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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>V. Pitoni);</journal-title>
      </journal-title-group>
      <issn pub-type="ppub">1613-0073</issn>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Blueprint Personas to Epistemic Agents: A Comparative Study of ASP-Based and L-DINF-Based Approaches to Medical Appointment Scheduling</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Valentina Pitoni</string-name>
          <email>valentina.pitoni@univaq.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Stefania Costantini</string-name>
          <email>stefania.costantini@univaq.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Andrea Monaldini</string-name>
          <email>andrea.monaldini@student.univaq.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Alina Vozna</string-name>
          <email>alina.vozna@student.univaq.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="editor">
          <string-name>Multi Agent Systems, Modal Logic, Epistemic Logic, Answer Set Programming, Blueprint Personas</string-name>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Information Engineering</institution>
          ,
          <addr-line>Computer Science and Mathematics</addr-line>
          ,
          <institution>University of L'Aquila</institution>
          ,
          <country country="IT">Italy</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Gruppo Nazionale per il Calcolo Scientifico - INdAM</institution>
          ,
          <addr-line>Roma</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>University of Pisa</institution>
          ,
          <addr-line>Largo B. Pontecorvo, Pisa, 56127</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>1850</year>
      </pub-date>
      <volume>000</volume>
      <fpage>0</fpage>
      <lpage>0002</lpage>
      <abstract>
        <p>This paper investigates the evolution from a medical appointment scheduling framework based on Answer Set Programming (ASP) integrated with Blueprint Personas to a more cognitively rich, agent-based scheduling system employing the L-DINF epistemic logic framework. We illustrate how agent-oriented models incorporating beliefs, intentions, and dynamic reasoning capabilities can efectively enhance or replace the persona-based constraint optimization traditionally used. Key advantages of the L-DINF model, such as improved adaptability, enhanced explainability, and more human-like decision-making, are emphasized. Furthermore, a structured translation methodology from static personas into dynamic epistemic agents is proposed, accompanied by a modular logical architecture supporting real-time, responsive scheduling.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <sec id="sec-1-1">
        <title>The scheduling of medical appointments remains a significant challenge due to the inherent com</title>
        <p>
          plexity of balancing limited resources, patient urgency, and individualized preferences. Traditional
manual scheduling methods and simple heuristic-based solutions [
          <xref ref-type="bibr" rid="ref1 ref2">1, 2</xref>
          ] often do not accommodate this
complexity, resulting in ineficiencies, prolonged waiting times, and compromised care quality.
        </p>
      </sec>
      <sec id="sec-1-2">
        <title>In an earlier paper recently accepted, we introduced a scheduling framework based on Answer Set</title>
      </sec>
      <sec id="sec-1-3">
        <title>Programming (ASP), a declarative, logic-based paradigm that is well suited for constraint satisfaction</title>
        <p>
          and combinatorial optimization [
          <xref ref-type="bibr" rid="ref3 ref4 ref5 ref6 ref7">3, 4, 5, 6, 7</xref>
          ], enriched with Blueprint Personas [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ]. These personas
encode structured representations of patients, capturing socio-clinical characteristics, preferences, and
accessibility constraints, thereby enabling a form of patient-aware scheduling.
        </p>
      </sec>
      <sec id="sec-1-4">
        <title>Although ASP with Blueprint Personas proved efective for static scheduling problems, its limitations</title>
        <p>become evident in dynamic settings. Personas are, by design, static abstractions and do not support
real-time reasoning, belief updates, or proactive behavior. As a result, they cannot easily accommodate
changing availability, evolving preferences, or unforeseen disruptions in clinical operations.</p>
        <p>
          To address these limitations, we explore the integration of L-DINF, a logic-based framework for
modeling intelligent agents with epistemic capabilities such as beliefs, intentions, preferences, and
contextual reasoning over actions and environmental changes [
          <xref ref-type="bibr" rid="ref10 ref11 ref12 ref9">9, 10, 11, 12</xref>
          ]. Rather than replacing ASP,
we propose an integration with the L-DINF framework to enable proactive behavior, intention review,
belief-driven planning, and agent coordination, features crucial for modern, responsive healthcare
systems.
