A Novel Approach to Ontological View-Based Semantic Mapping in

Decentralized Environments

Fateh Mohamed Ali Adhnouss

, Husam M. Ali El-Asfour and Kenneth McIsaac

Dept. of Electrical & Computer Engineering, University of Western, London, Canada

Keywords:

Ontological View, Extensional Semantics, Intensional Semantics, Semantic Integration.

Abstract:

Semantic integration and interoperability are vital for effective communication and data exchange in informa-

tion systems. This paper explores the signiﬁcance of shared referential semantics, ontological views (OVs),

and intensional semantics in achieving semantic integration. It addresses the challenges arising from diver-

gent OVs and emphasizes the role of accessibility relations in bridging gaps between different systems. The

paper presents theorems establishing relationships between accessibility relations, the overlap of non-logical

symbols, and the consistency and accessibility of OVs. It also examines mapping possibilities in decentral-

ized environments by considering scenarios with shared intended models, overlapping intended models, or no

intersection of intended models. The paper uses the healthcare domain as an illustrative example of applying

intensional semantics and semantic interoperability. To ensure efﬁcient semantic integration and interoper-

ability, systems must consider the shared meaning of the vocabulary, particularly non-logical symbols, along

with the underlying conceptualizations and intensional semantics.

1 INTRODUCTION

Ontologies represent a fundamental aspect of solu-

tions tailored towards achieving semantic integra-

tion(de Mello et al., 2022). They enable diverse

systems to comprehend and share information ef-

fectively. However, ontologies are conventionally

formed within limited environments. When multiple

system designers approach a single domain, they each

manifest a unique perspective corresponding to their

speciﬁc interests, which inevitably results in the de-

velopment of multiple models (Adhnouss et al., 2022;

Xue et al., 2012). Given that each perspective offers a

different view of the domain, there exists no singular

universally agreed-upon ontology. Instead, we see the

formation of unique, formally deﬁned OVs. Crucially,

explicit ontologies are often missing from informa-

tion systems, with inherent semantics typically incor-

porated within the information model (Wang et al.,

2009). This model reﬂects a particular conceptualiza-

tion view, thereby deﬁning an implicit Ov.

Current semantic integration strategies rooted in

extensional models are ill-suited to a decentralized

environment (Majki

c and Prasad, 2018; Ali and

McIsaac, 2020; Adhnouss et al., 2022) because they

https://orcid.org/0000-0003-4191-6894

fail to adequately address its ﬂuid nature, character-

ized by a set of entities and their evolving relation-

ships. Thus, the requirement arises for an encompass-

ing semantic integration model that accounts for the

ﬂuidity of a decentralized environment by capturing

the dynamic entity relations and shifts therein.

In Artiﬁcial Intelligence, OV pertains to an engi-

neering artifact, characterized by a distinctive vocab-

ulary depicting a particular reality, supplemented by

explicit assumptions about the intended interpretation

of the vocabulary. Each OV for any logical language

constitutes a set of carefully crafted axioms that faith-

fully mirror the language’s intended models at the in-

tensional semantic level. Therefore, OVs only indi-

rectly ’specify’ a conceptualization, approximating a

conceptualization when applied to a logical language,

assuming an intensional level exists where the lan-

guage’s intended models are encapsulated within the

OV’s models(Adhnouss et al., 2023).

Consequently, an OV is seen as a logical theory

expressing the intended meaning of a formal vocab-

ulary, with the intended models of a language using

such vocabulary in a way that is conﬁned by its inten-

sional semantic level. The OV indirectly denotes this

commitment (and the underlying conceptualization)

by closely mirroring these intended models.

Anchored in the fundamental principles of in-

Adhnouss, F., El-Asfour, H. and McIsaac, K.

A Novel Approach to Ontological View-Based Semantic Mapping in Decentralized Environments.

DOI: 10.5220/0012157600003598

In Proceedings of the 15th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2023) - Volume 2: KEOD, pages 155-163

ISBN: 978-989-758-671-2; ISSN: 2184-3228

155

tensional and extensional semantic levels delineated

in(Adhnouss et al., 2022), this paper narrows its focus

on semantic integration to contexts devoid of a com-

prehensive global perspective. This ongoing research

ambitiously endeavors to reveal the pivotal properties

that have their roots in the methodological structure

proposed in the aforementioned work. Such discov-

eries could potentially serve as structural pillars, en-

abling the establishment of integrative links amidst

varying OVs. While the focus of the previous con-

tributions has been on the notion of representation,

this paper takes a sharp turn towards integration - an

equally signiﬁcant facet- thereby interpreting seman-

tics through an innovative lens.

