We present a tool for modelling and reasoning with knowledge from various diverse (and possibly conlficting) 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.
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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 [
A recent proposal aiming to address these challenges is Standpoint Logic (SL) [
Example 1. A range of conceptualisations for the notion of forest have been specified for diferent
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
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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≥0.5ha]
(F2) □ LC[ForestEcosystem ≡ Ecosystem ⊓ TreeCanopy≥20%]
(F3) □ LU[Forest ≡ ForestlandUse ⊓ MCON] ∧ □ ∗[ForestlandUse ⊑ Land]
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 [
In recent work, Gómez Álvarez et al. [
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.
3Notice that the published translation [
We next introduce the theoretical background, starting with the “plain” (standpoint-free) description logic SROIQ, its standpoint-enhanced version, and the web ontology language OWL 2 DL.
, ∶∶=
A ∣ {} ∣ ⊤ ∣ ⊥ ∣ ¬ ∣ ⊓ ∣ ⊔ ∣ ∀ . ∣ ∃ . ∣ ∃ Let C, P1, and P
2 be finite, mutually disjoint sets called and role names, respectively. P2 is subdivided into simple role names P names P2ns, the latter containing the universal role u and being strictly ordered by some strict s order ≺.5 Then, the set Rs of simple role expressions is defined by 1, 2 ∶∶= s ∣ s−, with s ∈ P2, while the set of (arbitrary) role expressions is R = R ∪ Pns. The order ≺ is then extended to s
s2 and non-simple role individual names, concept names 2 s ≺-minimal. The syntax of concept expressions is given by ′.Self ∣ ⩽ ′. ∣ ⩾ ′ ., with A ∈ P1, ∈ C, ∈ R, ′ ∈ Rs, and ∈ ℕ . The diferent 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 is a standpoint name, and ∗ ∈ S is a special name referring to the universal standpoint, i.e. the standpoint comprising all precisifi5In 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. 6The original definition of SROIQ contained more axioms (role transitivity, (a)symmetry, (ir)reflexivity and disjointness; concept and role assertions, i.e., ABox axioms; (in)equality), but these are syntactic sugar in our setting. where B consists of all SROIQ RIAs and B is inductively defined: 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 [SROIQ] of sentential Standpoint-SROIQ sentences is now defined as the union [SROIQ] ∶= B ∪ B , • if is a SROIQ TBox axiom, then ∈ B ,
• if , ∈
B , then ¬, ∧ , ∨ ∈
B ; if ∈ B and e ∈ ES, then □ e , ♦ e ∈ B .
Any ∈ [SROIQ] can be transformed to an equivalent ∈ [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 socalled precisifications where each precisification corresponds to an ordinary
tion. Formally, the semantics of (sentential) Standpoint-SROIQ knowledge bases K ⊆ [SROIQ] is given by description logic standpoint structures = (Δ, Π, , ) where Δ is a non-empty set, the interpretation domain, Π is a non-empty set of precisifications , maps each standpoint name s ∈ S to a subset of Π, and maps each ∈ Π to a “plain” SROIQ interpretation with domain Δ. The satisfaction relation for DL standpoint structures and elements of [SROIQ] is then given by • , ⊧ • , ⊧
if ( ) ⊧
□ e[] if ,
for SROIQ TBox axioms , and
′ ⊧ for all ′ ∈ ( e) and , ⊧
♦ e[] if ,
′ ⊧ for some ′ ∈ ( e)
where 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 ⊆ [SROIQ], we consider all formulas not preceded by a modality to be
implicitly of the form □ ∗[] . For the full technical definitions we refer to the original paper [
We finally note that Gómez Álvarez et al. [
Moreover, to ensure that OWL 2 ontology structures can be translated into a SROIQ knowledge 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.
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 [
This section illustrates how to encode the sentential Standpoint-SROIQ (Section 2.1) constructs 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 B . While this is suficient 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 standard OWL 2 subclass or equivalence axioms with a standpoint operator, which facilitates the enhancement of pre-existing ontologies with standpoints.
