, concept expressions, RIAs and TBox axioms. 𝐶 ≡ 𝐷 abbreviates 𝐶 ⊑ 𝐷, 𝐷 ⊑ 𝐶.
Name Syntax Semantics Name Syntax Semantics
general concept 𝐶⊑𝐷 𝐶 I ⊆ 𝐷 I inverse role s− {(𝛿, 𝛿 ′ ) ∈ Δ × Δ ∣ (𝛿 ′ , 𝛿) ∈ s I }
inclusion (GCI) universal role u ΔI × ΔI
role inclusion 𝑟1 ∘ … ∘𝑟𝑛 ⊑ r nominal
𝑟1I ∘ … ∘ 𝑟𝑛I ⊆ r I {𝑎} {𝑎I }
axioms top
𝑟1 ∘ … ∘ 𝑟𝑛 ∘ r ⊑ r 𝑟1 ∘ … ∘ 𝑟𝑛I ∘ r I ⊆ r I
I ⊤ ΔI
(RIAs) bottom
r ∘ 𝑟1 ∘ … ∘𝑟𝑛 ⊑ r r I ∘𝑟1I ∘ … ∘ 𝑟𝑛I ⊆ r I ⊥ ∅
r∘ r ⊑ r negation
rI∘ rI ⊆ rI ¬𝐶 ΔI ⧵ 𝐶 I
conjunction 𝐶 ⊓𝐷 𝐶 I ∩ 𝐷I
In RIAs, r ∈ Pns2 , while 𝑟𝑖 ∈ R and 𝑟𝑖 ≺ r for all disjunction 𝐶 ⊔𝐷 𝐶 I ∪ 𝐷I
𝑖 ∈ {1, … , 𝑛}. univ. restriction ∀𝑟.𝐶 {𝛿 ∣ ∀𝑦.(𝛿, 𝛿 ′ ) ∈ 𝑟 I → 𝛿 ′ ∈ 𝐶 I }
exist. restriction ∃𝑟.𝐶 {𝛿 ∣ ∃𝑦.(𝛿, 𝛿 ′ ) ∈ 𝑟 I ∧ 𝛿 ′ ∈ 𝐶 I }
Self concept ∃𝑟.Self {𝛿 ∣ (𝛿, 𝛿) ∈ 𝑟 I }
qualified number ⩽𝑛 𝑟.𝐶 {𝛿 ∣ #{𝛿 ′ ∈ 𝐶 I ∣ (𝛿, 𝛿 ′ ) ∈ 𝑟 I } ≤ 𝑛}
restrictions ⩾𝑛 𝑟.𝐶 {𝛿 ∣ #{𝛿 ′ ∈ 𝐶 I ∣ (𝛿, 𝛿 ′ ) ∈ 𝑟 I } ≥ 𝑛}
2. Background
We next introduce the theoretical background, starting with the “plain” (standpoint-free) descrip-
tion logic SROIQ, its standpoint-enhanced version, and the web ontology language OWL 2 DL.
2.1. Standpoint Description Logic
Let C, P1 , and P2 be finite, mutually disjoint sets called individual names, concept names
and role names, respectively. P2 is subdivided into simple role names Ps2 and non-simple role
names Pns 2 , the latter containing the universal role u and being strictly ordered by some strict
order ≺. Then, the set Rs of simple role expressions is defined by 𝑟1 , 𝑟2 ∶∶= s ∣ s − , with s ∈ Ps2 ,
5
while the set of (arbitrary) role expressions is R = Rs ∪ Pns 2 . The order ≺ is then extended to
s
R by making all elements of R ≺-minimal. The syntax of concept expressions is given by
𝐶, 𝐷 ∶∶= A ∣ {𝑎} ∣ ⊤ ∣ ⊥ ∣ ¬𝐶 ∣ 𝐶 ⊓ 𝐷 ∣ 𝐶 ⊔ 𝐷 ∣ ∀𝑟.𝐶 ∣ ∃𝑟.𝐶 ∣ ∃𝑟 ′.Self ∣ ⩽𝑛 𝑟 ′.𝐶 ∣ ⩾𝑛 𝑟 ′.𝐶, with A ∈ P1 ,
𝑎 ∈ C, 𝑟 ∈ R, 𝑟 ′ ∈ Rs , and 𝑛 ∈ ℕ. The different types of SROIQ axioms are given in Table 1.6
Similar to FOL, the semantics of SROIQ is defined via interpretations I = (Δ, ⋅I ) composed
of a non-empty set Δ called the domain of I and a function ⋅I mapping individual names to
elements of Δ, concept names to subsets of Δ, and role names to subsets of Δ × Δ. This is
extended to role and concept expressions and used to define satisfaction of axioms (see Table 1).
