=Paper=
{{Paper
|id=Vol-2050/winks-paper3
|storemode=property
|title=Talking about Forests: An Example of Sharing Information Expressed with Vague Terms
|pdfUrl=https://ceur-ws.org/Vol-2050/WINKS_paper_3.pdf
|volume=Vol-2050
|authors=Lucía Gómez Álvarez,Brandon Bennett,Adam Richard-Bollans
|dblpUrl=https://dblp.org/rec/conf/jowo/AlvarezBR17
}}
==Talking about Forests: An Example of Sharing Information Expressed with Vague Terms==
https://ceur-ws.org/Vol-2050/WINKS_paper_3.pdf
Talking about Forests:
an Example of Sharing Information
Expressed with Vague Terms
Lucı́a Gómez Álvarez a , Brandon Bennett a and Adam Richard-Bollans a
a University of Leeds, The United Kingdom
Abstract. Most natural language terms do not have precise universally agreed defi-
nitions that fix their meanings. Even when conversation participants share the same
vocabulary and agree on taxonomic relationships (such as subsumption and mutual
exclusivity, which might be encoded in an ontology), they may differ greatly in the
specific semantics they give to the terms.
We illustrate this with the example of ‘forest’, for which the problematic arising
of the assignation of different meanings is repeatedly reported in the literature. This
is especially the case in the context of an unprecedented scale of publicly available
geographic data, where information and databases, even when tagged to ontologies,
may present a substantial semantic variation, which challenges interoperability and
knowledge exchange.
Our research addresses the issue of conceptual vagueness in ontology by pro-
viding a framework based on supervaluation semantics that explicitly represents
the semantic variability of a concept as a set of admissible precise interpretations.
Moreover, we describe the tools that support the conceptual negotiation between an
agent and the system, and the specification and reasoning within standpoints.
Keywords. concept negotiation, supervaluation, standpoint, forest, GIS, vagueness
1. Introduction
Since the shift in philosophy of language from logical positivism to behaviourism and
pragmatism, it is widely accepted that most natural language terms do not have precise
universally agreed definitions that fix their meanings. Even when conversation partici-
pants share the same vocabulary and agree on taxonomic relationships (such as subsump-
tion and mutual exclusivity, which might be encoded in an ontology), they may differ
greatly in the specific semantics they give to the terms in a particular situation. More-
over, except for certain technical terms, individuals do not hold permanent and precise
interpretations of the meaning of terms themselves [1].
Humans generally cope with these imprecisions of language by using context and
other pragmatic information to narrow the semantic variability of the terms. We say, they
‘take a standpoint’ on the semantics of the terms. If conflicts occur during the conversa-
tion, participants may adapt dynamically their standpoints in order to maintain the coop-
eration principles (Grice [2]) and achieve successful information exchange. In settings
where precision is necessary, such as in scientific or policy making domains, an explicit
concept negotiation may be needed if the participants expect or detect conflicting stand-
points.
To support human-machine interactions, ontologies are aimed at providing a com-
mon vocabulary in which shared knowledge can be represented [3]. However, in most
ontology-driven systems, concepts have rigid and static semantics that do not take ac-
count of vagueness or context dependence, and in this respect fail to reproduce the con-
ditions of human conversation. Meanwhile, the extensive and increasing amount of data
accessible through the internet encourages research on the remaining core challenges
facing ontology construction, among them semantic heterogeneity.
In this paper we take the example of negotiating the interpretation of the term ‘for-
est’, and propose a framework based on supervaluation semantics to allow for seman-
tic variability within the ontology. We first introduce what we understand as vagueness
and how it affects geographical objects in general, followed by the specific case of for-
est. We then summarise different approaches to vagueness and how they relate to our
research. We propose a framework based on standpoint semantics and its tools for sup-
porting share of information, concept negotiation and querying and reasoning within an
agent’s standpoint.
