DOLCE in OWL: The Core Theory

Abstract

Foundational ontologies, like dolce (an ISO standard), are often implemented in applications via their formalisations in the OWL language. These OWL formalisations are approximations of the theory to cope with the limited expressivity of OWL. With this paper, we start presenting a core OWL2 module of dolce, and discuss how to extend it in diferent directions. After discussing earlier versions of dolce in first-order logic and in OWL, we present the architecture of our modular approach. We select a core fragment of dolce in OWL2 (termed “DOLCEbasicOWL”), which provides the main taxonomy and binary relations of the foundational ontology. Then, we discuss how to extend DOLCEbasicOWL with a module for expressing the -ary relations of dolce ( > 2). After this, we give a proof that this OWL2 version is compatible with the original version of dolce. Finally, we illustrate the functioning of our OWL2 rendering by means of an example. We conclude by discussing a number of other modules to cope with other core concepts and specific domains.

Keywords

• eol>Descriptive Ontology for Linguistic and Cognitive Engineering
• OWL version
• DOLCEbasicOWL
• OWL -ary relation
• Ontology modularisation

1. Introduction

Most foundational ontologies have been formalized in rich logical languages, such as quantified modal logic. While an expressive logical language enables the faithful expression of proponents’ ontological views and facilitates subtle analysis, the complexity of reasoning tasks often renders the practical application of such services infeasible. For this reason, computationally manageable versions of foundational ontologies have been proposed, in particular as fragments of first-order logic, i.e., Description Logics, and particularly in OWL2.

This paper focuses on the Descriptive Ontology for Linguistic and Cognitive Engineering (dolce) [ 1, 2 ]. dolce originated as a formal theory in first-order modal logic, specifically, in the Proceedings of the Joint Ontology Workshops (JOWO) - Episode X: The Tukker Zomer of Ontology, and satellite events co-located with the 14th International Conference on Formal Ontology in Information Systems (FOIS 2024), July 15-19, 2024, Enschede, The Netherlands. logic QS5. This version is commonly referred to as the ‘D18’ version, after the technical report (deliverable) where it was first presented [ 1 ]. Due to the richness of dolce, proving consistency and exhibiting a model of the theory is not easy. A modular proof of consistency was detailed in [ 3 ].1 To achieve that, a number of simplifications of the D18 version have been made, for instance the modal logic part and the axiom schemata of dolce have been removed.2 More recently, a novel version of dolce has been designed in Common Logic (also an ISO standard, ISO/IEC 24707) as required for inclusion in the Top-level ontologies standard ISO 21838.3 This novel version, termed “dolce Simple” is available online.4

The format of this version includes the rendering of dolce Simple in Common Logic (CLIF5). The theory does not use the additional features of Common Logic that extend first-order logic, it is indeed a first-order theory. Moreover, this version have been presented, beside in CLIF, in the usual input formats for theorem prover (tptp, Prover9). Therefore, throughout this paper we denote this theory by DOLCEsimpleFOL.

DOLCEsimpleFOL is based on Kutz and Mossakowski’s version [ 3 ], although a few further simplifications w.r.t D18 were required and a few axioms have been added to enhance the proximity to D18. The objective of DOLCEsimpleFOL is to enable standard model finders (such as Mace4) to be capable of returning at least a “small model” of dolce.6 Other foundational ontologies follow suit to facilitate the application of provers and model finders, such as BFO [ 4 ], TUPPER [ 5 ], and UFO [ 6 ]. For an overview and test of these implementations, see [ 7 ].

A requirement of this OWL2 version is the ‘compatibility’ with the (first-order logic) version submitted in CLIF. Compatibility here means that the translation into first-order logic of the axioms of the OWL version of dolce can be proved from the (first-order) CLIF version DOLCEsimpleFOL. That is, every model of DOLCEsimpleFOL is also a model of the OWL version. Although the OWL version is less specific, as expected, and allows for many more, possibly unintended, models, the models of the original ontology are preserved. This result was achieved for DOLCEsimpleFOL and a preliminary OWL2 version of dolce: the proof that the CLIF version entails the OWL2 version was done by means of Prover9 (after translating both CLIF and OWL into first-order logic) 7.

A number of OWL versions of dolce, inspired by D18, have been developed in the past. Notably, the first OWL version of dolce, i.e. the dolce lite version [ 8 ]; see [ 2 ] for a chronology of previous OWL versions of dolce. A preliminary OWL2 version of dolce Simple was also developed for the inclusion in ISO 21838 standard8.