In Standpoint-SROIQ, “plain” SROIQ axioms may be preceded by a standpoint modality,
expressing a standpoint relative to which the axiom is stated to hold. Within such modalities,
standpoints may be either referred to by name (e.g. as in F1–F5), or by expressions constructed
from names inductively using set operators. Formally, the set ES of standpoint expressions is
defined by e1 , e2 ∶∶= ∗ ∣ s ∣ e1 ∪ e2 ∣ e1 ∩ e2 ∣ e1 ⧵ e2 , where 𝑠 ∈ S is a standpoint name, and ∗ ∈ S
is a special name referring to the universal standpoint, i.e. the standpoint comprising all precisifi-
5
In the original definition of SROIQ, simplicity of roles and ≺ are not given a priori, but meant to be implicitly
determined by the set of axioms. Our choice to fix them explicitly upfront simplifies the presentation without
restricting expressivity.
6
The original definition of SROIQ contained more axioms (role transitivity, (a)symmetry, (ir)reflexivity and disjoint-
ness; concept and role assertions, i.e., ABox axioms; (in)equality), but these are syntactic sugar in our setting.
cations. A sharpening statement e1 ⪯ e2 expresses that e1 pertains to a viewpoint that is at least
as narrow as that of e2 and is syntactic sugar for the axiom □e1 \e2 [⊤ ⊑ ⊥]. The set 𝕊[SROIQ]
of sentential Standpoint-SROIQ sentences is now defined as the union 𝕊[SROIQ] ∶= B𝑅 ∪ B𝑇 ,
where B𝑅 consists of all SROIQ RIAs and B𝑇 is inductively defined:
• if 𝜙 is a SROIQ TBox axiom, then 𝜙 ∈ B𝑇 ,
• if 𝜙, 𝜓 ∈ B𝑇 , then ¬𝜙, 𝜙 ∧ 𝜓 , 𝜙 ∨ 𝜓 ∈ B𝑇 ; if 𝜙 ∈ B𝑇 and e ∈ ES , then □e 𝜙, ♦e 𝜙 ∈ B𝑇 .
Any 𝜙 ∈ 𝕊[SROIQ] can be transformed to an equivalent 𝜓 ∈ 𝕊[SROIQ] in normal form, where
negation only occurs directly before a SROIQ TBox axiom or a standpoint modality □e /♦e ,
and no standpoint modality appears in the scope of another.
In the semantics of sentential Standpoint-SROIQ, standpoints are represented by sets of so-
called precisifications where each precisification corresponds to an ordinary SROIQ interpreta-
tion. Formally, the semantics of (sentential) Standpoint-SROIQ knowledge bases K ⊆ 𝕊[SROIQ]
is given by description logic standpoint structures 𝔇 = (Δ, Π, 𝜎 , 𝛾 ) where Δ is a non-empty set,
the interpretation domain, Π is a non-empty set of precisifications, 𝜎 maps each standpoint name
s ∈ S to a subset of Π, and 𝛾 maps each 𝜋 ∈ Π to a “plain” SROIQ interpretation with domain Δ.
The satisfaction relation for DL standpoint structures and elements of 𝕊[SROIQ] is then given by
• 𝔇, 𝜋 ⊧ 𝜉 iff 𝛾 (𝜋) ⊧ 𝜉 for SROIQ TBox axioms 𝜉, and
• 𝔇, 𝜋 ⊧ □e [𝜙] iff 𝔇, 𝜋 ′ ⊧ 𝜙 for all 𝜋 ′ ∈ 𝜎 (e) and 𝔇, 𝜋 ⊧ ♦e [𝜙] iff 𝔇, 𝜋 ′ ⊧ 𝜙 for some 𝜋 ′ ∈ 𝜎 (e)
where 𝜎 is extended from standpoint names to standpoint expressions in the obvious way,
and the satisfaction relation for the Boolean connectives is as usual. In a Standpoint-SROIQ
knowledge base K ⊆ 𝕊[SROIQ] , we consider all formulas 𝜙 not preceded by a modality to be
implicitly of the form □∗ [𝜙]. For the full technical definitions we refer to the original paper [4].