2. Vagueness and Knowledge Sharing in a Geographic Ontology
Vagueness is pervasive in language [4] and arises whenever a concept or linguistic ex-
pression admits of borderline cases of application [5]. We adopt here the distinction pro-
posed in [6] between sorites vagueness and conceptual vagueness. While Sorites vague-
ness occurs when the applicability of a predicate depends on specific measurable param-
eters but their thresholds are undetermined, conceptual vagueness arises when there is
a lack of clarity on which attributes or conditions are essential to fix the meaning of a
given term, so that it is controversial how it should be defined [7,6]. This is different
from ‘simple ambiguity’, where a term has more than one distinct meaning.
Moreover, the geographic domain is particularly characterised by objects lacking
bona fide boundaries and by the inherent vagueness in the definition of geographic de-
scriptors, frames of reference and context [8,9]. When thinking about geographic space,
people typically employ several different concepts, and change between them frequently
depending on the scale and the perceptual and geometrical properties of the space [10]
in addition to the contextual and pragmatic information.
While the value of ontologies is now well established [11], their support of vague-
ness and semantic heterogeneity1 remains challenging. One of the main advantages of
ontologies is that they improve the interoperability acting to enforce a consensus view
reached by a community regarding a certain domain [7]. This is done by formalising the
semantics of the terminology of the domain of discourse in some logic formalism. Typ-
ically this process involves the cooperation of domain experts which results in a unified
decision on the formalization of the semantics of the terminology. However, as a result
of the semantic heterogeneity and vagueness of the concepts to define, strong semantic
commitments favour specific interpretations of language and involve a loss of general-
ity, thus restricting the opportunities for interoperability. On the other hand, approaches
with shallower semantics rely fundamentally on taxonomic relationships, such as sub-
sumption and mutual exclusivity, thus leaving uncertainty on the specific semantics of
instances of these terms and potentially compromising the sound reuse of information.
1 Occurs when ontologies, schemas or datasets of the same domain present differences in meaning and inter-
pretation of categories and/or data values, thus challenging interoperability.
2.1. The Case of Forests
In this research we examine the term ‘forest’, for which a broad range of definitions
(more than 600 were reported in [12]) have been specified for different purposes. Be-
yond the spatio-temporal context dependence and fuzziness of their boundaries, many
factors contribute to the semantic variability of ‘forest’. They arise from: fundamental
differences between the land cover / land use2 perspectives, specific uses of the term
in different disciplines (ecology, forestry, environmental science, ...) and for different
management objectives [14], pragmatic differences between conceptualizations created
for science and policy [15], different aspects involved in classifying land as opposed to
individuating and demarcating geographic objects [7], and the modelling from endurant
or perdurant perspectives on fundamental ontology [16,14].
This scenario poses challenges both for the acquisition of global forest knowledge,
particularly its extent and spatial distribution [17,18,19], and for the sound reuse of in-
formation and knowledge extraction from the many resources that are increasingly pub-
licly available [20,21]. Moreover, different pieces of research point at cases of cross-
disciplinary information reuse among semantically non-interoperable datasets in science,
resulting in misleading results [15,14]. At the same time, the option of a centralised and
standard definition of ‘forest’ (the definition of the FAO3 plays that role de facto) only
supports the discourse of certain institutions and is reported to be unsuitable to capture
the needs of different contexts, disciplines and agents [15,14]. In these cases, the lack
of recognition for alternate definitions may distort the understanding of certain scenarios
such as in the case of contested spaces [16].
Despite the call for addressing the variability of interpretations and definitions of
‘forest’ in the literature [19,14,15,20], most public ontologies containing the concept
‘forest’ either avoid any semantic commitments beyond those embedded in the tax-
onomies or reduce them to the FAO definition. In the best scenarios, the forest concept
has a fuzzy boundary thus not committing to that fixed by the FAO. In this paper we
propose a framework that explicitly recognises a variety of acceptable definitions of ‘for-
est’ and we outline how such a system can support different interactions in a context of
semantic heterogeneity. Specifically, we support agents to discover the semantic hetero-
geneity of a concept in the ontology, to analyse it and to take their standpoint. Subse-
quently, they can reason and query the ontology according to their standpoint.