CEUR
        </p>
        <p>ceur-ws.org</p>
      </sec>
      <sec id="sec-1-5">
        <title>We show how the cognitive properties of L-DINF can be layered on top of the ASP scheduling backbone, supporting dynamic adaptation without the need to recompute entire schedules. The resulting hybrid architecture retains the ASP’s optimization strength while enriching it with real-time reasoning and explainability.</title>
      </sec>
      <sec id="sec-1-6">
        <title>This paper presents a structured methodology for translating Blueprint Personas into epistemic</title>
        <p>agents, articulates the rationale for the integration of L-DINF into ASP-based systems, and demonstrates
how such integration addresses the limitations of purely static models. We argue that this hybrid
approach is particularly well-suited to the healthcare domain, where scheduling must be responsive to
constant change.</p>
        <p>The paper is organized as follows: Section 2 reviews the Personas and L-DINF frameworks; Section 3
elaborates on the motivation to integrate epistemic agents into persona-based scheduling; Section 4
analyzes the feasibility of this integration; Section 5 details the translation of personas into L-DINF
agents; Section 6 provides a running example; and Section 7 summarizes our findings and outlines
future research directions.</p>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>2. Background</title>
      <sec id="sec-2-1">
        <title>2.1. Blueprint Personas</title>
        <sec id="sec-2-1-1">
          <title>Blueprint Personas, originally introduced in digital health transformation projects, act as structured</title>
          <p>
            archetypes representing prototypical patients. They combine clinical information (e.g., chronic
conditions), social context (e.g., dependency on caregivers), cognitive attributes, and digital literacy levels
[
            <xref ref-type="bibr" rid="ref8">8</xref>
            ]. When embedded in ASP models, these personas enable individualized constraint modeling while
preserving scalability across patient populations.
          </p>
        </sec>
        <sec id="sec-2-1-2">
          <title>In our framework, appointment scheduling is modeled as a constraint satisfaction problem (CSP) with embedded optimization goals. Each appointment must satisfy a set of hard constraints (e.g., resource availability, physical accessibility) while optimizing soft constraints such as patient preferences for time, clinic, and physician.</title>
        </sec>
        <sec id="sec-2-1-3">
          <title>It is important to note that the examples presented in this section are purely illustrative. Personas in</title>
          <p>our system should be understood as abstract ontological templates, conceptual structures that define
variables and relationships related to the patient. These templates are instantiated using real patient
data, EHR (Electronic Health Records), and system-level parameters, which populate the factual layer
of the ASP model.</p>
          <p>Each persona defines a structured combination of clinical status, socio-environmental context, and
digital capabilities. This layer of abstraction allows the system to reason over complex, human-centered
scheduling needs without hard-coding per-patient logic. Specifically, a patient persona may include
attributes such as: personal identity and geographical location, physical or mobility conditions (e.g.,
disability status), clinic preferences or accessibility needs, sensory sensitivities (e.g., noise or light
sensitivity), preferences over physician specialization and experience, preferred time windows for
appointments and distance or travel time to clinics. These high-level profiles are encoded as ASP facts,
forming the basis for reasoning:
1 patient(p1, "Mario", "Rossi", "L'Aquila").
2 disabled(p1).
3 preference(p1, c3).
4 sensory_preference(p1, "noise").
5 doctor_preference(p1, "GP", "chronic_diseases", 10).
6 appointment_preference(p1, c3, 1850, 2000).
7 distance(p1, c3, 15).</p>
        </sec>
        <sec id="sec-2-1-4">
          <title>Listing 1: Patient Profile with Preferences and Constraints</title>
          <p>Clinician personas are modeled in the same way. They include attributes such as medical expertise,
experience, and operational limitations, enabling the system to consider stafing constraints and match
appropriate providers to patient needs, in fact each visit is identified by: name, cost and classification
indicating its chronicity (0 = non-chronic, 1 = chronic):
1 doctor(m1, "Marco", "Bianchi", 52, "L'Aquila", "GP").
