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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>A Behaviouristic Approach to Representing Processes and Procedures in the OASIS 2 Ontology</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Giampaolo Bella</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Gianpietro Castiglione</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Daniele Francesco Santamaria</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Mathematics and Computer Science, University of Catania</institution>
          ,
          <addr-line>Viale Andrea Doria 6 - 95125 - Catania</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Semantic Web</institution>
          ,
          <addr-line>Ontology, OWL, Agent, Process, Procedure, Event, Process, Procedure</addr-line>
        </aff>
      </contrib-group>
      <abstract>
        <p>Foundational ontologies devoted to the efective representation of processes and procedures are not widely investigated at present, thereby limiting the practical adoption of semantic approaches in real scenarios where the precise instructions to follow must be considered. Also, the representation ought to include how agents should carry out the actions associated with the process, whether or not agents are able to perform those actions, the possible roles played as well as the related events. The OASIS 2 ontology [1, 2] provides an established model to capture agents and their interactions but lacks means for representing processes and procedures carried out by agents. This motivates the research presented in this article, which delivers an extension of the OASIS 2 ontology to combine the capabilities for representing agents and their behaviours with the full conceptualization of processes and procedures. The overarching goal is to deliver a foundational OWL ontology that deals with agent planning, reaching a balance between generality and applicability, which is known to be an open challenge.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>The notions of process and procedure are broadly known in the literature, even outside the
computer science field, although they bear subtle diferences. According to ISO 9001-2015
definitions, a process is a set of correlated or interactive activities that transform inputs into
outputs describing the specified way of carrying out an activity , whereas a procedure describes
how to carry out all or part of a process. Hence, we can argue that a process may be composed of
many procedures.</p>
      <p>
        Representing processes and procedures through foundational Web Ontology Language (OWL)
ontologies is necessary both for easing the exchange of process descriptions among systems and
to provide a machine-understandable interpretation of the related activities. One of the main
benefits of using Semantic Web technologies in such a context is the reasoning capability that
permits the inference of new facts from existing data and the verification of the knowledge base.
For example, in the context of operating systems, race conditions [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ] could lead to problems
related to the lock of resources by concurrent processes. A formalization of the processes,
procedures and agents together with semantic reasoning could reduce the ambiguity that may
occur when agents attempt to perform more operations at the same time.
      </p>
      <p>
        Defining an ontological architecture for processes and procedures aims at improving so-called
“automated planning and acting” [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. One of the most remarkable attempts to standardize the
planning problem is the PDDL (Planning Domain Definition Language) [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], which separates
the planning problem into a) domain description and b) problem description. For instance,
the PDDL in its current version introduces derived predicates for dependency modelling of
properties between objects. Therefore, processes and procedures benefit from the adoption of
ontological representations because ontologies can fully address both planning sub-problems.
      </p>
      <p>Although many ontological approaches are available in the literature, they sufer from the
lack of a complete and general approach to efectively represent processes and procedures,
especially one that a) combines the representation of processes and procedures with agents and
their commitments, b) models the events generated during the executions of processes and c)
accounts for the roles that are played by the committer agents.</p>
      <p>
        The current paper is motivated by the delivery of such a model. We start by considering the
ontological foundations for the domain of multi-agent systems. Specifically, we take into account
OASIS 2 [
        <xref ref-type="bibr" rid="ref1 ref2">1, 2</xref>
        ], a foundational OWL 2 ontology that leverages the behaviouristic approach derived
from the Theory of Agents and the related mentalistic notions. The behaviouristic approach is an
efective way of semantically describing agents by characterizing their capabilities. Agents are
enabled to report the set of activities that they can perform, the types of data required to execute
those activities as well as the expected outputs, through the description of their behaviours.
Agents’ implementation details are abstracted away to make the discovery of agents transparent,
automatic, and independent of the underlying technical infrastructure. In consequence, agent
commitments are clearly described, and the entire evolution of its environment is unambiguously
represented, searchable, and accessible: agents may join a collaborative environment in a
plugand-play fashion, as there is no more need for third-party interventions.