In this paper, starting from the OWL2 version developed for the ISO 21838, we document our advancement in the project of developing an OWL2 version of dolce. The main motivation for 1For an implementation of this strategy, see also https://github.com/spechub/Hets-lib/tree/master/Ontology/Dolce 2A comprehensive documentation of the simplifications of this version w.r.t the D18 is available at https://github. com/spechub/Hets-lib/blob/master/Ontology/Dolce/DolceSimpl.dol 3https://www.iso.org/standard/78927.html 4http://www.loa.istc.cnr.it/index.php/dolce/. See also the repository COLORE, https://github.com/gruninger/colore/ tree/master/ontologies/dolce. This version has been expanded to discuss the alignments between foundational ontologies in the OntoCommons project, cf. https://zenodo.org/records/10894153. 5https://www.iso.org/standard/66249.html 6For the full list of simplifications w.r.t D18 see the documentation at http://www.loa.istc.cnr.it/index.php/dolce. 7See footnote 3. 8See http://www.loa.istc.cnr.it/index.php/dolce. the present novel proposal is driven by the intention to present dolce in OWL2 as a basic theory (as faithful as possible to the original dolce in the D18 and justified by the axioms of D18), that can be expanded for practical applications via a library of dolce modules, either subtheories or extensions, also in OWL2. For this reason, we will explore the conceptual expressivity of OWL2 to capture, as far as possible, the original spirit of the ontological analysis presented in the D18.

In this paper, we will introduce and discuss a core theory, here termed “DOLCEbasicOWL”, which includes the main taxonomy of dolce and axiomatises, as far as possible, the main classes and a rich number of binary relations of dolce. The use of this theory is illustrated on an example taken from the literature. We also discuss the modular approach and the strategy adopted to extend this core module. In particular, a module to handle the -ary relations ( > 2) of dolce, among which the temporalised relations (e.g. temporary parthood, constitution, paticipation, etc.) is planned. These implementations are available online.9

The paper is organised as follows. Section 2 presents the overall approach to develop the OWL version of dolce, and Section 3 illustrates the formalization in OWL2. The proposed ontology is tested by automatically proving its axioms from the axioms of DOLCEsimpleFOL in Section 4, and is exemplified via a use case in Section 5. Finally, Section 6 draws the conclusions.

2. Approach

Our goal is to develop an OWL2 version of dolce that is close to and justified by the original theory presented in D18 [ 1 ] and simplified in DOLCEsimple FOL. Specifically, we are working with a fragment of the Description Logic ℛℐ, a sub-logic of OWL2 [ 9 ]10.

It is well-established that the expressive power of ℛℐ does not allow for directly writing the first-order axioms (and theories) required by the D18 version of dolce. This is caused by two types of restrictions, which are imposed to guarantee the decidability of ℛℐ ontologies: a syntactic restriction on single formulas, which does not allow for writing, e.g., -ary predicates, for ≥ 3 and a structural restriction on theories, specifically on the role box, which demands regularity and simplicity, cf. [ 9 ]. Regularity demands only simple dependencies between roles in the role hierarchy and is a structural property of the role box.

Methodologies for approximating FOL-theories with ℛℐ have been developed for instance in [ 10 ] and [ 11 ]. The strategy in [ 10 ] involves checking a large number of candidates ℛℐ theories and assess which of them are “closer” to the original FOL-theory by experimenting on automatically generated models.

Here, our aim is not to find the “closest” ℛℐ version to the FOL-dolce. Instead, we will select the axioms or theorems from the D18 version that we wish to keep in OWL2, focusing on the practical use and understandability of such constraints and axioms.