3. Approaches to Vagueness
Our intent is to provide a novel way of tackling the prior issues by approaching them
from the perspective of vagueness in ontology, more specifically conceptual vagueness.
In this section, we briefly review some approaches to vagueness and concept creation
and negotiation, and how they relate to our research on forest definitions.
The most broadly used logic-based techniques to model vagueness in information
systems are multivalued logics [22], in particular fuzzy logic [23]. Fuzzy logic works
by assigning degrees of truth to statements rather than making truth valuation a binary
choice. As a result, this approach provides a reasonably intuitive model for sorites vague-
ness[7], assigning a gradually increasing value to borderline cases as they transition from
2 While the former defines forest in terms of the ecological layer and the physical characteristics of the land,
the latter does it with regard to the purpose to which the land is put to use by humans [13].
3 The Food and Agriculture Organization of the United Nations.
less to more likely. However, fuzzy sets do not fully characterise the different precise
overlapping meanings that a term can adopt, which can be sharp but diverse, and fails to
incorporate penumbral connections [24] among them. For these reasons, we consider that
Fuzzy logic and similar formalisms are not suitable for the problem under consideration.
Conceptual spaces (Gardenfors, [25]), have received great attention in the last years.
Although they are not a formal theory of vagueness, they are relevant for this research
as they deal with concept formation and representation, expressed within a geometrical
space. A concept, say vanilla flavour, is then defined as some region of a four dimensional
space of taste, where the dimensions are salt, sour, sweet and bitter. This approach shows
interesting features for concept comparison through geometrical operations within a spe-
cific n-dimensional space, conceptual adaptation to context (location) in GIS [26] and an
account of prototypicality and borderline cases [27]. However, it remains unclear how
to tackle the issue of conceptual vagueness, as every concept is defined within a fixed
set of quality dimensions; choosing the relevant ones and thus describing the underlying
conceptual space for complex and ambiguous categories is not trivial [25].
Semantic heterogeneity and concept negotiation in information systems have been
mainly investigated as a separate phenomenon from that of concept creation and vague-
ness. Instead, they are approached as a phenomenon that arises in the context of the need
for interoperability of two systems, ontologies or agents, and the necessary conciliations
for their successful interoperation. In the area of ontology matching, a wide literature
review is provided in [28]. It is our intention to provide a complementary approach to the
existing work on the topic, based on the explicit support for semantic variation within an
ontology. Thus, the framework aims to support the semantic negotiation of the meaning
of its concepts, by providing agents with expressive power to represent their interpreta-
tion of the terms of the ontology both when instantiating its concepts and when querying
and reasoning within it.
4. A Framework Based on Standpoint Semantics
Standpoint Semantics is our theoretical framework for representing, interpreting and rea-
soning about information expressed using vague terminology. This theory is an elabora-
tion of the Supervaluation approach, in which the semantics of a vague language is mod-
elled by a set of precise interpretations called precisifications, where each precisification
corresponds to a precise and coherent interpretation of all vocabulary of the language.
4.1. Supervaluation Semantics
Consider a formal language based on classical first order logic, with a vocabulary V =
N ∪ C ∪ R, where N is a set of name symbols (these may be used as constants or as
variables when used with a quantifier), C a set of unary concept terms and R a set of
binary relation symbols. The set L of formulae of the language is the smallest set that
contains Ca and Rab for every C ∈ C every R ∈ R and every a, b ∈ N , and, for every ϕ
and ψ in L , formulae ¬ϕ, ϕ ∧ ψ and ϕ ∨ ψ are also in L .4
We define an interpretation structure I = hP, D, V , δ i, where:
• P is a set of precisifications,
• D is a set of individuals (the domain of discourse),
4 Here we omit the implication symbol ‘→’ from the syntax. But it can easily be defined by
ϕ → ψ ≡def ¬ϕ ∨ ψ.