      </p>
      <p>Our work rests on the observation that OASIS 2 has lacked a specific characterization of
processes and procedures so far, even though it models so-called plans, which are ways of
depicting a sequence of (planned) actions to be tackled once. Therefore, plans cannot be applied
again once they are performed by agents. In this paper, we extend OASIS 2 to deal with general
specifications of processes and procedures that can be consumed by agents, including events and
the played role, that can be practically leveraged in real scenarios such as the one concerning
race conditions.</p>
      <p>The paper is organized as follows. Section 2 presents the related work through a comparison
with the OASIS 2 approach; Section 3 introduces the model of OASIS 2 devoted to the
representation of agents and their behaviours. Section 4 presents the novel extension of OASIS 2 that
deals with the notions of processes and procedures. Section 5 closes the paper with some hints
for future outcomes.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <p>
        In DOLCE [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ], the concepts of processes and events are presented as special types of perdurants,
whereas functions and roles are formalized in some extensions of the ontology [
        <xref ref-type="bibr" rid="ref7 ref8">7, 8</xref>
        ]. Aware of
the general definitions provided by DOLCE, OASIS 2 focuses on the behaviouristic approach
which is leveraged to provide agents with novel means for representing complex planning and
related actions, dealing also with events. Specifically, roles are conceived by OASIS 2 as ways of
enabling agents with additional behavioural capabilities, whereas events are represented to be
aligned with the definition of agent behaviours. From this point of view, OASIS 2 introduces a
diferent conceiving of events and roles since it describes agents in terms of their capabilities. A
full mapping of OASIS 2 in DOLCE is feasible and one of our planned future works.
      </p>
      <p>
        Wang et al. introduce a model for processes related to water quality monitoring [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. The model
is strictly focused on the description of observational processes concerning water pollution
monitoring, thus being limited to general applicability outside of the domain.
      </p>
      <p>
        Within CIDOC-CRM [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ], there is a work-in-progress extension called CRMact [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ] that
defines the classes and properties for planning future activities and events. However, CRMact
is mainly focused on cultural heritage and documentation records and hence is not generally
applicable.
      </p>
      <p>
        Concerning business processes, it is worth mentioning several works. Thomas et al. propose
an ontological approach for representing business processes together with a system architecture
prototype, exploiting the proposed model [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ]. Greco et al. use ontologies as facilities within
a framework for assisting designers in the realization and analysis of complex processes [13].
Corea et al. present an approach to verify whether a business process is compliant with given
business rules combining logic programming and ontologies [14], while Calvanese et al. propose
an approach for using Ontology-Based Data Access (OBDA) to govern data-aware processes,
and in particular, those executed over a relational database that issue calls to external services to
acquire new information and update data [15]. Finally, a comparison among ontologies related
to business processes for task monitoring, measurements and evaluation strategies, and for
modelling process information was built [16], [17], [18].
      </p>
      <p>However, the downside of limiting ontological models to business processes lies in the
absence of relationships between agents and their commitments that instead represent the core
of agent-oriented representation. That implies the inability of finding agents/services with
specific capabilities, invoking them, and enabling their interoperability. Notably, the benefits
of process-oriented representations, such as the facilitation mechanisms for the search and
selection of process models, are also ofered by the agent-oriented ones as long as they are
suficiently general although flexible.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Preliminaries on OASIS 2</title>
      <p>The first version of OASIS [19] is a foundational ontology that leverages the behaviouristic
approach to characterize agents in terms of the actions they are able to perform, including
purposes, goals, responsibilities, information about the world they observe and maintain, and
their internal and external interactions. It models the executions and assignments of tasks,
restrictions and constraints used to establish agent responsibilities and authorizations.</p>
      <p>In the recent past, OASIS has been extended and applied to deal with so-called Ontological
Smart Contracts [20] and with the ontological models for smart contracts on the blockchain [21].
OASIS is also part of the POC4COMMERCE project [22], funded by the NGI-ONTOCHAIN
consortium [23].</p>
      <p>
        The last version of OASIS is OASIS 2 [
        <xref ref-type="bibr" rid="ref1">24, 1</xref>
        ]1, which extends OASIS with some new features,
such as the entrustment of agents, and reshapes the model adopted for the representation of
agents and their commitments.
      </p>
      <p>Inspired by the Tropos methodology [25] which devises from Agent Oriented Programming
(AOP), OASIS 2 represents agents through three essential and publicly shared mental states,
namely (expected) behaviours, goals and tasks. Behaviours represent the mental state of the
agent associated with its ability to modify its environment or, in general, act or do something.