The remainder of this paper is structured as fol-

lows: In Section 2, we provide a comprehensive re-

view of relevant literature on semantic integration, ex-

ploring existing approaches, techniques, and models

proposed in the ﬁeld. Section 3 delves into the impor-

tance of shared referential semantics in semantic in-

tegration and discusses the concept of OVs. We then

explore the relationship between OV equivalence and

shared semantics in Section 4. In Section 5, we exam-

ine accessibility relations and their impact on the con-

sistency and overlap of non-logical symbols in OVs.

Section 6 and 7 focuses on the formal deﬁnitions and

mapping possibilities in decentralized environments,

discussing different scenarios and proposing an ap-

proach for achieving completeness and usability of

mapped OVs. In Section 8, we apply the concepts

of intensional semantics and semantic interoperability

in the healthcare domain. Finally, Section 9 concludes

the paper by summarizing the key ﬁndings and contri-

butions, highlighting the importance of shared under-

standing for semantic interoperability, and providing

guidance for achieving effective integration and inte-

gration itself in information systems.

2 LITERATURE REVIEW

The traditional database systems have faced ongoing

challenges due to semantic heterogeneity, which is

essentially a result of differences in the representa-

tion of real-world entities across various models de-

veloped independently (Xue et al., 2012). These vari-

ations in structure, terminology, and interpretation

have proved to be hurdles in the semantically coher-

ent interoperation of such models. Consequently, re-

searchers and developers have proposed numerous so-

lutions over the years (Adhnouss et al., 2022; Wang

et al., 2009). These solutions, however, largely fall

into two categories- structure-based and semantics-

based- with their effectiveness heavily dependent on

the presence of a pre-deﬁned schema or ontology.

In the realm of information integration, solutions

often resort to establishing semantic correspondences

or mappings between vocabularies originating from

distinct data sources. Various methods such as lin-

guistic term analysis (Melluso et al., 2022), mapping

to a common reference ontology (Cao et al., 2022),

and the utilization of heuristics to discern concept def-

inition patterns (Zhang et al., 2022), have been em-

ployed. These strategies, however, invariably call for

a comprehensive global knowledge representation or

some form of human intervention.

Concurrently, numerous studies have delved into

the different aspects of ontology, with early research

efforts primarily focusing on its deﬁnition and math-

ematical representation (Gruber, 1995; Guarino et al.,

2009; Wang et al., 2009). Ontology was hence con-

ceptualized as a meticulously constructed artifact,

employing a speciﬁc vocabulary to depict a selected

reality, bolstered by explicit assumptions regarding

the meanings of the vocabulary symbols.

Within this framework, the concept of ’intensional

semantics’—introduced by (Adhnouss et al., 2022;

Adhnouss et al., 2023)—emerges as a cornerstone.

This concept shapes the intrinsic meanings and the

internal content of the vocabulary symbols, thereby

turning ontology into a logical theory that unfolds

these intended meanings, expressing an intensional

semantic to a speciﬁc world view.

Despite this, it is crucial to highlight that funda-

mentally, ontology resides in ’extensional semantics.’

This aspect is embodied by the ontology’s ’intended

models,’ representing speciﬁc instances or scenar-

ios that the ontology aims to encapsulate (Adhnouss

et al., 2022).

Ontology thus evolves from being a mere reﬂec-

tion of reality to a sophisticated system of extensional

semantics, encapsulating a unique world interpreta-

tion. Further research has been carried out to inves-

tigate ontology classiﬁcation (Dhakal et al., 2022),

development of ontology languages (Chandrashekar

et al., 2023), construction (Du et al., 2022), and reuse

(Polenghi et al., 2022). Efforts have also been made to

explore methodologies for ontology integration (Cao

et al., 2022).

In more contained environments, ontologies are

typically agreed upon by consensus. However, this

consensus often breaks down in decentralized envi-

ronments due to their inherent characteristics. The

lack of a global ontology and the impracticality of

frequent human intervention in decentralized infor-

mation systems underline these systems’ unique at-

tributes. Existing solutions largely depend on a global

ontology, human intervention, or both, highlighting

KEOD 2023 - 15th International Conference on Knowledge Engineering and Ontology Development

156

the need to broaden inquiry in this area to cater to the

specialized requirements of decentralized systems.