• δ is a denotation function, which, for each precisification and each vocabulary
symbol in V , gives the semantic value of that symbol. It is a compound of the
following sub-functions:
— δN : (P × N ) → D maps name symbols to elements of the domain,
— δC : (P × C ) → 2D maps concept terms to subsets of the domain,
— δR : (P × R) → 2D×D maps relation symbols to sets of ordered pairs of
elements of the domain.
The only difference from the usual classical logic semantics is that the denotation of each
symbol is relative to a precisification p ∈ P, which determines a precise interpretation of
that predicate. We write p I ϕ to mean that the formula ϕ is true for precisification p,
in interpretation structure I . This determines the truth of propositions as follows:
• p I Ca iff δ (p, a) ∈ δ (p,C)
• p I Rab iff hδ (p, a), δ (p, b)i ∈ δ (p, R)
• p I ¬ϕ iff it is not the case that p I ϕ
• p I ϕ ∧ ψ iff p I ϕ and p I ψ
• p I ϕ ∨ ψ iff p I ϕ or p I ψ
• p I ∀x[ϕ] iff p I 0 ϕ for every interpretation structure I 0 = hP, D, V , δ 0 i
that is identical to I , except that the value of δ 0 (p, x) may be any element of D.5
Notice that this semantics not only accounts for variability in the meaning of vocab-
ulary terms but also allows one to enforce dependencies between the terms occurring in
a formula. For example, precisifications might vary in the set of people considered tall.
If precisification p1 sets a greater height threshold than p2 for applicability of the vague
property Tall, we might have δ (p1 , Tall) = {sally, tom}, δ (p2 , Tall) = {sally, tom, uli}.
Hence, we would have p1 I Tall(uli) and p2 I ¬Tall(uli). But no precisification can
make the formula Tall(uli) ∧ ¬Tall(uli) true. Moreover, we can also enforce constraints
between different terms in a formula. For instance, we might require that the denota-
tions of Tall and Short are disjoint for all precisifications. Thus, no formula of the form
Tall(x) ∧ ¬Short(x) would be true in any precisification.
The supervaluation semantics allows us to to augment the logical language with
operators that are interpreted relative to the set of precisifications. In particular, we can
specify a semantics for Uϕ, meaning that ϕ is unequivocally true, and Sϕ, meaning that
ϕ is in some sense true:
• p I Uϕ iff q I ϕ for every precisification q ∈ P,
• p I Sϕ iff q I ϕ for some precisification q ∈ P.
4.2. Standpoint Semantics
Standpoint semantics adds detail to the basic supervaluation approach in several ways.
The semantic choices that determine each particular precisification are modelled explic-
itly. These consist of choices of (a) threshold values that determine the applicability of
‘sorites vague’ predicates such as ‘tall’ and ‘bald’; and (b) choices of definitions that
resolve conceptual ambiguities, such as which kinds of vegetation species can be consid-
ered as constituting a forest.
5 Here, for simplicity, we are assuming that the domain of entities will be the same for every precisification.
This is not plausible in general.
Standpoint semantics explicitly models the variability of vague terminology in re-
lation to precise observable measurements and properties. Such measurements could be
heights, weights, distances and the properties might relate to physical composition, topo-
logical relationships. This is the kind of information one might store in a database (or
compute directly from the information in a database). Of course, in practice such infor-
mation might be inaccurate for various reasons such as limitations of measuring equip-
ment or errors in data capture. But these issues are not due to vagueness of terminology,
so in formulating the standpoint theory we need not worry about the correctness of the
measurement data: we take it as we find it.
4.2.1. A Sublanguage of Objective Observables
We now specify a classical first order language Lo for describing entities in terms of
objective measurements, properties and relations. Let its vocabulary be the set Vo =
N ∪D ∪F ∪G ∪C ∪R, where N is a set of names, D is a set of numerical expressions
(e.g. standard decimals), F is a set of unary function symbols, G is a set of binary
function symbols, C is a set of (precise) unary concepts and R is a set of (precise) binary
relations. So in a forestry related domain a vocabulary might be something like:
h{tree1, ..., boris, ...}, {height, radius}, {distance}, {Oak, Beech, ...}, {Owns, ...}i .