Goals describe mental attitudes representing preferred progressions of a particular system that
the agent has chosen to put efort into bringing about [ 26]. Tasks depict how to carry on such
progressions and describe atomic operations that agents perform.</p>
      <p>Agents and their interactions are represented by carrying out three main steps, namely: a)
an optional step that consists of modelling descriptions of general abstract behaviours, called
templates, conceptual characterization of behaviours from which concrete agent behaviours are
drawn; b) modelling concrete agent behaviours, possibly, drawn by agent templates; c) modelling
actions and associating them with the corresponding behaviours. The first step, not mandatory,
consists in defining the agent’s behaviour template, namely a higher-level description of the
behaviour of abstract agents that can be leveraged to define concrete behaviours of real agents;
for example, a template is designed to describe the abstract behaviour consisting in obtaining
and releasing locks on resources. Additionally, templates are useful to guide developers in the
definition of the behaviours of their specific agents. To describe abstract agent’s capabilities
to perform actions, an agent template comprises three main elements, namely behaviour, goal
and task. The latter constitutes the most simple (atomic) operations that agents are able to
actually perform including, possibly, input and output parameters required to accomplish
them. The second step consists of representing concrete agent behaviours either by relying
on a template or by defining it from scratch. In both cases, concrete behaviours are modelled
analogously to those of templates, where the models of outstanding features are replaced with
actual characteristics. Behaviours drawn by shared templates are associated with them in order
to depict the behaviour inheritance relationship. In the last step, actions performed by agents
are described as direct consequences of some behaviours and are associated with the behaviours
of the agent that performed them. To describe such an association, OASIS 2 introduces plan
executions. Plan executions describe the actions performed by an agent, associating them
with one of its behaviours. Associations are carried out by connecting the description of the
performed action to the behaviour from which the action has been drawn: actions are hence
described by suitable graphs that retrace the model of the agent’s behaviour.</p>
      <p>Plans can be additionally either submitted to agents as requests for performing some actions
or they can be assigned by specific agents called entruster agents.</p>
      <p>
        In OASIS 2, agent templates are defined according to the UML class diagram in Fig. 1. To
consider how both abstract and concrete agents perform actions, the description of agents
comprises three main elements, namely behaviour, goal, and task. Agent tasks, in their turn,
describe atomic operations that agents perform, including possibly input and output parameters
required to accomplish them. Those elements in OASIS 2 are introduced by way of the following
1The OASIS 2 ontology can be reached at [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]
refersAsNewTo
      </p>
      <p>or
refersExactlyTo (1,1) TaskOperatorArgument and</p>
      <p>TemplateThing
refersAsNewTo</p>
      <p>or
refersExactlyTo
(1,1)</p>
      <p>TaskInputParameter and</p>
      <p>TemplateThing
(1,1) TaskObject and</p>
      <p>TemplateThing
(1,1)
hasTask</p>
      <p>Operator
(1,1)
hasTaskObject
(0,1)</p>
      <p>hasTaskOperatorArgument
(0,1)
hasTaskInputParameter
Agent and
TemplateThing</p>
      <p>owl:Thing
(0,*) (0,*) (0,*)
(0,*)
• Agent: This class comprises all the individuals representing agents. Instances of such a
class are connected with one or more instances of the class Behaviour using the OWL
object-property hasBehaviour.
• Behaviour: Behaviours can be seen as collectors comprising all the goals that an agent
may achieve. Instances of Behaviour are connected with one or more instances of the
class GoalDescription by means of the object-property consistsOfGoalDescription.
• GoalDescription: Goals represent containers embedding all the tasks that the agent can
achieve. Instances of GoalDescription comprised by a behaviour may also satisfy
dependency relationships introduced by the object-property dependsOn. Goals are connected
with the tasks that form them and are represented by instances of the class TaskDescription
through the object-property consistsOf TaskDescription.
• TaskDescription: This class describes atomic operations that agents perform. Atomic
operations are the most simple actions that agents are able to execute and, hence, they
represent what agents can do within their environment. Atomic operations may depend
on other atomic operations when the object-property dependsOn is specified. Atomic
operations whose dependencies are not explicitly expressed are intended to be performed
in any order.</p>
      <p>The core of agent behaviour revolves around the description of atomic operations represented
by instances of the class TaskDescription that characterizes the mental state corresponding to
commitments. In their turn, instances of the class TaskDescription are related to the following
ifve elements that identify the operation:
• An instance of the class TaskOperator, characterizing the mental state corresponding to
the action to be performed. Instances of TaskOperator are connected either by means
of the object-property refersExactlyTo or refersAsNewTo to instances of the class Action.
The latter class describes physical actions represented by means of entity names in the
form of infinite verbs (e.g., produce, sell). Specifically, the object-property refersExactlyTo
is used to connect the task operator with a precise action having a specific IRI, whereas
refersAsNewTo is used to connect a task operator with an entity representing an action of
which only a general abstract description is given (for example, an action for which only
the type is known).</p>
      <p>In the latter case, the entity representing the action is also defined as an instance of
the TemplateThing: such instances are used to define entities that represent templates
for the referred element and that describe the characteristics that such element should
satisfy. TemplateThing is the class used to characterize all the individuals involved in the
definition of behaviour templates and to distinguish them from the entities representing
concrete behaviours, plans or actions, thus eliminating the need of having separated
models for those aspects.</p>
      <p>In order to specify the classes of which the entity must be an instance, it is eventually
possible to connect such entity by means of the object-property refersAsInstanceOf with
the individual instances of the desired classes.