We finally note that Gómez Álvarez et al. [4] have presented a sentential standpoint version
of the description logic SROIQ𝑏𝑠 , which extends SROIQ by safe Boolean role expressions, i.e. role
expressions of the form 𝑟1 ∪𝑟2 , 𝑟1 ∩𝑟2 and 𝑟1 ⧵𝑟2 , denoting union, intersection and difference of roles,
respectively. Since to our knowledge there is no reasoner which supports these safe Boolean
role expressions, we have restricted the implementation to sentential Standpoint-SROIQ.
2.2. OWL 2 DL
The Web Ontology Language OWL 2 [1] is an expressive knowledge representation language
and a W3C-recommended standard for modelling ontologies. There are two alternative ways
of defining the semantics of OWL 2 ontologies: the RDF-Based Semantics [7], which assigns
meaning to RDF graphs and thus only indirectly to ontology structures via the mapping to RDF
graphs [8], and the Direct Semantics [9] which assigns meaning directly to ontology structures.
The latter results in a semantics compatible with the model-theoretic semantics of SROIQ.
Moreover, to ensure that OWL 2 ontology structures can be translated into a SROIQ knowl-
edge base, certain conditions have to be fulfilled, for instance transitive properties cannot
be used in number restrictions. A complete list of restrictions can be found in the OWL 2
Structural Specification document [10, Section 3]. Ontologies that satisfy these conditions
are called OWL 2 DL ontologies. Our focus is on OWL 2 DL since this compatibility with
SROIQ ontologies allows us to implement the translation from sentential Standpoint-SROIQ
to standard SROIQ in OWL 2.
3. Standpoint-OWL 2 DL
In order to support standpoint-based reasoning in the semantic web, one may either extend
current standards such as OWL 2, or provide procedures to encode the standpoint operators
within these languages. We take the latter approach following the lines of the work of Bobillo
and Straccia [11], who proposed a methodology to represent fuzzy ontologies in OWL 2 using
annotation properties. These properties are broadly used to add comments or labels to entities
and axioms of the ontology, as a way to provide supplementary information to the user. In
our case, we define the annotation property “standpointLabel ”, which will be used to add
standpoint operators to axioms and to create Boolean combinations of standpoint axioms.
This section illustrates how to encode the sentential Standpoint-SROIQ (Section 2.1) con-
structs that are not available in OWL 2. Most importantly, we provide the syntax to encode
Boolean combinations of standpoint axioms, i.e. the axioms in B𝑇 . While this is sufficient to
encode standpoint ontologies, we also introduce syntax for the specification of sharpening
statements, which are syntactic sugar in Standpoint-SROIQ, and also for labelling single stan-
dard OWL 2 subclass or equivalence axioms with a standpoint operator, which facilitates the
enhancement of pre-existing ontologies with standpoints.
Boolean combinations Complex standpoint axioms can be added to an ontology by anno-
tating the ontology itself by a standpointLabel with a BoolComb value:7
BoolComb ∶∶= Formula
Formula ∶∶= Axiom | Axiom |
Formula Formula | Formula Formula
Axiom ∶∶= StdAxiom | |
SPExpr StdAxiom | SPExpr StdAxiom
StdAxiom ∶∶= Class Class |
Class Class
SPExpr ∶∶= | SPExpr |
SPExpr | SPExpr
where §ax matches the regular expression §[a-zA-Z]+[0-9]* , s either matches
[a-zA-Z]+[0-9]* or is the universal standpoint * , and Class is a class expression in
OWL 2 Manchester syntax [12]. If a named standpoint axiom is mentioned, there has to be
an annotated axiom with the same name attribute in the ontology, which then replaces the
reference in the Boolean combination.
Example 2. We can encode the axiom (F3) in Example 1 by annotating the ontology with a
standpointLabel in the following way:
7
The elements in the XML syntax are not case-sensitive, but the name attribute is.
Forest
ForestlandUse and MCON
ForestlandUse Land
Sharpening statements Sharpening statements e1 ⪯ e2 are encoded via annotation of the
ontology with a standpointLabel of the form SPExpr SPExpr .
Simple standpoint axioms Standard subclass and equivalence axioms can be turned into
standpoint axioms by adding a standpointLabel annotation of the form
SPAxiom ∶∶= SPOperator |
SPOperator
SPOperator ∶∶= SPExpr | SPExpr
with §ax and SPExpr defined as above. This effectively prepends a standard subclass or equiv-
alence axiom by a standpoint operator □e /♦e for some standpoint expression e. If the name
attribute of the standpointAxiom element is given, it can be used as a reference in Boolean
combinations. A standpoint axiom with a name attribute will not be translated outside of the
Boolean combinations that refer to them, since this would render any reference to it tautological.