Our investigation pivots around deﬁning and

mathematically portraying partial knowledge related

to a particular domain. After an extensive explo-

ration, we found that the OV deﬁnition proposed by

(Adhnouss et al., 2022) aligns seamlessly with our

objectives. This work offers a top-down formal model

as a theoretical framework where each possible world

presents unique views of the overarching conceptual-

ization, reﬂecting information system modeling.

This methodology underscores the importance of

semantics within decentralized environments where a

global view might be purely theoretical. It empha-

sizes the theoretical aspects of these notions, utilizing

epistemology as a conduit to convey intensional se-

mantics, which can be actualized into multiple OVs

(extensions), leading to extensional semantics.

Our research stands out by focusing on seman-

tic integration in the absence of a global view. We

aim to pinpoint shared axioms or pivotal properties of

OVs identiﬁed in the top-down approach that could

serve as foundational elements to bridge these possi-

ble worlds. Our work capitalizes on a detailed under-

standing and analysis of diverse OVs within the sys-

tem, referred to as ”Epistemology” (Adhnouss et al.,

2023). As a result, our focus shifts from representa-

tion to integration as we study semantics across differ-

ent views without a global viewpoint—a perspective

that provides a distinct and equally vital insight.

3 REFERENTIAL SEMANTICS IN

SEMANTIC INTEGRATION

Proceeding from our literature review, it becomes ap-

parent that shared referential semantics hold vital im-

portance in the realm of semantic integration. An

OV, as discussed earlier, doesn’t necessarily repre-

sent a single, objective reality. Instead, it portrays a

unique interpretation or perspective of a particular do-

main. Therefore, different designers or organizations

might conceive distinct OVs for the same domain, in-

ﬂuenced by differing assumptions, interpretations, or

objectives.

For instance, consider two information systems

designed for the same domain, but adopting unique

OVs. Each OV encapsulates a speciﬁc viewpoint on

the underlying concepts and relationships, reﬂecting

the distinct goals, assumptions, or interpretations of

the designers. Thus, within a particular business do-

main, each system’s semantics presents a unique on-

tological viewpoint, or an OV.

Semantics, in many domains, can be articulated

at various explicit and implicit levels within the do-

main knowledge, design, and the structure of the in-

formation model. This inherent complexity can make

seamless integration a daunting task, especially when

semantics are not immediately apparent or accessible.

Nevertheless, every information system harbors a

conceptualization of the observed (modeled) domain,

which can serve as a bedrock for semantic-based in-

tegration. When different systems have overlapping

intended models of the same domain, this shared un-

derstanding can be harnessed to facilitate integration,

ensuring consistency in data meaning and interpreta-

tion. This process is intrinsically tied to our explo-

ration of intensional and extensional semantics, en-

suring continuity and coherence in our research.

4 OV EQUIVALENCE AND

SEMIOTICS

Delving into the complex intersections of information

semantics and OVs, we must comprehend the signif-

icance of semantic equivalence between OVs. While

a shared vocabulary forms the bedrock of communi-

cation in an ontological scenario, understanding the

deeper interconnections between terms unlocks the

shared conceptualization that an OV encapsulates.

Semantic equivalence between OVs arises when

the ontologies delineate identical concepts and rela-

tionships within the domain. This implies that despite

differences in their symbolic or linguistic represen-

tations, semantic equivalence holds if the ontologies

revolve around the same subject or entity.

Nevertheless, it is crucial to distinguish between

logical and semantic equivalence. Logically equiva-

lent ontologies retain the same logical structure and

consistent truth values. However, differences in the

speciﬁc concepts and relationships they symbolize

can create scenarios where ontologies are logically

but not semantically equivalent.

To discern whether ontologies are semantically

equivalent, it is necessary to examine both the logi-

cal constructs and the unique concepts and relation-

ships they represent. If ontologies convey the same

meanings and relate to the same subject or entity, they

are semantically equivalent. Conversely, ontologies

that express dissimilar meanings or pertain to differ-

ent subjects or entities are not semantically equiva-

lent, irrespective of their logical equivalence.

To illustrate, consider two sets of formulas - OV 1

and OV 2, representing a patient treatment domain

and expressed using the formalism of ﬁrst-order logic

(FOL).