• Possibly, an instance of the class TaskOperatorArgument, connected using the
objectproperty hasTaskOperatorArgument and representing additional specifications or
subordinate characteristics of task operators (e.g., on, of , left, right). Instances of
TaskOperatorArgument are referred to the operator argument by using either the object-property
refersAsNewTo or refersExactlyTo.
• An instance of the class TaskObject, connected by means of the object-property
hasTaskObject and representing the template of the object recipient of the action performed
by the agent (e.g., price). Instances of TaskObject are referred to the action recipient by
specifying either the object-property refersAsNewTo or refersExactlyTo.
• Input parameters and output parameters are introduced by instances of the classes
TaskInputParameter and TaskOutputParameter, respectively. Instances of TaskDescription
are related to instances of the classes TaskInputParameter and TaskOutputParameter by
means of the object-properties hasTaskInputParameter and hasTaskOutputParameter,
respectively. Instances of TaskInputParameter and of TaskOutputParameter are referred to
the parameter by specifying either the object-property refersAsNewTo or refersExactlyTo.
Moreover, the classes TaskInputParameter and TaskOutputParameter are also subclasses
of TaskParameter.</p>
      <p>Finally, in the case of agent behaviour templates, instances of Agent, Behaviour,
GoalDescription, TaskDescription, TaskOperator, TaskOperatorArgument, TaskObject TaskInputParameter, and
TaskOutputParameter are also instances of TemplateThing.</p>
      <p>Fig. 2 illustrates the case study mentioned above where a lock on a resource can be obtained
and released by agents. Specifically, Fig. 2 presents a template describing an abstract agent
that is able to request a lock on a resource. The agent template comprises a single behaviour,
Agent and TemplateThing
consumer_agent_template
hasBehavior</p>
      <p>Behavior and TemplateThing
request_lock_behavior
_template
constituted by a single goal that in its turn comprises a single task. The task, which represents
the ability to request a lock, provides four elements:
• request_lock_task_operator, representing the mental state associated with the behaviour’s
action (the task operator), which in its turn is associated with the individual request, the
latter describing the capability of requesting something.
• request_lock_task_operator_argument, introducing an additional feature (the operator
argument) associated with the action and represented by the individual lock. The argument
describes the fact that the request action is referred to a lock. Task operator and its
argument describe together the capability of requesting a lock;
• request_lock_task_object_template, representing the recipient of the operation, which is
related to an instance of the class Lock by means of the object-property refersAsNewTo.
Such an instance comprises all the features that the recipient of the adopting action should
own: the concrete actions implementing the behaviour template for requesting a lock are
supposed to efectively request a lock with the desired features;
• request_lock_task_output_template, representing the input of the operation, namely a
resource on which the lock is requested.</p>
      <p>In the second step, concrete agent behaviours are defined either by instantiating one or more
templates or from scratch. In OASIS 2, the modelling pattern of concrete behaviours has a
structure analogous to one of the behaviour templates, illustrated above, with the diference
that individuals used to define a concrete behaviour, instead of being instances of the class
TemplateThing, are instances of the class BehaviourThing. The latter class is devoted to describe
all the mental states associated with concrete behaviours of real agents that induce actions.</p>
      <p>Concrete behaviours may be connected with the template they are drawn from. In order
to describe the fact that concrete agents inherit their behaviours from a commonly shared
template, the instances related to the concrete behaviours are connected with the instances
of the template through the sub-properties of the object-property overloads as follows. The
association is carried out by connecting the instances of the classes:
• Behaviour, by means of overloadsBehaviour;
• GoalDescription, by means of overloadsGoalDescription;
• TaskDescription, by means of overloadsTaskDescription;
• TaskObject, by means of overloadsTaskObject;
• TaskOperator, by means of overloadsTaskOperator;
• TaskInputParameter, by means of overloadsTaskInputParameter;
• TaskOutputParameter, by means of the object-property overloadsTaskOutputParameter.</p>
      <p>As the last step, agent commitments devised from behaviours are introduced to describe agent
actions. In OASIS 2, commitments are represented by adopting the same pattern presented for
abstract behaviours with the diference that instances of the class TemplateThing are instead
modelled as instances of the class ExecutionThing and the agent responsible for the execution of
the action is related with the plan representing the commitment by means of the object-property
performsPlanExecution, subproperty of performs. The class ExecutionThing is introduced to