Here we have identifiers for individual trees, names of people, unary functions giv-
ing height and (canopy) radius measurements of the trees, a binary function giving the
distance between any two trees, predicates specifying the species of trees and an owen-
ership relation between trees and people.
In addition to the predications, Ca and Rab, of L , the vocabulary of Vo enables us
to include in Lo atomic formulae of the forms τ1 = τ2 and τ1 ≤ τ2 , where each of τ1 and
τ2 can be either a functional term (of the form f (a) or g(a, b)) or a numerical expression
(e.g. in standard decimal notation). So we can write formulae such as:
distance(tree1, tree2) = 23.5 or height(tree6) ≤ height(tree57).
Like L , the language Lo is also closed under combination by Boolean connectives and
the quantification operators. An interpretation of Lo is determined by a structure Io =
hD, Vo , δo i, where
• D is a domain of entities,
• δo maps the vocabulary in Vo to their semantic denotations and is a compound of
the following sub-functions:
— δN : N → D maps names to elements of the domain,
— δD : D → Q maps numerical expressions to rationals,
— δF : F → (D → Q) maps unary function symbols to functions from el-
ements of the domain to rationals,
— δG : G → ((D×D) → Q) maps binary function symbols to functions from
pairs of elements of the domain to rationals,
— δC : C → 2 D maps concept terms to subsets of the domain,
— δR : R → 2D×D maps relation symbols to sets of ordered pairs of
elements of the domain.
The truth conditions of the language Lo relative to interpretation Io are as follows:
• Io Ca iff δ (a) ∈ δ (C)
• Io Rab iff hδ (a), δ (b)i ∈ δ (R)
• Io τ1 = τ2 iff δ (τ1 ) = δ (τ2 )
• Io τ1 ≤ τ2 iff δ (τ1 ) ≤ δ (τ2 )
The interpretation of formulae formed by the Boolean connectives and quantifiers
will be exactly the same as for standard first order logic, so we do not specify it here.
4.2.2. Adding Vague Predicates
We now specify a language Lv in which we can specify possible precise interpretations
of vague predicates. In adition to Vo , we also have the vocabulary Vv = Cv ∪ Rv ∪ Tv .
where Cv is a set of vague unary predicates, R a set of vague binary relations Tv a set
of threshold variables. The specification is technically complex, although it has a rela-
tively simple informal explanation. Each precisification determines a mapping of vague
conceptual terms and relations to possible definitions and also determiens a valuation of
threshold variables that fix the limits of applicability of vague graded predicates. Thus
each precisification provides a translation from formulae containing vague terms of Vv
into formulae containing only the precise objective vocabulary of Vo .
Let Ld be the set of possible defining formulae. These are any well formed formulae
over the vocabulary Vo ∪ Tv , where as well as measurement functions and decimals,
the terms that can occur in atomic formulae of Ld formed with the = and ≤ relations
also include threshold variables. So for example, we could have height(x) ≤ thresh1.
We write Ldn to refer to the subset of Ldn containing those formulae that have exactly n
distinct free variables — i.e. formulae in which exactly n symbols in N occur outside
the scope of any quantifier.
We now give an explicit specification of the particular interpretation associated with
a precisification. Let each precisification p be associated with a tuple hpT , pC , pR i, where:
• pT : Tv → Q maps each threshold variable to a number,
• pC : Cv → Ld1 maps each vague unary predicate to a precise unary definition,
• pR : Rv → Ld2 maps each vague binary predicate to a precise binary definition.
So for example, for precisification p we could have:
pC (Tree) = Plant(x) ∧ Woody(x) ∧ min tree height thresh ≤ height(x)
and pT (min tree height) = 10, so precisification p defines Tree to be a woody plant of
height greater than or equal to 10 (metres).