Given these axiom sets:

A Novel Approach to Ontological View-Based Semantic Mapping in Decentralized Environments

157

OV 1 :

• ∀x(patient(x) → human(x))

• ∀x(has-disease(x,y) → patient(x))

• ∀x(has-symptoms(x,y) ∧ has-disease(y,z) →

prescribed-treatment(x,z))

• ∀x(has-treatment(x,y) → patient(y))

• ∀x(patient(x)∧has-disease(x,y) ∧

has-treatment(y,z) → cured(x))

• patient(John)

• has-disease(John,Cancer)

• has-symptoms(John,Headache)

And another set:

OV 2 :

• ∀x(P1(x) → P3(x))

• ∀x(P4(x,y) → P1(x))

• ∀x(P5(x,y) ∧ P4(y,z) → P2(x,z))

• ∀x(P6(x,y) → P1(y))

• ∀x(P1(x)∧P4(x,y) ∧ P6(y,z) → P7(x))

• P1(A)

• P4(B,A)

• P5(A,B)

In the context of both OV 1 and OV 2, it’s evident that

the non-logical symbols they contain, though repre-

sented differently, refer to the same entities in the

patient treatment domain. This situation gives rise

to a deeper level of equivalence—semantic equiv-

alence—when non-logical symbols are interpreted

within the ontology.

A set of formulas is semantically equivalent if,

apart from demonstrating logical equivalence, they re-

fer to the same domain and convey identical mean-

ings for the non-logical symbols. These symbols em-

body speciﬁc concepts and relationships in the do-

main, hence their interpretation directly inﬂuences the

semantic correspondence.

In our case, despite differences in predicates and

individuals, the non-logical symbols in both OV 1

and OV 2 signify the same concepts and relationships.

Thus, even if the syntactic presentation differs, the

semantic content they encapsulate remains identical.

Therefore, OV 1 and OV 2 are semantically equivalent.

Understanding semantic equivalence is paramount

for assessing the alignment of different OVs, as it

captures the essence of meanings embodied by non-

logical symbols, transcending mere syntactic and log-

ical equivalence. This understanding is vital for en-

suring effective semantic integration, especially in en-

vironments where multiple OVs represent the same

domain in a decentralized information system.

5 ACCESSIBILITY RELATIONS

AND NON-LOGICAL SYMBOLS

IN OVs

In the previous discussion, we recognized the criti-

cal role of intensional and extensional semantics in

achieving semantic equivalence and successful inte-

gration. Now, we extend this exploration to discern

how accessibility relations in the context of different

OV can inﬂuence the consistency and overlap of non-

logical symbols. Understanding this relationship is

key for effective semantic integration in decentralized

systems.

Reﬂecting upon the insights presented in

(Adhnouss et al., 2023; Adhnouss et al., 2022), we

acknowledge that each possible world represents an

OV of the domain. The accessible relation denotes

that all possible worlds share some overlapping

conceptualizations, a feature that can be utilized for

fostering semantic integration and interoperability

between systems. Our approach involves establishing

a shared understanding of the domain by ﬁrst deﬁning

high-level concepts, relationships, and terminology.

This shared understanding can then be tailored and

specialized for different possible worlds, which may

have speciﬁc requirements or nuances.

Consequently, a multitude of ontological perspec-

tives are created, with the most general concepts po-

sitioned at the top, becoming increasingly speciﬁc as

we delve deeper.

As we traverse the intricate landscape of informa-

tion semantics in decentralized systems, it becomes

paramount to understand how accessibility relations

impact the underlying structures within these environ-

ments. This understanding paves the way for our ﬁrst

theorem, which explores the conditions under which

an accessible relation between two distinct worlds

suggests the consistency of non-logical symbols in

these worlds.

Theorem 1 (Consistency via Accessibility Relations).

Let W

= (E

,Σ

) and W

= (E

,Σ

) be two distinct

worlds, where E

is the set of entities and Σ

is the

set of non-logical symbols in W

, for i = 1,2. Let

R : E

× E

→ {0,1} be an accessible relation be-

tween W

and W

, where R(e

) = 1 if and only if

the entity e

in E

can be accessed or understood as

in E

. Furthermore, let f : E

→ E

be a bijective

mapping function from entities in E

to entities in E

such that for every entity e

in E

, f (e

) is a corre-

sponding entity e

in E

that preserves certain proper-

ties represented by the non-logical symbols. Formally,

we require that for every symbol s ∈ Σ

that repre-

sents a property of e

, there exists a symbol s

∈ Σ

that represents the same property of e

= f (e

), and

KEOD 2023 - 15th International Conference on Knowledge Engineering and Ontology Development

158

vice versa.