characterize all the entities involved in the definition of concrete and already performed actions
and to distinguish them from the ones introduced for templates, behaviours and plans.</p>
      <p>In order to relate agent commitments with the behaviour from which they are drawn,
subproperties of the object-property drawnBy are introduced. Specifically, planExecutionDrawnBy
connects the instance of GoalDescription of the agent action to its analogue of agent behaviour;
much in the same way, goalExecutionDrawnBy connects the instance of the class GoalDescription
of the commitment with its analogue, while taskExecutionDrawnBy, taskObjectDrawnBy,
taskOperatorDrawnBy, taskInputParameterDrawnBy, and taskOutputParameterDrawnBy are introduced
for TaskDescription, TaskObject, TaskOperator, TaskInputParameter, and TaskOutputParameter,
respectively.</p>
      <p>Usually, agents proposing plans identify the behaviours responsible for their realization
beforehand, in such a way as to completely describe and trace how agent intentions are
realized. In this case, the entities representing the submitted plan are related to the entities
describing the responsible behaviour by means of suitable subproperties of the object-property
submittedTo, relating instances of PlanningThing with instances of BehaviourThing as follows:
a) planDescriptionSubmittedTo, for instances of Behaviour; b) goalDescriptionSubmittedTo, for
instances of GoalDescription; c) taskDescriptionSubmittedTo, for instances of TaskDescription; d)
taskObjectSubmittedTo, for instances of TaskObject; e) taskOperatorSubmittedTo, for instances
of TaskOperator; f) taskInputParameterSubmittedTo, for instances of TaskInputParameter; g)
taskOutputParameterSubmittedTo, for instances of TaskOutputParameter.</p>
      <p>In a similar way, plans are also related to the agent’s actions realizing them. For this purpose,
the subproperties of the object-property hasExecution are introduced, namely hasPlanExecution,
hasGoalExecution, hasTaskExecution, hasTaskObjectExecution, hasTaskOperatorExecution,
hasTaskInputParameterExecution, and hasTaskOutputParameterExecution. Analogously, actions are
connected with the behaviour responsible for their execution by means of suitable subproperties
of the object-property executionDrawnBy.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Processes and procedures in OASIS 2</title>
      <p>Since the first version, OASIS was already capable of describing how agent activities are carried
out by suitably combining behaviours, plans and actions. Plans, in particular, can be used
to describe in detail how inputs are processed to be turned into outputs, but they are not
suficient to describe general complex processes. Plans require the presence of a committer
agent beforehand and can be applied only once. This is because the mental state related to the
desire or wish to perform actions does not abstract from the committer agent. Plans can be
leveraged to represent single applications of procedures but they should be combined properly.
Then, plans can be associated with the behaviours responsible for their executions thus carrying
out the actions required to accomplish the procedures. The approach is illustrated in Fig. 3.
Leveraging the ISO definition, processes defined by agents are constituted by procedures. In
the behaviouristic vision, the procedures states are associated with plans that are executed thus
leading to actions. Actions derive from agent behaviours that in their turn can rely on specific
templates. Agents performing actions are provided with behaviours either intrinsically or
through a played role. Finally, actions could lead to events either incidentally or as foreseen by
procedures. In the first case, events are conceived as noteworthy and extraordinary happenings
that have not been previously planned, in the second case, as recurrent situations.</p>
      <p>adopts</p>
      <p>For example, agents may play the role of resource manager, hence they are able to request
and release locks on resources according to such role. A process describing the steps required
to request and release locks is formalized, so that they can tackle a plan for each step. Plans
are executed so that the resource is released and modified. Actions are performed thanks to
agent behaviours provided by the resource manager’s role. During the execution of one of those
actions, the system exceptionally sends a message to the committer agent. We will partially see
this scenario together with the presentation of the model.</p>
      <p>In light of the above considerations, OASIS 2 introduces the following novel OWL classes:
• Process, which encompasses the procedures describing how activities are carried out and;
• Procedure, the subclass of the class Activity, which introduces the set of plans required
to accomplish the procedure itself and to be realized through actions. In OASIS 2
procedures are constituted by one or more ProcedureState, each one connected to a specific
plan describing how the activity is carried out. Specifically, we identify two types of
ProcedureState: a) TerminatingProcedureState, which includes InitialProcedureState and
FinalProcedureState, and b) NonTerminatingProcedureState.</p>
      <p>Procedures are constituted by procedure states that describe single steps of the procedure.