An obvious constraint when approximating a FOL theory in OWL2 is that all description logic languages are limited to binary relations, so -ary relations ( > 2) cannot be directly represented as such. dolce extensively uses temporalised relations as a major efort has been 9https://github.com/appliedontolab/DOLCE. 10Protégé classifies the Description Logic Expressivity of DOLCEbasic OWL as the logic ℛℐℱ. In fact, we are using transitive roles (aka object properties), complex roles inclusions, inverse roles, functionality of roles. dedicated to axiomatise how endurants and perdurants behave across time. Those temporalised relations are all at least ternary relations. In addition, mereological operators (e.g., the mereological sum) are at least ternary relations. In the modular approach chosen, we firstly develop the basic core module (DOLCEbasicOWL) presented in this paper, which is limited to: ) the original binary relations of dolce, plus the ) the constant versions of the temporalised relations of dolce. For instance, the participation of an endurant to a perdurant at a time in dolce (PC, in D18), appears in DOLCEbasicOWL as the object property (i.e. binary) constantParticipantOf. Another module, termed dolce n-ary rel, not presented in this paper, will be dedicated to properly introduce and treat the -ary relations (for > 2) in OWL2. We shall follow the “reification” approach advocated by the W3C 11, inspired by the neo-Davidsonian approach to handling events and their arguments in natural language semantics. This implies the introduction of a new category of entities called “relation instances” (not included in DOLCEbasicOWL), to which each argument of the original relation will be related, by a distinct new binary relation. For example, the mereological sum12 between perdurants or abstracts is defined by a ternary relation sum(, , ) (indicating that the sum of and results in ). Mereological sums will be represented in dolce n-ary rel by the following assertions.

SumInstance(), sumAddendum1(, ), sumAddendum2(, ), sumResult(, ) The class SumInstance will be then a subclass of the relation instances. An important ontological question regards the nature of these relation instances: whether this new category ifts within the original dolce taxonomy, and if so, under which main category, and if not, how to handle it. An option is to view a relation instance as some sort of “state of the relation holding” aka “situation”13 or “state of afairs”, or “facts”. Hence, the question is whether, in dolce terms, they can be seen as perdurants or as abstracts (states and situations, which are in time, are perdurants in dolce which are disjoint with facts, which are out of time and thus abstracts in dolce). Considering them as perdurants is in line with the neo-Davidsonian approach to events, and seems quite natural for temporalised relations and perhaps for ternary relations between perdurants. However, it is not general enough, as it appears inappropriate for ternary relations between abstracts such as the mereological sum over spatial regions, which are intended to be out of time in dolce. Furthermore, a delicate aspect arises when considering the axiom of dolce which states that all perdurants have endurants that participate in them at some time. If we consider relation instances as perdurants, they too must adhere to that axiom, potentially leading to a regress. On the other hand, considering relation instances as abstracts again forces us to question the dolce axioms for mereology, on pain of a potential regression: if identifies the sum of and , then we have to introduce an identifier for the sum of and , then one for the sum of and , and so on.

We thus handle relation instances as mere technical additions to the ontology, unrelated with the original rationale of the taxonomy. One is forced to introduce them in OWL versions of dolce because of the limited expressivity of ℛℐ, not for genuine ontological reasons.

Several other approaches, with and without reification, to deal with temporalised relations in OWL have been discussed [ 12 ]. In particular, the “Temporally Qualified Continuants Pattern” 11https://www.w3.org/TR/swbp-n-aryRelations 12The binary operator + in the D18 can be equivalently encoded as a ternary relation, as usual. 13See, e.g., https://nemo-ufes.github.io/gufo/#situations approach considers that the temporal argument can be embedded in the other arguments by considering their relevant “phases”. Handling ternary temporalised relations directly as binary ones in OWL has the considerable advantage of enabling the expression of transitivity and other properties supporting reasoning, which is extremely limited with the standard W3C approach. Unfortunately, the Temporally Qualified Continuants Pattern approach cannot be generalised in OWL to non-temporalised ternary relations, such as the mereological sum between abstracts, nor to temporalised relations of arity above 3, such as the temporalised mereological sum between endurants. The adopted modular approach will allow for adding still other modules to extend DOLCEbasicOWL with core concepts or domain-level concepts.

3. OWL2 Formalization

We now turn to illustrate and motivate the main features of the core module DOLCEbasicOWL.

3.1. Class and Property Hierarchy

The taxonomy of the proposed DOLCEbasicOWL ontology is represented in Figure 1. There are a few diferences with respect to the dolce taxonomy shown in D18: Atom and ConstantAtom are not new categories, as they can be defined in dolce and are not disjoint with their siblings.14 14A definition of this categories is included in DOLCEsimple FOL, see https://github.com/appliedontolab/DOLCE/tree/ main/OWL/Proof.

The hierarchy of the object properties in DOLCEbasicOWL is represented in Figure 2. Notice the constant versions of the temporalised relations of dolce, some of them not defined in D18, like constantlyOverlaps or constantAtomicPartOf, although they are definable in dolce.

3.2. Focus on Endurants and Perdurants

Figure 3 shows the possible relations for classes Endurant and Physical Endurant in DOLCEbasicOWL, such as parthood (constantPartOf, constantProperPartOf), constitution (constantConstituentOf), presence (presentAt, temporallyLocatedAt), participation (constantParticipationOf), spatial location (constantlySpatiallyLocatedAt), and quality characterization (directQualityOf).