Then the theorem states: If for all e

∈ E

there ex-

ists an e

∈ E

such that R(e

) = 1 and f preserves

the properties of e

and e

as described, then Σ

and

are derived from the same set of non-logical sym-

bols in Θ, ensuring consistency between W

and W

Formally,

∀e

∈ E

,∃e

∈ E

R(e

) = 1 ∧ (∀s ∈ Σ

,∃s

∈ Σ

= f (s))

→ (Σ

∩ Σ

0).

Theorem 2 (Overlap via Accessibility Relations).

Let W

= (E

,Σ

) and W

= (E

,Σ

) be two distinct

worlds, where E

is the set of entities and Σ

is the

set of non-logical symbols in W

, for i = 1,2. De-

ﬁne R(W

) to be an accessible relation between

and W

. We say that: If R(W

) holds, then

there is a non-empty intersection between Σ

and Σ

signifying an overlap of non-logical symbols between

the two worlds. Formally,

R(W

) → (Σ

∩ Σ

0).

Theorem 3 (Accessibility Relations via Overlap).

Let W

= (E

,Σ

) and W

= (E

,Σ

) be two distinct

worlds, where E

is the set of entities and Σ

is the

set of non-logical symbols in W

, for i = 1,2. Deﬁne

R(W

) to be an accessible relation between W

and W

. We then assert: Given the same sets of non-

logical symbols Σ

and Σ

for worlds W

and W

, if

there is a non-empty intersection between Σ

and Σ

it implies an accessibility relation R(W

) between

the two worlds, meaning the entities and properties in

can be accessed or understood in W

. Formally,

(Σ

∩ Σ

0) → R(W

Each theorem reﬁnes our understanding of the re-

lationship between accessible relations and the over-

lap of non-logical symbols between different worlds.

The accessible relation among possible worlds reveals

the commonalities between them, a feature that can be

employed to bridge understanding gaps and facilitate

information exchange between different systems. As

each possible world shares aspects of the conceptual-

ization, this overlapping knowledge serves as a foun-

dation for semantic integration, aiding in achieving

interoperability between the OVs.

The three theorems presented above lay the

groundwork for understanding the dynamics of se-

mantic integration in decentralized systems. They

also further enrich our understanding of how semantic

equivalence operates within these OVs.

6 FORMAL DEFINITIONS

This section extends the foundational concepts pro-

vided by Adhnouss (2023), with an emphasis on un-

derstanding semantic integration within decentralized

information systems.

6.1 Conceptualization

The conceptualization (C) for a domain D is repre-

sented by the triple C =< D,W,ℜ >, where D rep-

resents the domain, W is a set of maximal exten-

sional structures within the domain, and ℜ stands for

a set of intensional structures over the domain space

< D,W >. Intensional relations ρ

: W → 2

are de-

ﬁned over this domain space, and the set of admissi-

ble extensions of ρ, E

= ρ(w)|w ∈ W , is also deﬁned

here.

The intended extensional structure of w as per

C is symbolized as SwC =< D,R

>, with R

ρ(w)|ρ ∈ ℜ, denoting the set of extensions (relative

to w) of the elements of ℜ. The set SC is deﬁned

as SwC|w ∈ W , representing all the intended world

structures of C.

The structure of the domain in its extensional form

is expressed as C

=< D, R >= SwC, which models

the structure of the Conceptualized Extension (CE).

6.2 Intensional Semantic Level

(Epistemology)

The intensional semantic level corresponds to the

concept of epistemology described in (Adhnouss

et al., 2023). We denote this as Θ =< C, ℑ >, where C

stands for the conceptualization of a unique perspec-

tive of the domain and ℑ is an intensional interpreta-

tion function that maps elements of D to the constant

symbols of V and elements of ℜ to predicate symbols

of V . This is expressed as ℑ : V → D ∪ ℜ.

To align Θ with a speciﬁc domain, an extensional

interpretation function I and a set of axioms are intro-

duced.

6.3 Extensional Semantic Level (OV)

Given the intensional semantic level Θ and an ex-

tensional interpretation I, a model M =< Sw,I > of

L (extensional semantic Φ) is considered compatible

with Θ if:

• The subset SwC is included in SC.

• For every c ∈ V , ℑ(c) is equal to I (c).

• For every predicate p ∈ V , if ℑ(p) = ρ then there

exists a world w ∈ W such that ρ(w) = I(p).