Initial procedure states describe the beginning of the procedure, while final procedure states
its termination. Moreover, the initial procedure state coincides with the final procedure state
in the case of a single-step procedure. Finally, non-terminating procedure states describe the
intermediate steps to be performed, including all the steps between the initial state and the final
state. The schema for processes and procedures is illustrated in Fig. 4. The subproperties of the
object-property procedureConsistsOfProcedureState are used to suitably connect a procedure with
its procedure states. Specifically, the object-properties procedureConsistsOfInitialProcedureState
and procedureConsistsOfFinalProcedureState (both subproperty of procedureConsistsOf
TerminatingProcedureState) connect the procedure with its initial and final procedure state, respectively,
while the object-property procedureConsistsOfNonTerminatingProcedureState connects the
procedure with its non-terminating states. The initial procedure state is connected with the
subsequent non-terminating procedure states by means of the object-property
hasNextNonTerminatingProcedureState. The latter property is also used to connect non-terminating procedure
states with their subsequent non-terminating procedure states. Whenever the next procedure
state is the final state, the object-property hasFinalProcedureState is adopted in its place. Both
hasNextNonTerminatingProcedureState and hasFinalProcedureState are defined as subproperty of
the object-property hasNext.</p>
      <p>Finally, since the intended meaning of processes and related procedures is to give a description
of how activities should be carried out, the instances introduced so far are also instances of
the class PlanningThing. To complete the representation of processes, it is now suficient to
connect an instance of the class Process with the ones of the class Procedure that model the
process activities. In case a process is constituted by more than one procedure, the latter can be
sorted by connecting them through the object-property hasNextProcedure.</p>
      <p>To describe how process activities should be carried out, we introduce a behaviour as in Fig. 1,
where the instances of TemplateThing are instead defined as instances of PlanningThing. The
choice is motivated by the fact that templates describe abstract behaviours that are instantiated
to introduce concrete behaviours, whereas plans describe actions that agents wish to perform
or see accomplished: this is exactly the case of process, where a set of actions must be tackled
in order to achieve the desired end. Additionally, plans allow one to describe in detail what
actions are required to accomplish the activity associated with the procedure state, the input
parameters and the expected output, without the need of selecting an agent responsible for
those actions beforehand. To associate a procedure state with the planned behaviour, OASIS 2
introduces the object-property isDescribedBy.</p>
      <p>The process concerning the case study considered at the beginning of the section is depicted
in Fig. 5. The process describes the modification of a resource which requires the acquisition</p>
      <sec id="sec-4-1">
        <title>Process and PlanningThing modifyResourceProcess processConsists</title>
      </sec>
      <sec id="sec-4-2">
        <title>OfProcedure procedureConsistsOfInitial</title>
        <sec id="sec-4-2-1">
          <title>Procedure and PlanningThing ProcedureState</title>
          <p>modifyResourceProcedure</p>
          <p>procedureConsistsOfNonTerminatingProcedureState
procedureConsistsOf</p>
        </sec>
      </sec>
      <sec id="sec-4-3">
        <title>FinalProcedureState</title>
        <sec id="sec-4-3-1">
          <title>FinalProcedureState hasFinalProcedureState</title>
          <p>and PlanningThing
releaseLockProcedureState
isDescribedBy</p>
        </sec>
      </sec>
      <sec id="sec-4-4">
        <title>InitialProcedureState and PlanningThing requestLockProcedureState hasNextNon</title>
      </sec>
      <sec id="sec-4-5">
        <title>Terminating</title>
      </sec>
      <sec id="sec-4-6">
        <title>ProcedureState</title>
      </sec>
      <sec id="sec-4-7">
        <title>NonTerminatingProcedureState and PlanningThing modifyResource isDescribedBy</title>
      </sec>
      <sec id="sec-4-8">
        <title>Behaviour and PlanningThing requestLockPlan isDescribedBy</title>
      </sec>
      <sec id="sec-4-9">
        <title>Behaviour and PlanningThing</title>
        <p>modifyResourcePlan
(1,*) hasNextProcedure (1,*)</p>
        <p>Activity
(1,*) processConsists Procedure and PlanningThing
OfProcedure (1,*)</p>
        <p>Process and
PlanningThing
(1,*) procedureConsistsOf
FinalProcedureState (1,*)
(1,*) procedureConsistsOfInitial</p>
        <p>ProcedureState (1, *)
(1,*) procedureConsistsOfNon
TerminatingProcedureState (1,*)</p>
        <p>Activity</p>
        <p>ProcedureState</p>
        <p>TerminatingProcedureState
InitialProcedureState and PlanningThing
(0, *) hasNextNon</p>
        <p>Terminating
ProcedureState (1,*)</p>
        <p>Activity</p>
        <p>ProcedureState</p>
        <p>TerminatingProcedureState</p>
      </sec>
      <sec id="sec-4-10">
        <title>FinalProcedureState and PlanningThing (0,*) hasFinalProcedureState (0,*)</title>
        <p>Activity</p>
        <p>ProcedureState
NonTerminatingProcedureState and PlanningThing