We can now give an interpretation function for the full language Lv in which formu-
lae containing vague terms are interpreted relative to a precisification, which maps them
into precise formulae of Lo . The interpretation is specified by Iv = hD, Vo , δo , P, Vv , δv i,
where the interpretation of symbols in Vo is given as for the structure Vo given above,
and the interpretation of formulae in Lv is given by:
• p Iv ϕ is evaluated as Io ϕ iff ϕ does not contain any symbol in Vv ,
• p Iv τ1 = τ2 iff δ 0 (p, τ1 ) = δ 0 (p, τ2 ), where δ 0 (p, τ) = δo (τ) for all terms in
the precise language Lo (for whose interpretation p is not relevant) and δ 0 (p, τ) =
pT (p, τ), where τ is a threshold variable (i.e. τ ∈ Tv ),
• p Iv τ1 ≤ τ2 iff δ 0 (p, τ1 ) ≤ δ 0 (p, τ2 ), where δ 0 (τ) is defined the same way
as in the previous clause,
• p Iv Ca iff Io pC (C)(a/x), where pC (C)(a/x) is the result of substituting
a for the free variable x occurring in the precise definition of C determined by the
function pC of precisification p,
• p Iv Rab iff Io pR (R)(a/x, b/y), where pR (R)(a/x, b/y) is the result of
substituting a and b for the free variables x and y, in order of their occurrence in
the definition of R determined by the function pR of precisification p,
5. Towards Sharing Information Linked to Different Precisifications
In this section we explore the potential of the proposed system to enable communication
between agents holding diverse standpoints, by providing a shared ontology that sup-
ports vague semantics. Our framework enables agents to both link data to the ontology
according to their precise interpretation and also to query and reason within the ontol-
ogy according to a specific standpoint, which can be modified during the interaction. In
a context of sharing information, the proposed framework offers tools that enable both
the analysis of the relations that hold between precisifications and the execution of mod-
ifying operations such as calculating the intersection or union of a pair of precisifica-
tions. This, together with information on the instances satisfying these precisifications,
serves as a support to the agent for the specification of sound standpoints that guarantee
integrity and enable interoperation with the ontology.
5.1. Relations
Assuming that a concept negotiation is necessary, we support the analysis of the relations
that hold between precisifications. We identify five main relations, analogous to RCC5,
to be inferred by the system. These are:
1. Equivalence: p1 ↔ p2 . Anything that is a ‘forest’ in p1 must be a ‘forest’ in p2
and vice versa.
2. Subsumption: p2 → p1 . Anything that is a ‘forest’ in p2 must be a ‘forest’ in p1 .
3. Inverse subsumption: p1 → p2 . Anything that is a ‘forest’ in p1 must also be in
p2 .
4. Disjunction: p1 → ¬p2 . No entity can be a ‘forest’ in both p1 and p2
5. Overlap: None of the previous (NP) relations hold between p1 and p2 . Thus there
may be entities that are classified as ‘forest’ in both p1 and p2 , although neither
precisification has a stronger definition that the other.
Relations between precisifications show, to some degree, the connections among
them. While overlap is the most common scenario, other relations such as subsumption
and disjunction provide valuable information to the agent, to the point of interoperation
becoming trivial (such as when information is linked to a definition that is subsumed by
the agent’s definition) or not feasible because of explicitly conflicting commitments (in
the case of disjoint definitions).
It must be noted that the relation between precisifications is purely logical, i.e. is
a relationship that holds between the formal representation of two interpretations of the
semantics of the ontology, p1 and p2, which is not dependent on the real world objects
that may instantiate them. Consequently, the relation between the logical relations of the
precisifications and that of the sets of the real instances (in this world) may not match up.
However, the former do constrain the possibilities of the latter. This is shown in Table 2
and discussed in more detail in Section 5.4.