Figure 4 illustrates the possible relations for class Perdurant, including parthood (partOf, properPartOf,temporalPartOf), presence (presentAt, temporallyLocatedAt), participation (constantParticipationOf), spatial location (constantlySpatiallyLocatedAt), quality characterization (directQualityOf).

3.3. Focus on Time

dolce provides a rich representation of how entities behave through time, and this attention to time is present in this OWL2 rendering although in DOLCEbasicOWL we only have binary constant versions. Here we intend to highlight how some of those temporal aspects are encoded on DOLCEbasicOWL, what could be implemented, and what could not.

As sketched in Figure 4, a perdurant has temporal qualities (e.g. the duration of an event), among which a unique quality in the class TemporalLocation. The temporal location of a perdurant is related, through qualeOf, to the unique time interval which is the whole temporal extension of the perdurant. Time intervals are abstract entities in dolce, they are mereologically organised by the binary partOf relation. They can be atomic and non-convex, i.e., scattered through time (as generalised intervals). The perdurant is also directly related to the same time interval of its whole temporal extension through temporallyLocatedAt. Also endurants and qualities are temporally located at a time interval, their temporal extension.15 The relation presentAt relates perdurants, endurants and qualities to any time interval that is part of their whole temporal extension.

Although the expressivity of OWL2 doesn’t enable a proper characterization of mereological relations16 and despite the simplicity and the regularity constraints on properties in OWL2, we were able to guarantee a few facts.

Here, we opt to keep the transitivity of partOf and properPartOf and to drop the irreflexivity of properPartOf. We have also to drop the reflexivity of partOf because the reflexivity is implemented in Protégé globally, while partOf doesn’t range over the whole of owl:Thing, but only over perdurants and abstracts. To implement local reflexivity, with the use of the ∃. ℛℐ constructs, requires a simple property , which is unfortunately incompatible with transitivity. Antisymmetry is impossible to express. Moroever, partOf is a sub-property of overlaps, which is symmetric, but we can only partially enforce the characterisation of overlaps in terms of parthood. Similar observations hold regarding constant versions of temporalised mereological relations over endurants such as constantPartOf.

Moreover, that the temporal extension is the maximal time interval at which an entity is present is somehow captured, not directly by an axiom on presentAt, temporallyLocatedAt and partOf (enforcing the dissectivity of presentAt would cause irregularity), but by a similar axiom on overlaps. We can also enforce that a quality and its bearer share the same temporal extension. On the other hand, these expressivity limitations do not allow for enforcing the unicity of the temporal extensions, nor acceptable characterisations of other classes and object properties. For instance, temporalPartOf simply is a subproperty of partOf between perdurants, failing to grasp the fact that a temporal part of a perdurant is a “temporal slice” of it, i.e., a maximal part during some time interval.

Several constant versions of the temporalised relations defined in dolce, with a specific temporal pattern regarding the presence of their arguments, have been introduced. For instance, constantPartOf and constantConstituentOf are defined such that the part is present when the whole is present, and the substrate is present when the entity it constitutes is present (see section 4). When completing with constant versions of all temporalised relations, a decision has to be made on which argument has its temporal extension included in the other’s or what other pattern is suitable. For constantlyOverlaps, which is symmetric, the decision has to be compatible with constantPartOf which is a sub-property with its own temporal pattern. The option that both arguments of constantlyOverlaps share the same temporal extension is rejected as it forces to change the definition of constantPartOf. As seen in next section, 15The time intervals at which endurants, perdurants and qualities are temporally located are sometimes called the “temporal locations" of such entities. In order not to confuse them with the temporal qualities belonging to the TemporalLocation class, we will here stick to the term “temporal extension”. 16This fact is well-known, see [ 13 ]. an axiom enforcing that the temporal extensions of both arguments overlap is expressible in OWL2, but not supported by the reasoner Pellet in Protégé. We are therefore left with the characterization of constantlyOverlaps in terms of the arguments sharing a constant part, without being able to exclude a model in which the two arguments are temporally disjoint.