A Novel Approach to Ontological View-Based Semantic Mapping in Decentralized Environments

159

We denote the set of all extensions (models) of L that

are compatible with Θ as the set of intended exten-

sions I

(L) of L in accordance with Θ.

The extensional semantic level (Φ) of an (Ov) is a

speciﬁcation of C deﬁned by a language L, an exten-

sional interpretation I, and a set of axioms that align

the intensional interpretation with the intended exten-

sions I

(L).

In conclusion, we note that:

• The Extensional Semantic Level (Φ) commits to

a Conceptualization C if it has been designed to

represent C and approximate the reality D through

its extensions.

• A language L commits to Θ if it adheres to the

Conceptualization C such that Φ is consistent with

• L commits to Φ for a given Θ such that I

(L) is

incorporated in the models for Φ.

This rigorous framework lays the groundwork for se-

mantic integration discussions, promoting interoper-

ability within decentralized information systems.

7 OV MAPPING POSSIBILITIES

Understanding the relationship between conceptual-

ization, the intended model, and the OV is crucial

in a decentralized environment. This correlation is

illustrated in Figures 1,2 and 3. These illustrations

delineate three distinct scenarios that encapsulate the

potential for mapping between two independent OVs,

which are conceptualized as possible worlds (PW):

1. Uniﬁed Intended Model: This scenario features

two independent OVs reﬂecting an identical in-

tended model, signifying that they embody the

same possible world. Condition:

(|W | = 1) and (|D| = 1)

This unity of the intended model implies that

these OVs coexist within an isolated system,

where they share the exact same conceptualiza-

tion of the domain and illustrate a shared perspec-

tive. In such an environment, the overlap of these

OVs encapsulates the mutual understanding of the

domain, paving the way for an effective system-

to-system mapping. Deciphering the uniﬁed in-

tended model and its connotations is imperative

for realizing semantic integration and interoper-

ability.

2. Intersecting Intended Models: This scenario oc-

curs when two independent OVs have overlapping

Figure 1: Scenario (1).

intended models, implying they depict two unique

and independent possible worlds. Condition:

(|W | > 1 and |D| = 1) and W ∩ D 6=

This scenario is the primary interest of our re-

search. In this situation, several OVs intersect,

contributing to a single conceptualization of the

Domain. This situation emerges in a decentral-

ized environment, which is the central focus of

our investigation. Even though the OVs share cer-

tain elements through the intersection of their in-

tended models, they also portray diverse perspec-

tives of the same domain. The accessibility rela-

tions among the possible worlds are instrumental

in forming connections and facilitating mappings

between the overlapping sections of the intended

models. These relations ensure that the mapping

between the OVs is exhaustive and dependable,

enabling effective integration.

Figure 2: Scenario (2).

3. Distinct Intended Models: In the ﬁnal scenario,

two independent OVs exhibit no overlap in their

intended models, suggesting the absence of a

shared domain. Condition:

(|W | > 1 and |D| > 1)

This scenario transpires when there are multiple

PWs and multiple Domains. Each OV might in-

dependently map to a different Domain, with no

obligatory overlap or shared components. Conse-

quently, mapping one OV onto the other becomes

unfeasible in this scenario. Without an intersec-

tion of intended models, there is no mutual under-

standing or shared ground that can aid the inte-

gration process. This absence of overlap presents

signiﬁcant challenges for attaining semantic inte-

gration and interoperability between the two OVs.

KEOD 2023 - 15th International Conference on Knowledge Engineering and Ontology Development

160

Figure 3: Scenario (3).

These scenarios depict varying degrees of map-

ping possibilities between OVs in decentralized envi-

ronments, where each OV represents a possible world

(PW). The crux of our study lies within the ambit

of mapping possibilities (scenario 2), where two in-

dependent OVs intersect in their intended models.

We propose a method to tackle this scenario, aim-

ing to ensure the thoroughness and applicability of the

mapped OV within the target information systems.

Theorem 4. For a given conceptualization C

hD,W,ℑi, a language L with non-logical symbols V ,

and an intensional semantics Θ = hC

,ℑi, there ex-

ists a unique set of intended models of L according to

Θ.

Proof. Let’s assume the existence of two sets of in-

tended models I

(L)

and I

(L)

, which are different.