Table 1. The operations (columns) than can be performed between p1 and p2 and the result with respect to
the relations holding between them
Logic definitions
Operations
p1 ↔ p2 p2 → p1 p1 → p2 p1 → ¬p2 NP
Union p1 ∪ p2 p1, p2 p1 p2 p1 ∨ p2* p1 ∨ p2
Intersection p1 ∩ p2 p1, p2 p2 p1 ø p1 ∧ p2
Complement p2 \ p1 ø ø p2 ∧ ¬p1* p2 p1 ∧ ¬p2
Symmetric difference p1 ∆ p2 ø p1 ∧ ¬p2 p2 ∧ ¬p1 p1, p2 p1 ⊕ p2
5.2. Operations
In order to support both the analysis of the differences and variation among the existing
instantiations of the concepts of the ontology and also to facilitate the specification of
standpoints that comprise the appropriate subset of precisifications, we define four basic
operations between precisifications.
1. Union: p1 ∪ p2. All the instances that satisfy either p1 or p2 (or both). E.g. Both
p1 and p2 are considered admissible precisifications for a specific use of the
ontology by a certain agent.
2. Intersection: p1 ∩ p2 . All the instances that satisfy both p1 and p2. E.g. An agent
is interested on the intersection between their own interpretation p1 and a pre-
cisification in the ontology p2.
3. Complement: p2 \ p1. All instances that satisfy p2 but not p1. E.g. An agent finds
p1 conflicting with its interpretation and wants to prevent instances of p1 from
his query on p2.
4. Symmetric difference: p1 ∆ p2. All instances that satisfy either p1 or p2 but not
both. E.g. An agent is interested in exploring the borderline scenarios in which
p1 and p2 disagree.
Table 1 shows the analysis of these operations with respect to the relations holding
between p1 and p2, which allows for the simplification of the result in some scenarios
and shows the operation to be trivial or the empty set (ø) in others. In the table, two cases
are marked with a star (*), the union of two disjoint precisifications and the complement
of a precisification p1 subsumed in p2. Albeit legal, both operations are potentially prob-
lematic and the agent should be aware of the explicit inconsistencies between p1 and p2
in the former and the subsumption of p1 in p2 in the latter.
5.3. Applications in the Context of Interoperability and Knowledge Sharing
In the context of knowledge sharing, operations between precisifications are expected
to be used for two main purposes, namely concept negotiation and specification of the
standpoints. In practice, concept negotiation not only involves the analysis of the objec-
tive meaning and ontological commitments formalised on the different precisifications,
but also of the real world implications of such commitments. This analysis is possible
by querying the ontology with the previous operations, as the agent can gain insight on
which instances fall within the borderline scenarios, which instances comply with all the
desired precisifications and so on. In the case of GIS, this is enhanced because a spa-
Table 2. Relations between the logical relations among two definitions, p1 and p2 (columns), and the RCC5
spatial relations between the projections of the instances satisfying those definitions, s1 and s2 (rows).
Spatial Logic definitions
extension p1 ↔ p2 p2 → p1 p1 → p2 p1 → ¬p2 NP
The weakness of The weakness of
p1 with respect to p2 with respect to The only instances
Expected p2 does not man- p1 does not man- Impossible lay in the intersec-
ifest in any in- ifest in any in- tion of p1 and p2.
stance. stance.
The only instances
of p2 lay in the
Impossible Expected Impossible Impossible
intersection of p2
and p1.
The only instances
of p1 lay in the
Impossible Impossible Expected Impossible
intersection of p2
and p1.
Despite the def-
initions overlap-
ping, there are no
Impossible Impossible Impossible Expected
known instances
on the intersection
between them.
Impossible Impossible Impossible Impossible Expected
tial projection is available, thus providing powerful means for understanding the way
definitions perform in specific areas of interest.
Moreover, once the process of concept negotiation is complete for a particular use
of the ontology, operations can be used to support the formalization of the agent’s stand-
point s1. During further interactions of the agent with the ontology, queries will be as-
sociated with this standpoint. s1 acts by restricting the admissible precisifications of the
ontology to those which are consistent with s1 and enabling reasoning and information
retrieval within the subset.