2 doctor_experience(m1, "GP", 25).
3 doctor_experience(m1, "chronic_diseases", 5).
4
5 visit_type(v1, "Cardiology", "Heart Attack", 0, 0, 0).
6 visit_cost(v1, 1000).
7 required_sessions(v1, 2).
8 session_interval(v1, 14, 28).</p>
        </sec>
        <sec id="sec-2-1-5">
          <title>Listing 2: Doctor Profile and Medical Expertise</title>
        </sec>
        <sec id="sec-2-1-6">
          <title>This ontology-based modeling allows the system to infer constraints and utility values for scheduling</title>
          <p>in a way that is both medically sound and personalized. It also enables scenario-based validation, where
synthetic patients are simulated to test how the system handles edge cases or vulnerable populations.</p>
        </sec>
        <sec id="sec-2-1-7">
          <title>In the ASP encoding, inference ruletrsansform base facts into utility values and feasibility checks,</title>
          <p>guiding the solver toward optimal, patient-centered outcomes. Preferences are modeled as soft rules,
contributing weighted terms to the objective function.</p>
          <p>For instance, a patient’s preference for a particular doctor type is captured by a scoring rule:
1 appointment_preference_effect(Patient, Time, Clinic, 1)
:2 patient(Patient, _, _, _),
3 clinic(Clinic, _),
4 availability(Clinic, _, _, Time),
5 appointment_preference(Patient, _, Start, End),
6 X = (((Time \ 86400) * 3600) * 100) + (((Time \ 3600) / 60) / 3) * 5,
7 X &lt;= End, X &gt;= Start.</p>
        </sec>
        <sec id="sec-2-1-8">
          <title>Listing 3: Efect of Patient Preference on Doctor Assignment</title>
        </sec>
        <sec id="sec-2-1-9">
          <title>Other utility-generating rules model preferences related to clinic selection, time windows, and environmental sensitivity. Collectively, these soft constraints steer the optimization process toward maximizing user satisfaction and care appropriateness.</title>
        </sec>
        <sec id="sec-2-1-10">
          <title>In parallel, hard constraindtesfine the space of valid solutions by enforcing rules grounded in clinical,</title>
          <p>operational, and ethical requirements. These constraints ensure the feasibility of assignments.</p>
        </sec>
        <sec id="sec-2-1-11">
          <title>For example, the following constraint ensures that patients are scheduled for the exact number of sessions required for a particular treatment:</title>
          <p>1 Sessions { appointment(Patient, Clinic, Doctor, Visit, Time) :
2 availability(Clinic, Doctor, Visit, Time) } Sessions
:3 need(Patient, Visit, _),
4 required_sessions(Visit, Sessions).</p>
        </sec>
        <sec id="sec-2-1-12">
          <title>Listing 4: Choice Rule for Appointment Allocation Based on Patient Needs</title>
        </sec>
        <sec id="sec-2-1-13">
          <title>Additional constraints—such as time slot exclusivity, priority handling, clinic capacity, and service</title>
          <p>delivery modes—are implemented to ensure system realism. For full access to the rules, we provide our
codebase online1.</p>
        </sec>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. Logical Framework: L-DINF</title>
        <p>
          The logical framework L-DINF, that we illustrate in this subsection, allows the modeling of group
dynamics of cooperative agents. Consequently, one can model agents that can form groups and support
each other in performing collective mental actions [
          <xref ref-type="bibr" rid="ref13 ref14">13, 14</xref>
          ]. Moreover, agents can consider preferences
about performing one action instead of another [
          <xref ref-type="bibr" rid="ref15">15</xref>
          ]. The logical framework also encompasses the
        </p>
        <sec id="sec-2-2-1">
          <title>1https://github.com/DawidPado/An-ASP-based-Solution-to-the-Medical-Appointment-Scheduling-Problem/tree/main</title>
          <p>
            possibility for agents to have roleswithin their group of agents. Roles determine which actions each
agent is enabled by its group to perform [
            <xref ref-type="bibr" rid="ref16">16</xref>
            ]. A mental action is considered executable if at least one
agent of the group can perform the action, with the group’s approval and on behalf of the group. An
agent can join or leave a group whenever it wants (and, consequently, the role of an agent may change
as it joins another group).