4. Proof

To establish the adequacy of our OWL version of dolce, we prove that the first-order logic version DOLCEsimpleFOL entails the axioms of DOLCEbasicOWL. To achieve that, our strategy is to translate DOLCEbasicOWL into first-order logic, then use Prover9 17 to automatically prove each axiom of DOLCEbasicOWL from DOLCEsimpleFOL. The translation from DOLCEbasicOWL into first-order logic was done automatically by means of the translation tool developed in [ 14 ].18 A minor technicality is that DOLCEsimpleFOL uses the original abbreviated D18 labels of classes and relations (e.g., ed for Endurant, p for partOf), while DOLCEbasicOWL employs fully spelled-out labels to comply with standard use. Thus, to perform the proof, we translated the alphabet of DOLCEbasicOWL into the alphabet of DOLCEsimpleFOL.

Prover9 is able to directly prove each axiom of DOLCEbasicOWL that does not involve the constant version of the temporalised relations of dolce (e.g. constantParticipantOf), which are novel to the DOLCEbasicOWL, as expected. To prove the axioms of DOLCEbasicOWL involving constant temporalised relations, we added their definitions to the theory of DOLCEsimple FOL. Notice that such relations are definable in dolce, since they always use relations and classes that have been already axiomatised by the theory (e.g. mereology, participation, or constitution). For instance, constant part of and constantly overlaps are captured by means of definitions of the following form (omitting outermost universal quantifications).

constantPartof(, ) ↔ (ed() ∧ ed() ∧ ∃pre(, ) ∧ ∀(pre(, ) → tp(, , ))) constantlyOverlaps(, ) ↔ (ed() ∧ ed() ∧ ∃(pre(, ) ∧ pre(, )) ∧ ∃(cp(, ) ∧ cp(, )) where ed, pre, tp, tpp are the class Endurant, the relation presentAt, the relations of temporary parthood and temporary proper parthood defined in DOLCEsimple FOL (respectively), and cp stands for constantPartOf.19

The definitions for constant atom, constant atomic part, and constant proper part follow the pattern of constantPartOf; those of constantlyOverlaps is motivated by the goal of proving symmetry and compatibility with constantPartOf. Notice that, in DOLCEsimpleFOL, we can also prove that the temporal extension of two constantly overlapping entities overlaps, however this fact cannot be enforced in OWL for the reasons at the end of Section 3.3.20 17https://www.cs.unm.edu/~mccune/prover9/ 18The Python package is available at https://github.com/gavel-tool/python-gavel-owl/blob/dev/README.rst 19Notice that the relation of constant parthood was already present in D18, cf. Axiom Dd25. 20Formula ∀∀′(∃∃(temporallyLocatedAt(, )∧cov(, )∧temporallyLocatedAt(, ′)) → ov(, ′))) is a theorem of DOLCEsimpleFOL and could be added to DOLCEbasicOWL, but it clashes with Pellet in Protégé (ver. 5.6.3), so we omit it.

The constant versions of participation, constitution, quale of, and spatial location follow a similar pattern. We present the definition of constantConstituentOf and we refer to the documentation for the other definitions.

constantConstituentOf(, ) ↔ (ped() ∧ ped()) ∨ (nped() ∧ nped()) ∨ (pd() ∧ pd()) ∧ ∃pre(, ) ∧ ∀(pre(, ) → k(, , ))

Here, ped corresponds to PhysicalEndurant, nped to NonPhysicalEndurant, pd to Perdurant, k is (time-dependent) constitution, defined in DOLCEsimple FOL.

The proofs, the documentation, and all the required files are available online 21. In particular, the repository contains: ) the version of DOLCEsimpleFOL in the format of Prover9/Mace4 and the proof of its consistency; ) the translation of DOLCEbasicOWL into first-order logic, in the format of Prover9, ) a report of the axioms of DOLCEbasicOWL proved from DOLCEsimpleFOL.

5. Use Case

This section outlines a use case focusing on composition and constitution, illustrating how DOLCEbasicOWL can be instantiated to demonstrate its efectiveness. The reference case, derived from Case n.1 in Borgo et al. [ 2 ], deals with the modeling of a physical object like a table. The table and its components are artefacts, i.e., intentionally produced products. For the sake of the example, it is assumed that a table is identified through time by its tabletop; also, the quantity of wood constituting the table changes if a leg is substituted. Accordingly, the existence of the table does not imply that it is made of the same matter throughout its whole life. The table undergoes three lifecycle phases:

P1 Construction of a wooden table (T) consisting of a table top (Ttop) and four legs (Leg1, Leg2, Leg3, Leg4) during time interval t0. The tabletop and legs are made of wood material (Wtop, W1, W2, W3, W4, respectively).