5.4. Interpreting the Spatial Projections of Precisifications/Standpoints
In the case of geographical information, the spatial projection of the instances can be par-
ticularly relevant to complement the analysis of the relations that hold between precisi-
fications. One might expect that the possible relations holding between precisifications
(equivalence, subsumption, inverse subsumption, overlap and disjunction) would map
to the analogous RCC5 relations (equal, proper part, inverse proper part, partial overlap
and discrete) between the total spatial area covered by sets of instances satisfying each
precisification. However, that does not necessarily need to be the case. Instead, relations
between precisifications only restrict the space of possibilities but leave some variation
open.
(a) (b)
Figure 1. Example forest diagrams. Figure 1(a) shows four numbered forests with stricter and loser extensions.
Figure 1(b) shows the overlap with a different definition of forest
In Table 2 we show the possible relations holding in the different scenarios. While
the analogous to RCC5 is the expected relation to hold, other possibilities are allowed.
These may be symptomatic of different circumstances. Take, for example, the case where
the spatial projection of p1 is equal to that of p2. It may be the case that p1 and p2 are
equivalent. p1 could also be weaker than p2 by allowing some more scenarios, but they
never manifest in the available data about the state of the world. Even, it could be that
p1 and p2 describe forest in a logically different way (e.g. one uses tree proximity and
the other canopy cover) that is highly correlated, and therefore both map to the same
objects. In other cases it may be due to mere exemplar clustering6 . Finally, even when
the expected spatial relation holds between the projections, it is expected to be useful
for the agent to know how populated are the intersections or borderline scenarios of the
definitions under consideration.
6. Examples from Implementation Prototype
The diagrams in Figure 1 give some output examples from our prototype standpoint se-
mantics based software, which enables visualisation of forest data in accordance with
different standpoints. In Figure 1(a) we see forest extensions according to three different
precisifications in different shades of green. The darker green corresponds to a stricter
definition, which requires trees to be closer together to count as constituents of a forest.
None of these precisifications consider the shrubs (small brown discs) to be forest con-
stituents. In Figure 1(b) another precisification (demarcated by a black dashed line) is
overlayed over the map. According to this precisification the shrubs are counted as for-
est constituents, so the forest takes on a very different shape, overlapping the extensions
associated with the other precisifications.
6 In ordinary situations, objects that exhibit one property, will very often also exhibit another property and
vice versa, even though there is no necessary connection between the properties. The cause may be because of
patterns and regularities that are essentially contingent [6].
7. Conclusion
It is widely agreed that, while domain specific ontologies can be used within a commu-
nity of users for achieving a consensus about conceptualizing, structuring and sharing
domain knowledge [29], it is unrealistic to expect that a fixed interpretation could satisfy
the needs of different communities in real-world applications. In that scenario, seman-
tic heterogeneity challenges the successful interoperation of systems and agents within
decentralized environments. In this paper we have analysed the needs of the multidisci-
plinary forest community. The semantics of the key concepts of their ontology need to
be negotiated depending on the context of use, and systems should be semantically rich
to guarantee the sound reuse of information between different domains.
We present a novel approach, consisting on a framework based on ‘Standpoint Se-
mantics’, that makes explicit the semantic variability of the terms of an ontology. We
suggest that our framework can support agents with different interpretations and stand-
points on their interoperation with a common ontology. Our aim is to provide a descrip-
tion of such a theory and to outline the particular features that can support the conceptual
negotiation between agents.
Further work remains to be done to provide a fully operable standpoint semantics
ontology, so, in a sense, this paper is only a preliminary step. However, we expect to
open the possibility for a complementary approach to the research on semantic align-
ment in distributed systems. We consider that, in the current context, it is key to support
ontologies that can both bring together the views of interdisciplinary domains and that
are expressive enough to prevent reasoning and inference from what can be inconsistent
interpretations. Moreover, we believe that the explicit acknowledgement of the semantic
variability of the terms of the ontology is key for that purpose.
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