          </p>
        </sec>
        <sec id="sec-2-2-2">
          <title>The agents of a group can share their beliefs, so that any agent can access beliefs of other agents.</title>
        </sec>
        <sec id="sec-2-2-3">
          <title>This ability opens up the possibility of modeling aspects of “Theory of Mind”[17]. For instance, an agent</title>
          <p>can maintain a version (possibly outdated) of the mental state of other agents and perform inferences
about such knowledge.</p>
        </sec>
        <sec id="sec-2-2-4">
          <title>It models agents not just as data structures but as intelligent entities capable of forming beliefs, revising intentions, reasoning over equivalent actions, and adapting to environmental changes. This makes L-DINF particularly well-suited for contexts like healthcare, where schedules must often respond to evolving patient needs and real-world disruptions.</title>
        </sec>
        <sec id="sec-2-2-5">
          <title>Below we illustrate the syntax and semantics of L-DINF, moreover a formal axiomatic system exists</title>
          <p>
            for the logic’s core, and it is proven to be strongly complete, but that does not guarantee computational
tractability, reasoning in such a rich system is PSPACE-hard; for more detail refer to [
            <xref ref-type="bibr" rid="ref10 ref11 ref12 ref9">9, 10, 11, 12</xref>
            ].
          </p>
        </sec>
        <sec id="sec-2-2-6">
          <title>L-DINF is a logic composed of a static component and a dynamic component. The first, called</title>
          <p>L-INF, is
a logic of explicit beliefs and background knowledge. The second component extends the static one
with dynamic operators that express the consequences of agents’ mental actions.
2.2.1. Syntax</p>
        </sec>
        <sec id="sec-2-2-7">
          <title>A comprehensive exposition of the logical framework, encompassing its truth conditions, and axiomatic structure, is provided in the referenced publication: https://ceur-ws.org/Vol-3428/paper10.pdf.</title>
          <p>Let Atm = {, , …}
be a countable set of atomic propositions. The set 
 is the set of the physical
actions that agents can perform, including “active sensing” actions (e.g., “let’s check whether it ra,ins”
“let’s measure the temperatu, reet”c.). Let Agt be a set of agents and Grp the set of groups of agents.</p>
          <p>The language of L-DINF, denoted by ℒL-DINF, is defined by the following grammar:</p>
          <p>pref _do (  , ) ∣ pref _do (,   ) ∣

.
,  ∶∶=  ∣ ¬ ∣  ∧  ∣</p>
          <p>B  ∣</p>
          <p>K  ∣
do (  ) ∣ doG (  ) ∣ can_doG (  ) ∣
intend (  ) ∣ exec () ∣
[ ∶ ]  ∣</p>
          <p>Cl(  ,  ′ ) ∣ fCl (  )
∶∶=</p>
          <p>+ ∣ ⊢(, ) ∣ ∩(, ) ∣ ↓(,  ) ∣ ⊣(,  )
defined from
form [ ∶ ] 
where  ranges over Atm,   ,  ′ ∈ 
¬ and ∧ in the standard manner.2 The language of mental actionosf type  is denoted by
 ,  ∈ Agt,  ∈ ℕ , and  ∈</p>
        </sec>
        <sec id="sec-2-2-8">
          <title>Grp. Other Boolean operators are</title>
          <p>ℒACT. The static part L-INF of L-DINF, includes only those formulas not having sub-formulas of the</p>
        </sec>
        <sec id="sec-2-2-9">
          <title>Let us briefly describe the intended informal meaning of basic formulas of L-INF. As mentioned, we</title>
          <p>are interested in modelling the reasoning of agents acting cooperatively. We consider the set of agents
as partitioned in groups: each agent  ∈ Agt always belongs to a unique group in Grp. We assume that
all agents initially belong to an initial group. Any agent  , at any time, can perform a (physical) action
joinA(, ) , for  ∈ Agt, in order to change her group and join  ’s group. The special case in which  = 
denotes the action that allows agent  to leave her current group and form the new singleton group {} .</p>
          <p>
            The formula intend (  ) indicates the intention of agent  to perform the physical action   , in the
sense of the BDI agent model [
            <xref ref-type="bibr" rid="ref18">18</xref>
            ]. Formulas of this form can be part of agent’s knowledge base from
the beginning or it can be derived later. In this paper we do not cope with the formalization of BDI, for
which the reader may refer, e.g., to [
            <xref ref-type="bibr" rid="ref19">19</xref>
            ]. Hence, we will deal with intentions rather informally, also
assuming that intend (  ) holds whenever all agents of group  intend to perform   .