4. Tool Description
Our command-line tool implements an adaptation to SROIQ of the translation from sentential
Standpoint-SROIQ𝑏𝑠 to standard SROIQ𝑏𝑠 proposed by Gómez Álvarez et al. [4]. In this section,
we describe how a standpoint-annotated OWL 2 DL ontology is translated to an OWL 2 DL
ontology that can be processed by an OWL 2 DL reasoner. Subsequently, we explain how to
use the command-line tool and outline some of its additional features.
4.1. Implementation
Our command-line tool8 can parse a sentential Standpoint-SROIQ ontology in the syntax
provided in Section 3, and translate it to standard OWL 2 DL, for which efficient reasoners
already exist, e.g. HermiT [13]. We use the OWL API for creating, parsing and manipulating
OWL 2 ontologies, hence the format of the input ontology can be one of a variety of standardised
syntaxes, such as RDF/XML [14] or Manchester syntax [12].
The implemented translation exploits the fact that satisfiable 𝕊[SROIQ] knowledge bases are
guaranteed to have a model with a bounded number of precisifications, which are represented
by integers 𝜋 ∈ {0, … , 𝑝 − 1} in the encoding. While Gómez Álvarez et al. [4] set this bound to
8
The source code can be found on the GitHub repository: https://github.com/cl-tud/standpoint-owl2
the size of the knowledge base, for our implementation we use the more fine-grained count of
the diamonds occurring in positive polarity and the boxes occurring in negative polarity in the
standpointLabel annotations. There are two syntactic impediments of SROIQ that need to be
addressed by the translation: (a) SROIQ does not provide nullary predicates, which we simulate
by concept expressions of the form ∀𝑢.𝑃, where 𝑢 is the universal role and 𝑃 encodes the predicate
via a concept name, and (b) SROIQ does not directly allow for arbitrary Boolean combinations
of axioms, but an equivalent encoding is possible using the universal role 𝑢; for instance the
expression ¬(𝐴 ≡ 𝐵) ∨ (𝐴 ⊑ 𝐶) can be converted to ⊤ ⊑ ∀𝑢.(𝐴 ⊓ ¬𝐵) ⊔ ∀𝑢.(𝐵 ⊓ ¬𝐴) ⊔ ∀𝑢.(¬𝐴 ⊔ 𝐶).
The translation proceeds in the following way. For each concept name 𝐴, role name 𝑟 and
standpoint 𝑠 in the input ontology, we generate the fresh concept and role names 𝑀_𝑠_𝜋, 𝐴_𝜋
and 𝑟_𝜋 for each 𝜋 ∈ {0, … , 𝑝 − 1}, where 𝑀 is a prefix for the nullary standpoint predicates. To
avoid altering the original ontology file, we additionally rebase all concept, role and individual
names, i.e. update their IRIs with that of the output ontology.
Then, for each 𝜋 ∈ {0, … , 𝑝 − 1}, we add the axioms (⊤ ⊑ ∀𝑢.𝑀_* _𝜋) and for each standpoint
axiom 𝜙 ∈ B𝑇 the set of GCIs consisting of (⊤ ⊑ trans(𝜋, 𝜙)), with trans defined as follows.
trans(𝜋, 𝐶 ⊑ 𝐷) = ∀𝑢.(¬𝐶_𝜋 ⊔ 𝐷_𝜋), transE (𝜋, 𝑠) = ∀𝑢.𝑀_𝑠_𝜋,
trans(𝜋, ¬(𝐶 ⊑ 𝐷)) = ∃𝑢.(𝐶_𝜋 ⊓ ¬𝐷_𝜋), transE (𝜋, e1 ∩ e2 ) = transE (𝜋, e1 ) ⊓ transE (𝜋, e2 ),
trans(𝜋, 𝜙1 ∧ 𝜙2 ) = trans(𝜋, 𝜙1 ) ⊓ trans(𝜋, 𝜙2 ), transE (𝜋, e1 ∪ e2 ) = transE (𝜋, e1 ) ⊔ transE (𝜋, e2 ),
trans(𝜋, 𝜙1 ∨ 𝜙2 ) = trans(𝜋, 𝜙1 ) ⊔ trans(𝜋, 𝜙2 ), transE (𝜋, e1 ⧵ e2 ) = transE (𝜋, e1 ) ⊓ ¬transE (𝜋, e2 )
𝑝−1
′ ′
trans(𝜋, □e ) = ⨅𝜋 ′=0 (¬transE (𝜋 , e) ⊔ trans(𝜋 , 𝜙)),
𝑝−1
trans(𝜋, ♦e ) = ⨆𝜋 ′=0 (transE (𝜋 ′ , e) ⊓ trans(𝜋 ′ , 𝜙)),
Equivalence axioms are treated as a conjunction of subclass axioms, and negation in front
of standpoint modalities is resolved by duality, viz. ¬□e [𝜙] = ♦e [¬𝜙] and ¬♦e [𝜙] = □e [¬𝜙].