and release of an exclusive lock before and after the modification, respectively.</p>
      </sec>
      <sec id="sec-4-11">
        <title>Behaviour and PlanningThing releaseLockPlan</title>
        <p>The process consists of a single procedure that, in its turn, consists of three distinct states,
an initial state, a non-terminating state, and a final state. The initial state is associated with a
behaviour describing how to request a lock on a resource. The behaviour follows the template
in Fig. 2, where instances of the class TemplateThing are replaced with instances of the class
PlanningThing as stated in Section 3. Analogously, the non-terminating state is associated with
a behaviour describing how to modify the resource, while the final state is associated with the
behaviour describing how to release the lock.</p>
        <p>Once the process is fully described, it is possible to model its application. To do so, a model
retracing the structure of a process (see Fig. 4) is introduced, where instances of the class
PlanningThing are instead defined as instances of the class ExecutionThing. In a similar way
to TemplateThing and PlanningThing that are introduced to represent descriptions of abstract
behaviours and planned actions, respectively, ExecutionThing is conceived for those mental
states that represent actions already committed. In the case of processes, the class provides a
means for characterizing the realization of the process, the achievement of the related activities,
and the commitment of the planned actions. Moreover, to uniquely relate the elements of the
process with the ones of its realization, two subproperties of the object-property drawnBy are
introduced. Specifically, processDrawnBy and procedureDrawnBy are introduced to connect
the instances of Process and Procedure, respectively. Hence, it is clear how to trace back to the
agent’s behaviour responsible for the execution of a process, thus unambiguously identifying
actors and actions of arbitrarily complex environments.</p>
        <p>For instance, the process of the example in Fig. 5 can be realized as partially depicted in Fig. 6
that illustrates the modification process on a resource. The schema retraces the one introduced
for the process, where instances of the class PlanningThing are suitably replaced by instances
of the class ExecutionThing. Specifically, the process realization introduces three behaviour
executions, one for each plan of the process, namely a) requestLockBehaviourExec,
representing the execution of the requestLockPlan plan; b) modifyResourceBehaviourExec, representing
the execution of the modifyResourcePlan plan; c) releaseLockBehaviourExec, representing the
execution of the releaseLockPlan plan.</p>
        <p>Moreover, each behaviour of the process is connected with its analogous of the process
realization by means of the object-property hasPlanExecution. Finally, each plan execution can
be connected with the responsible behaviour by means of the object-property
planExecutionDrawnBy (subproperty of executionDrawnBy, see Section 3).</p>
      </sec>
      <sec id="sec-4-12">
        <title>InitialProcedureState and ExecutionThing requestLockProcedureStateExec hasNextNon</title>
      </sec>
      <sec id="sec-4-13">
        <title>Terminating</title>
      </sec>
      <sec id="sec-4-14">
        <title>ProcedureState</title>
      </sec>
      <sec id="sec-4-15">
        <title>NonTerminatingProcedureState and ExecutionThing modifyResourceProcedureStateExec isDescribedBy</title>
      </sec>
      <sec id="sec-4-16">
        <title>Behaviour and ExecutionThing modifyResourceExecution</title>
      </sec>
      <sec id="sec-4-17">
        <title>Process and ExecutionThing modifyResourceProcessExec processConsists</title>
        <p>OfProcedure procedureConsistsOfInitial</p>
        <sec id="sec-4-17-1">
          <title>Procedure and ExecutionThing ProcedureState</title>
          <p>modifyResourceProcedureExec
Behaviour and ExecutionThing
requestLockBehaviourExec
isDescribedBy
procedureConsistsOfNonTerminatingProcedureState
hasFinalProcedureState
n
o
it
u
c
e
x
E
s
s
e
c
o
r
P
s
s
e
c
o
r
P
procedureConsistsOf</p>
        </sec>
      </sec>
      <sec id="sec-4-18">
        <title>FinalProcedureState</title>
      </sec>
      <sec id="sec-4-19">
        <title>FinalProcedureState and ExecutionThing releaseLockProcedureStateExec isDescribedBy</title>
      </sec>
      <sec id="sec-4-20">
        <title>Behaviour and ExecutionThing</title>
        <p>releaseLockExecution
hasPlanExecution Behaviour and PlanningThing
releaseLockPlan
Behaviour and PlanningThing hasPlanExecution
modifyResourcePlan</p>
      </sec>
      <sec id="sec-4-21">
        <title>Behaviour and PlanningThing hasPlanExecution</title>
        <p>requestLockPlan</p>
        <p>As stated above, in OASIS 2 specific events can be associated with procedure states. In OASIS
2 events are semantically represented by instances of the class Event, while the procedure state
is related to the triggered event by means of the object-property triggersEvent. The phenomenon
associated with the event is introduced by means of OASIS 2 actions. These are in fact suficiently
general and powerful to potentially cover up any type of phenomenon springing from an event
that is fully within the vision of a behaviouristic approach.</p>
        <p>In the case of the case study, when the system is triggered to send a message to selected users
when a resource is modified, for example, because an error occurred, an action such as the one