2For simplicity, whenever  = {}
of exec{} (  ) and similarly for other constructs.
          </p>
          <p>we will write  as subscript in place of {} . So, for instance, we often write exec (  ) instead</p>
          <p>The formula doi(  ) indicates the actual executioonf action   by agent, automatically recorded
by the new belief do (  ) (postfix “  ” standing for “past” action). Note that, we do not provide an
axiomatization for do (and similarly for doG , that indicates the actual execution of   by the group of
agents  ). In fact, we assume that in any concrete implementation of the logical framework, do and
doG are realized by means of a semantic attachmen[t20], that is, a procedure which connects an agent
with its external environment in a way that is unknown at the logical level. The axiomatization only
concerns the relationship between doing and being enabled to do.</p>
          <p>The expressions can_doi(  ) and pref _do (  , ) are closely related to doi(  ). In particular,
can_doi(  ) must be seen as an enabling condition, indicating that the agent  is enabled to perform the
action   , while pref _doi(  , ) indicates the level  of preference/willingness of agent  to perform   .</p>
          <p>The formula pref _doG (,   ) indicates that agent  exhibits the maximum level of preference on
performing action   within all group members. Notice that, if a group of agents intends to perform
an action   , this will entail that the entire group intends to do   , that will be enabled to be actually
executed only if at least one agent  ∈  can do it, i.e., it can derive can_doi(  ).</p>
          <p>The formula Cl(  ,  ′ ) denoted the equivalence of the two physical actions   and  ′ . Intuitively,
this means that in the specific practical context at hand, the two actions have “something in common”,
i.e., for instance, they use similar resources, perform in a similar way, can be used by an agent to
obtain equivalent results, etc. Notice that the predicate Cl induces a partition of   in a collection of
equivalence classes.</p>
        </sec>
        <sec id="sec-2-2-10">
          <title>Agents modeled through L-DINF deal with two kind of memories, namely, a working memoryused</title>
          <p>to represent beliefs, i.e., facts and formulas acquired via perceptions during an agent’s operation, and
a long-term memoryused to model agent’s background knowledge. Such knowledge is assumed to
satisfy omniscienceprinciples, such as: closure under conjunction and known implication, closure under
logical consequence, and introspection.</p>
          <p>Background knowledge of an agent  is specified by means of the modal operator K , which is actually
the usual S5 modal operator often used to model knowledge. The fact that background knowledge is
closed under logical consequence is justified because we conceive it as a kind of stable and reliable
knowledge bas.eThe modal operator B , instead, is used to represent the beliefs of agents  kept in
 ’s working memory. The contents of the working memory is determined by the mental actions 
has executed. We assume the background knowledge to include: facts/formulas known by the agent
from the beginning, and facts the agent subsequently decided to store in its long-term memory (via
a decision-making mechanism not covered here) after processing them in its working memory. We
therefore assume that background knowledge is irrevocable, in the sense of being stable over time.</p>
          <p>Whenever an agent wants to perform a physical action  ′ , it can exploit the equivalence described by
the facts of the form Cl(  ,  ′ ) to execute a most convenient action   (in terms of resources requires,
preferences, etc.) drawn from the equivalence class of  ′ . The formula fCl (  ) indicates that   is the