This would imply the existence of a model Φ compat-

ible with Θ, such that Φ ∈ I

(L)

but Φ /∈ I

(L)

However, by deﬁnition, if Φ ∈ I

(L)

, it is compati-

ble with Θ, and similarly, Φ should belong to I

(L)

Therefore, such a model Φ cannot exist, leading to the

conclusion that I

(L)

= I

(L)

Theorem 5. Consider two distinct intensional con-

ceptualizations C

in1

= hD

,ℜ

i and C

in2

,ℜ

i, a language L with non-logical symbols

V , and two intensional semantics Θ

= hC

in1

,ℑ

i and

= hC

in2

,ℑ

i, if the two sets of intended models for

in1

and C

in2

overlap, the overlapped part consists of

shared concepts and properties.

Proof. Let’s deﬁne the following: D

= {e

| 1 ≤ i ≤

n} D

= {e

2 j

| 1 ≤ j ≤ m} I

(L) = {Φ

| 1 ≤ i ≤ k}

(L) = {Φ

2 j

| 1 ≤ j ≤ l}

For each 1 ≤ i ≤ k, let Φ

= hCex

i, where

Cex

= hD

i. Similarly, for each 1 ≤ j ≤ l, let

2 j

= hCex

2 j

i, where Cex

2 j

= hD

2 j

If I

(L) ∩ I

(L) 6=

0, then the overlapped part

can be represented as hD

∩ D

∩ R

2 j

i for some

1 ≤ i ≤ k and 1 ≤ j ≤ l.

The non-empty intersection D

∩ D

implies the

presence of common concepts in the two conceptual-

izations. Furthermore, considering R

= {ρ(w) | w ∈

} and R

2 j

= {ρ(w) | w ∈ W

}, where ρ represents

the conceptual relation ”Has”, the non-empty inter-

section R

∩ R

2 j

suggests the existence of relations

{(e

) | e

∈ D

∧ e

∈ D

∧ e

∈ D

∧ e

∈ D

where each e

represents a shared property of the

shared concept e

These theorems establish a formal understanding

of the mappings between different conceptualizations

in a decentralized information system. Speciﬁcally,

Theorem 1 conﬁrms the uniqueness of the set of in-

tended models for a language L with respect to a spe-

ciﬁc intensional semantics Θ. Meanwhile, Theorem

2 delves into scenarios where the intended models of

two different conceptualizations overlap, demonstrat-

ing that the overlapped part is precisely deﬁned by

the shared concepts and properties in the conceptual-

izations.

These foundational theorems lay the groundwork

for developing a theoretical framework supporting

semantic interoperability in decentralized informa-

tion systems. Their implications extend far beyond

theoretical boundaries, enabling the identiﬁcation of

shared concepts and properties among diverse inde-

pendent OVs and facilitating data and information

mapping between disparate systems.

It is essential to acknowledge that while these the-

orems provide a solid foundation for semantic in-

teroperability, their practical implementation will re-

quire further research to develop effective algorithms

and protocols in real-world decentralized systems.

Addressing situations where the intended models of

independent OVs do not overlap or only partially

overlap will pose a signiﬁcant challenge, necessitat-

ing continuous investigation and exploration.

8 AN ILLUSTRATION OF

SEMANTIC INTEGRATION: A

HEALTHCARE SCENARIO

We consider a medical domain wherein we have enti-

ties represented by the set E:

• P represents the Patient

• N stands for Name

• M for Medical History

• C for Current Condition

• A for Address

• H for Healthcare Provider

Within this domain, we establish a binary relation r

such that r(P,X) signiﬁes that a Patient P has property

We opt for English as the language to model this

domain, deﬁning a vocabulary of non-logical symbols

V as follows:

A Novel Approach to Ontological View-Based Semantic Mapping in Decentralized Environments

161

• Patient

• Name

• MedicalHistory

• CurrentCondition

• Address

• HealthcareProvider

• has (as the predicate symbol)

All elements, except has, are constant symbols.

With the domain D = E and the single conceptual

relation ρ = r, our conceptual schema C

= hD,Ri

encompasses D and the set of relations R = {ρ}. In

this context, the possible world w posits that a patient

can possess the aforementioned properties.

We proceed to construct a model of the language,

denoted as Φ

= hC

i. Here, the relational struc-

ture R, which arises from the application of ρ to w,

yields R = {(P,N),(P,M),(P,C), (P,A),(P,H)}.

Let’s assume that I

is an interpretation function

assigning elements of R to predicate symbols in V .