P2 One table leg (i.e. Leg4) is replaced by a new leg (i.e. Leg4new made of wood material

W4new) during time interval t1.

P3 The table is dismantled, resulting in its cessation of existence, while the wood remains intact during time interval t2.

Herein, we focus only on phase P1, making the assumption that the table will not change its composition in the future. This simplified use case is instantiated by module Case01basic22 importing DOLCEbasicOWL, thus representing only constant binary relations between instances. The instantiation of the use case can be further extended in the future taking full advantage of the modular approach presented in Sect.2 to represent the evolution of the table along all phases P1-P3; indeed, the ternary relations from dolce n-ary rel are needed to represent time-based relations. Table 1 lists the relevant namespace prefix bindings. All modules are available online.

The instances representing the use case belong to the following classes: 21https://github.com/appliedontolab/DOLCE/tree/main/OWL/Proof 22https://w3id.org/DOLCE/OWL/UC/Case01basic • Artefact class, defined in module Case01basic according to Borgo and Vieu [ 15 ], as a subclass of PhysicalObject. • Subclasses of Artefact (i.e., Table, TableTop, and TableLeg) and AmountOfMatter (i.e. Wood) specifically defined in module Case01basic for this use case.

Figure 5 shows the novel classes specializing DOLCEbasicOWL and the related instances that are defined in module Case01basic.

Three types of relations are needed to complete the instantiation of the use case: • Presence of artefacts and amount of matter during a time interval. • Parthood, applying to entities of the same category. This relation is needed to formally represent the components of the table.

• Constitution, which is needed to specify the material of the table components.

Presence is a binary relation defined in DOLCEbasic OWL (cf. presentAt in Figure 3). Parthood and constitution can be modeled as either constant or time-dependant relations. In the first case, a binary relation sufices and the related OWL2 object properties are introduced in DOLCEbasicOWL (cf. constantProperPartOf and constantConstituentOf in Figure 3).

Focusing on a specific leg of the table (i.e., Leg1), we can show how the relations between instances can be represented taking advantage of DOLCEbasicOWL (see Figure 3). A similar pattern applies to the other table components (i.e., c01:Ttop, c01:Leg2, c01:Leg3, c01:Leg4).

The use case instantiation of module Case01basic has been tested with the reasoner Pellet available for Protégé and no inconsistency was detected.

6. Conclusions and further work

We presented the core aspects of the OWL2 version of the dolce ontology, in particular, the DOLCEbasicOWL module. This provides the taxonomy of dolce, its main binary relations, and a formal representation of the axioms of dolce in the expressivity of OWL2. Diferently from other existing Semantic Web formal representations of dolce, DOLCEbasicOWL is a closer match with the original D18 version of the ontology; for instance, diferently from other versions like the one presented in [ 8 ], it does not include modeling elements that are not present in the D18.

As said, DOLCEbasicOWL is the first ‘basic’ module in a library of modules for the exploitation of dolce through the Semantic Web. The library will (at least) include the dolce n-ary rel module for the representation of predicates with arity higher than 2, for instance, to include time parameters. This will allow for the representation of phenomena concerning objects’ change through time, e.g., change in parts or material constitution, which play a fundamental role in multiple application contexts. In compliance with dolce-driven research, another module will comprise the representation of concepts and descriptions [ 16 ], which often find their place for representing (social) roles but also engineering technical specifications [ 17 ], among other entities. A further module will introduce the use of OWL2 data properties, especially for enriching the representation of qualities and qualia when the latter are characterized through numerical values [ 18 ]. Last but not least, current research aims at developing modules for specific application domains, including product design and manufacturing [ 17 ].

From an ontology design perspective, the development of the library of modules will take the advantage of existing Semantic Web resources like the W3C Time Ontology23 and SSN/SOSA,24 which we will attempt to (at least partially) integrate into the modules.

Acknowledgments

We thank colleagues and friends at the CNR-ISTC Laboratory for Applied Ontology, in particular Claudio Masolo, Roberta Ferrario, and Nicola Guarino, for contributions and discussions. Support for this research is given by PRIN PNRR SORTT (Prot. P2022H74YP), PRIN I-TROPHYTS (Prot. 20224TAETP), PRIN BRIO (Prot. 2020SSKZ7R), Italian PNRR MUR project PE0000013-FAIR, and ERC project C-FORS (GA 101054836). 23https://www.w3.org/TR/owl-time/. 24https://www.w3.org/TR/vocab-ssn/.

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