more convenient action among those in the set { ′ |Cl(  ,  ′ )}.</p>
          <p>The formulas exec () express executability of mental actions by a group  (which is a consequence
of the fact that any member of the group is able to perform the action). They have to be read as: “ is a
mental action that an agent in  can perform”.</p>
        </sec>
        <sec id="sec-2-2-11">
          <title>A formula of the form [∶]  , where  must be a mental action, states that “ holds after action</title>
          <p>has been performed by at least one of the agents in  , and all agents in  have common knowledge
about this fact”.</p>
          <p>
            Let us now introduce the dynamic component of the framework. Borrowing from [
            <xref ref-type="bibr" rid="ref15 ref21">15, 21</xref>
            ], we
distinguish five types of mental actions  that capture some of the dynamic properties of explicit beliefs
and background knowledge. + , ↓(,  ) , ∩(, ) , ⊣(,  ) , and ⊢(, ) . These actions characterize the
basic operations of belief formation through inference:
• + : learning perceived belief: the mental operation that serves to form a new belief from a
perception  . A perception may become a belief whenever an agent becomes “aware” of the
perception and takes it into explicit consideration.
• ↓(,  )
          </p>
          <p>is the mental action which consists in inferring  from  , where  is an atom: an agent,
believing that  is true and having in its long-term memory that  implies  , starts believing that
 is true.
• ∩(, )
∩(, )
is the mental action which closes the beliefs  and belief  under conjunction. Namely,
characterizes the mental action of deducing  ∧ 
from  and  .
• ⊣(,  ) , where  and  are atoms, is the mental action that performs a simple form of “belief
revision”, i.e., it removes  from the belief set, in case  is believed and, according to the background
knowledge, ¬ is logical consequence of  .
• ⊢(, ) , where  is an atom; by means of this mental action, an agent believing that  is true (i.e.,
it is in the working memory) and that  implies  , starts believing that  is true. This last action
operates exclusively on the working memory without recovering anything from the background
knowledge.
2.2.2. Semantics</p>
        </sec>
        <sec id="sec-2-2-12">
          <title>Many relevant aspects of an agent’s behaviour are specified in the definition of</title>
          <p>L-INF model, including
what mental and physical actions an agent can perform, what is the cost of an action and what is the
budget that the agent has at its disposal, what is the degree of preference of the agent to perform each
action, what is the degree of preference of the agent to use a particular resource. This choice has the
advantage of keeping the complexity of the logic under control and making these aspects modular.</p>
        </sec>
        <sec id="sec-2-2-13">
          <title>Definitions 2.1 and 2.2 introduce the notion of L-INF model, which is then used to introduce semantics</title>
          <p>of the static fragment L-INF. A model  is composed of two parts. A corepart   and a collection of
packages  . More specifically:
Definition 2.1.</p>
          <p>The core part  of a mode l is a tuple( ,  , ℛ,  , )
, where
•  is a set of worlds (or situations);
• ℛ = {  }∈ Agt is a collection of equivalence relati on:s o n⊆  × 
;
•  ∶</p>
          <p>Agt ×  ⟶ 2 2 is a neighborhood function such that, fo r∈eaAcght, each ,  ∈ 
, and
each ⊆</p>
          <p>these conditions hold:
(C1) if  ∈  (,  )
(C2) if  
•  ∶  ⟶ 2
•  ∶  ⟶ 2
do (  ) anddo (  ).</p>
          <p>then ⊆ { ∈  ∣</p>
          <p>} ,
  then (,  ) =  (,  )</p>
          <p>;
Atm is a valuation function;</p>
          <p>{do (  ),do (  )|  ∈Atm ,∈ Agt,∈ Grp} is a valuation function for formulas of the forms