We deﬁne I

(has) = {(P,N), (P,M),(P,C)}. This def-

inition implies that our model prioritizes the clinical

aspects of a patient.

Similarly, we can establish another model

= hC

i, where I

is deﬁned as I

(has) =

{(P,N),(P,A),(P,H)}. This model underscores the

logistical and administrative aspects of patient care.

Assuming that Φ

and Φ

adhere to intensional

semantics Θ, they are the intended models of the lan-

guage L, given Θ. Hence, I

(L) = {Φ

,Φ

In this instance, we can observe that if two infor-

mation systems stick to identical conceptualizations

and use the same vocabulary, they can achieve mutual

agreement as the vocabulary symbols are consistently

interpreted.

Let’s consider two distinct intensional conceptu-

alizations C

in1

and C

in2

• C

in1

= hD

,ℜ

i, where:

– D

= {P,N,M,C},

– W

corresponds to ”Patient has property Name,

Medical History, and Current Condition”,

– W

= {W

– ℜ

= {r}.

• C

in2

= hD

,ℜ

i, where:

– D

= {P,N,A, H},

– W

corresponds to ”Patient has property Name,

Address, and Healthcare Provider”,

– W

= {W

– ℜ

= {r}.

Given the same language L and vocabulary V , we

construct intensional semantics Θ

= hC

in1

,ℑ

i and

= hC

in2

,ℑ

i, where:

• ℑ

(Patient) = P, ℑ

(Name) = N,

ℑ

(MedicalHistory) = M,

ℑ

(CurrentCondition) = C,

ℑ

(has) = r.

• ℑ

(Patient) = P,

ℑ

(Name) = N,

ℑ

(Address) = A,

ℑ

(HealthcareProvider) = H,

ℑ

(has) = r.

We then deﬁne models Φ

= hC

ex1

i and Φ

ex2

i, corresponding to these intensional seman-

tics. When we examine I

(L) ∩ I

(L), we notice a

convergence on the concept of Patient and its property

Name.

In such a scenario, when two information systems

commit to different conceptualizations but employ the

same vocabulary, partial agreement can be achieved.

Symbols related to shared concepts and properties are

consistently interpreted. In contrast, symbols associ-

ated with distinct concepts and properties might in-

duce misunderstandings and conﬂicts.

This discussion illustrates that semantic interoper-

ability between two information systems hinges not

only on syntactic compatibility (i.e., the vocabulary

used) but also on semantic congruity (i.e., the in-

tended models of the language per the intensional se-

mantics).

Therefore, to ensure efﬁcient semantic integration

and semantic interoperability, systems must consider

both the shared meaning of the vocabulary, speciﬁ-

cally non-logical symbols, and the underlying con-

ceptualizations and intensional semantics. A common

understanding of the domain’s concepts and relations

is essential to achieve effective interoperability.

9 CONCLUSIONS

In this paper, we have embarked on an exploration

of semantic integration within decentralized systems,

with a particular focus on OVs and their seman-

tics. We highlighted the importance of semantics, and

more speciﬁcally, referential semantics, in achieving

semantic integration in the absence of a global view.

The concept of semantic equivalence between OVs,

both at the syntactic and the semantic level, was dis-

cussed in detail, emphasizing its signiﬁcance in the

alignment of different OVs.

We also proposed three theorems that examine

the relationship between accessibility relations and

KEOD 2023 - 15th International Conference on Knowledge Engineering and Ontology Development

162

the overlap of non-logical symbols between different

worlds. These theorems offer a novel perspective on

semantic integration, revealing the potential of acces-

sibility relations and overlapping non-logical symbols

as critical factors in achieving semantic consistency

and integration.

Despite the insights this paper presents, several

areas of study demand future research. In particu-

lar, our approach could be extended and enriched by

further exploring the roles of axioms and their se-

mantics in the OVs. As axioms are often the source

of intensional semantics, understanding their function

could offer a deeper insight into semantic integration.

Moreover, the exploration of further ways to achieve

semantic integration, such as the development of on-

tology matching techniques or the use of machine

learning algorithms, could also enhance this work.

Finally, a critical area for future investigation is

the application of our theoretical framework to real-

world scenarios. Practical implementations in diverse

ﬁelds such as healthcare, ﬁnance, and e-commerce

could serve to validate our approach, providing essen-

tial feedback to reﬁne our understanding of semantic

integration within decentralized systems. This is an

area we are currently investigating, and we hope our

ﬁndings will stimulate further research and discussion

in this domain.

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