Boolean combinations
tating the ontology itself by a standpointLabel with a BoolComb value:7 BoolComb ∶∶= <booleanCombination>Formula</booleanCombination>
Formula ∶∶= Axiom | <NOT>Axiom</NOT> |
<AND>Formula Formula</AND> | <OR>Formula Formula</OR> Axiom ∶∶= StdAxiom | <standpointAxiom name="§ax"/> |
<Box>SPExpr StdAxiom</Box> | <Diamond>SPExpr StdAxiom</Diamond>
StdAxiom ∶∶= <subClassOf><LHS>Class</LHS> <RHS>Class</RHS></subClassOf> |
<equivalentClasses><LHS>Class</LHS> <RHS>Class</RHS></equivalentClasses>
SPExpr ∶∶= <Standpoint name="s"/> | <INTERSECTION>SPExpr</INTERSECTION> |
<UNION>SPExpr</UNION> | <MINUS>SPExpr</MINUS>
where §ax
matches the regular expression §[a-zA-Z]+[
Example 2. We can encode the axiom (F3) in Example 1 by annotating the ontology with a standpointLabel in the following way: 7The elements in the XML syntax are not case-sensitive, but the name attribute is.
<standpointLabel> <booleanCombination> <AND> <Box> <Standpoint name="LU"/> <equivalentClasses> <LHS>Forest</LHS>
<RHS>ForestlandUse and MCON</RHS> </equivalentClasses> </Box> <Box> <Standpoint name="*"/>
<subClassOf> <LHS>ForestlandUse</LHS> <RHS>Land</RHS> </subClassOf> </Box> </AND> </booleanCombination> </standpointLabel> Sharpening statements Sharpening statements e1 ⪯ e2 are encoded via annotation of the ontology with a standpointLabel of the form <Sharpening>SPExpr SPExpr</Sharpening>. Simple standpoint axioms Standard subclass and equivalence axioms can be turned into standpoint axioms by adding a standpointLabel annotation of the form
SPAxiom ∶∶= <standpointAxiom>SPOperator</standpointAxiom> |
<standpointAxiom name="§ax">SPOperator</standpointAxiom>
SPOperator ∶∶= <Box>SPExpr</Box> | <Diamond>SPExpr</Diamond> with §ax and SPExpr defined as above. This efectively prepends a standard subclass or equivalence 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.
Our command-line tool implements an adaptation to SROIQ of the translation from sentential
Standpoint-SROIQ to standard SROIQ proposed by Gómez Álvarez et al. [
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 eficient reasoners
already exist, e.g. HermiT [
The implemented translation exploits the fact that satisfiable [SROIQ] knowledge bases are
guaranteed to have a model with a bounded number of precisifications, which are represented
by integers ∈ {0, … , − 1} in the encoding. While Gómez Álvarez et al. [
The translation proceeds in the following way. For each concept name , role name and standpoint in the input ontology, we generate the fresh concept and role names _ _ , _ and _ for each ∈ {0, … , − 1} , where 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 ∈ {0, … , − 1} , we add the axioms (⊤ ⊑ ∀. _*_ ) and for each standpoint axiom ∈ B the set of GCIs consisting of (⊤ ⊑ trans( , )) , with trans defined as follows.
trans(, ⊑ ) = ∀.(¬ _ ⊔ _), trans(, ¬( ⊑ )) = ∃.( _ ⊓ ¬ _), trans(, 1 ∧ 2) = trans(, 1) ⊓ trans(, 2), trans(, 1 ∨ 2) = trans(, 1) ⊔ trans(, 2), trans(, □ e) = ⨅−′1=0(¬transE( ′, e) ⊔ trans( ′, )), trans(, ♦ e) = ⨆−′1=0(transE( ′, e) ⊓ trans( ′, )), transE(, ) = ∀. _ _, transE(, e1 ∩ e2) = transE(, e1) ⊓ transE(, e2), transE(, e1 ∪ e2) = transE(, e1) ⊔ transE(, e2), transE(, e1 ⧵ e2) = transE(, e1) ⊓ ¬transE(, e2) Equivalence axioms are treated as a conjunction of subclass axioms, and negation in front of standpoint modalities is resolved by duality, viz. ¬□ e[] = ♦ e[¬] and ¬♦ e[] = □ e[¬] . In line with treating plain SROIQ axioms as being prepended by □ ∗, we translate standard subclass and equivalence axioms as being of the form □ ∗[] , and RIAs are translated by simply replacing the original role names by _ for all precisifications ∈ {0, … , − 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 diferent 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
inconsistency. Popular reasoners, e.g. HermiT [
SimpleAxiom ∶∶= Class sub Class | Class eq Class where s and Class are as before. The operators [s] and <s> 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.
In this paper, we have proposed a syntax for sentential Standpoint-SROIQ using OWL 2
annotations, which have proved useful for implementing diferent 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 [
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 [
This work was supported by funding from BMBF within projects KIMEDS (grant no. GW0552B), MEDGE (grant no. 16ME0529), and SEMECO (grant no. 03ZU1210B).