In line with treating plain SROIQ axioms as being prepended by □∗ , we translate standard
subclass and equivalence axioms as being of the form □∗ [𝜙], and RIAs are translated by simply
replacing the original role names 𝑟 by 𝑟_𝜋 for all precisifications 𝜋 ∈ {0, … , 𝑝 − 1}.
4.2. Usage
Translate An annotated ontology can be directly translated via the command-line tool by
providing the ontology file or its IRI. When one or more of the options listed below are used,
the output ontology will not be translated automatically, but saved in a separate file. This can
be avoided by setting a separate translate flag. Note that the translated ontology is meant to be
passed to a reasoner, and hence not optimised for further editing by the user.
Import The import option first imports an ontology into the input file, and then annotates
all imported axioms for which standpoint annotation is supported by a box operator with a
specified standpoint name. This feature avoids that, for instance, two concepts with the same
name (and possibly different IRI bases) occuring in subclass or equivalence axioms will be
treated as the same concept during translation.
Query The most basic functionality of OWL 2 DL reasoners is checking the ontology for in-
consistency. Popular reasoners, e.g. HermiT [13], additionally offer to answer queries regarding
subclass relations, instances etc. However, these query services are impractical for translated
Standpoint-OWL 2 ontologies, since standpoint axioms can only be used in a query if they
are translated to standard OWL 2 beforehand. In order to simplify the specification of queries
containing standpoint axioms, we have added a query option to the command-line tool. The
query language is the language of Boolean combinations, i.e. we can ask if a given Boolean
combination is entailed by the translated ontology. A query can be given by an expression
of the form Formula defined in Section 3 (possibly in a separate file), or in a simplified query
syntax for single standpoint axioms. The syntax of a simple query is defined by:
SimpleQuery ∶∶= [s] (SimpleAxiom) | (SimpleAxiom)
SimpleAxiom ∶∶= Class sub Class | Class eq Class
where s and Class are as before. The operators [s] and stand for □s and ♦s , respectively,
sub for a subsumption relation and eq for equivalence of classes. The query is first negated, and
then added to the input ontology as a Boolean combination. If, after translation, the resulting
ontology is inconsistent, the query is a logical consequence of the ontology.
Dump Lastly, there is the option to dump the output ontology to the command-line, rather
than saving it to a new file, which facilitates reasoning over the translated ontology via pipeline
to an OWL 2 DL reasoner.
5. Conclusion
In this paper, we have proposed a syntax for sentential Standpoint-SROIQ using OWL 2
annotations, which have proved useful for implementing different non-standard description
logics. While in this paper we have focused on the sentential fragment of SROIQ, our approach
can be easily extended to more expressive fragments of standpoint SROIQ, e.g. to support
standpoint operators on the level of concepts and roles, which leads to fragments currently under
investigation and with interesting applications in ontology alignment [15, 16]. Subsequently,
we have provided a translation from sentential Standpoint-SROIQ to standard SROIQ, which
is an adjustment of the recently published translation for the more expressive SROIQ𝑏𝑠 , and
finally, we have implemented this translation as a command-line tool, thus effectively providing
standpoint-based reasoning support for OWL 2 DL ontologies.
Future work will focus on the usability of the system. The XML syntax for standpointLabel
annotations is not user-friendly, and annotating an ontology in this way can be time-consuming,
even when using an ontology editor like Protégé [17]. A possible approach to alleviating this
problem would be to develop a plugin for Protégé and to make use of its existing user interface
for adding and modifying standpoint axioms, similar to the Fuzzy OWL 2 Protégé plugin by
Bobillo and Straccia [11]. This will allow for the integration of the modelling support with the
translator and reasoner.
Acknowledgments
This work was supported by funding from BMBF within projects KIMEDS (grant no. GW0552B),
MEDGE (grant no. 16ME0529), and SEMECO (grant no. 03ZU1210B).
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