in Fig. 7 is introduced. Other information such as the type of event, its duration, or the time
window in which it happens, can be additionally specified.</p>
        <p>NonTerminatingProcedureState
and PlanningThing
modifyResource</p>
        <p>triggersEvent
TaskDescription and</p>
        <p>ExecutionThing
event2303191805task</p>
        <p>Event
event2303191805
consistsOf
TaskDescription</p>
        <p>eventIs</p>
        <p>DescribedBy
GoalDescription and</p>
        <p>ExecutionThing
event2303191805goal</p>
        <p>Finally, it is admissible that agents perform procedures exclusively according to the specific
role that they play. Roles permit the separation of the concerns of behaviours intrinsically
owned by agents from the ones temporarily at their disposal to execute a process. This implies
that the agent is able to perform an action only when such a role is played. Hence, the behaviour
responsible for performing those actions is not strictly associated with the agent but with the
role. To represent the scenario described above and to model the playing of roles, OASIS 2
introduces roles as depicted in Fig. 8.</p>
      </sec>
      <sec id="sec-4-22">
        <title>RoleType</title>
      </sec>
      <sec id="sec-4-23">
        <title>Role</title>
        <p>hasRoleType</p>
      </sec>
      <sec id="sec-4-24">
        <title>Agent</title>
        <p>playsRole
providesBehaviour</p>
      </sec>
      <sec id="sec-4-25">
        <title>Behaviour</title>
        <p>In OASIS 2 roles, introduced as instances of the class Role, provide agents with behaviours
by means of the object-property providesBehaviour. In its turn, a role is associated with the
agent playing it by means of the object-property playRole. Whenever agents cease to play a
role, the associated behaviours are no longer available. The end of a role is specified by making
the instance of Role deprecated, hence the instance of the class DeprecatedThing. This implies
that actions are associated with role-oriented behaviours until the corresponding role is not
deprecated. Concerning the case study, an agent playing the role consisting in requesting a lock
on a resource is depicted in Fig. 9. The role is introduced as a fresh instance of the class Role,
specifically provided for the agent’s representational needs. The role types, introduced as an
instance of the class RoleType, are defined accordingly to the domain to be described, hence
they are out of the OASIS 2 scopes: in the case of the case study, a specific role type, called
resource_consumer_role, is introduced to depict the roles dedicated for consuming resources.</p>
      </sec>
      <sec id="sec-4-26">
        <title>RoleType</title>
        <p>resource_consumer_role
hasRoleType</p>
      </sec>
      <sec id="sec-4-27">
        <title>Agent and</title>
      </sec>
      <sec id="sec-4-28">
        <title>BehaviourThing</title>
        <p>useraccount224
playsRole
useraccount224_lock_role</p>
      </sec>
      <sec id="sec-4-29">
        <title>Role providesBehaviour</title>
      </sec>
      <sec id="sec-4-30">
        <title>Behaviour and</title>
      </sec>
      <sec id="sec-4-31">
        <title>BehaviourThing request_lock_behaviour</title>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusions</title>
      <p>This paper introduced an extension of the OASIS 2 ontology and, therefore, inherits the
behaviouristic approach to semantically represent agents and their commitments through the
formalization of their mental states, namely, behaviour, goal and task. In particular, the proposed
extension of OASIS 2 deals with the modelling of processes and procedures, thereby providing a
general although practical way of representing processes and procedures to be tackled by agents
through their behaviours. Now that such a foundational ontology is available, our semantic
representation capabilities are substantially enhanced. In consequence, all application scenarios
where specific instructions must be followed have fallen into scope.</p>
      <p>For example, how agents reach a consensus, together with the modelling of their behaviours,
is one of the future challenges. An application of OASIS 2 is foreseen for the characterisation
of security directives, aiming at a structural solution for translating security documents to
a mathematically-driven world. The approach targets the NIS 2 directive but other similar
directives can be addressed. In addition, we intend to apply OASIS 2 to represent security
constraints for cybersecurity threat contexts, in particular for the purpose of semantically
representing authentication and confidentiality properties for agents.</p>
      <p>Also, we shall consider how to integrate OASIS 2 with the PDDL and with the main
frameworks such as JADE [27], all with the aim of automatically generating agents and artefacts.
Similarly, an integration with CArtAgO [28], a framework for building shared computational
worlds, appears to be valuable. The horizons of the semantic representation of agents have
substantially expanded but retain the vast potential for yet more expansion in the near future.</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>Gianpietro Castiglione acknowledges a studentship by Intrapresa S.r.l. and Italian “Ministero
dell’Università e della Ricerca” (D.M. n. 352/2022). Giampaolo Bella acknowledges financial
support from: PNRR MUR project PE0000013-FAIR.
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