To simplify the notation, let   ( ) denote the set { ∈  ∣  
  } , for ∈
. The set   ( ) identifies
the situations that agent  considers possible at world  . It is the epistemic stateof agent  at  . In
cognitive terms,   ( ) can be conceived as the set of all situations that agent  can retrievferom its
long-term memory and reason about. While   ( ) concerns background knowledge,  (,  )
of all facts that agent  explicitly believes at world  , a fact being identified with a set of worlds. Hence,
is the set
if  ∈  (,  )
that  (,  )</p>
          <p>then, the agent  has the fact  under the focus of its attention and believes it. We say
is the explicit belief setof agent  at world  . Constraint (C1) imposes that agent  can
have explicit in its mind only facts which are compatible with its current epistemic state. Moreover,
according to constraint (C2), if a world  is compatible with the epistemic state of agent  at world
 , then agent  should have the same explicit beliefs at  and  . In other words, if two situations are
equivalent as concerns background knowledge, then they cannot be distinguished through the explicit
belief set. This aspect of the semantics can be extended in future work to allow agents make plausible
assumptions.</p>
          <p>The packages of a model can be thought as modular extensions of the core part. Each package is used
to specify a specific feature, such as preferences, costs, executability, etc. Ideally, each package, (may)
correspond to some syntactic element of the syntax of L-INF. The connection between the syntactic
elements and the corresponding package will be established by a suitable component of the semantics
(so be seen). The following are some possible packages. Note that we are focusing on those of interests
for the purposes of this paper. Plainly, the designer of a particular MAS may decide to include only part
of the following packages or even to add/model other features (also providing a suitable adaptation of
the notion of truth).</p>
          <p>Definition 2.2. Given a core mode l  = ( ,  , ℛ,  , )
executability for mental actions
, the packages  are:
•  ∶ Agt ×  ⟶ 2 ℒACT is an executability function of mental actions such that, f∈orAegatcahnd
 ,  ∈  , it holds that:
(D1) if     then(,  ) = (,  )</p>
          <p>;
budget and costs for mental actions
(E1) if     then 1(,  ) =  1(,  ) ;
(F1) if     then 1(, ,  ) =</p>
          <p>1(, ,  ) ;
executability for physical actions</p>
          <p>(G1) if     then(,  ) = (,  )
budget and costs for physical actions
•  1 ∶ Agt ×  ⟶ ℕ is a budget function such that, for e∈acAhgt and ,  ∈ 
, the following holds
•  1 ∶ Agt × ℒACT ×  ⟶ ℕ is a cost function such that, for e∈acAhgt,  ∈ ℒ ACT, and ,  ∈ 
holds that:
, it
•  ∶
 ,  ∈</p>
          <p>Agt ×  ⟶ 2   is an executability function for physical actions such that, f∈orAegatcahnd
, it holds that:
agents’ roles</p>
          <p>(G2) if     then (,  ) =  (,  )
preferences on physical actions
•  ∶
 ,  ∈</p>
          <p>Agt ×  ⟶ 2   is an enabling function for physical actions such that, f o∈r Aeagtchand
, it holds that:
(E2) if     then 2(,  ) =  2(,  ) ;
(F2) if     then 2(,   ,  ) =  2(,   ,  ) ;
•  2 ∶ Agt ×  ⟶ Amounts is a budget function for physical action, such that, f o∈r Aeagct,hand
 ,  ∈  , it holds that:
•  2 ∶ Agt × AtmA ×  ⟶
  ∈ AtmA, and ,  ∈</p>
          <p>Amounts is a cost function for physical action, such that, f o∈r Aeagct,h
, it holds that:
;
;
•  ∶ Agt ×  ×
and ,  ∈</p>
          <p>AtmA ⟶ ℕ is a preference function for physical act iosnusch that, for eac∈h Agt
, it holds that:
(H1) if     then(,  , 
 ) = (,  ,</p>
          <p>);
For each and  , the functio n induces a preference ord⪯e,r on Atm , such that
(,  ,   ) ≤ (,  ,  ′ ).
⪯,  ′ if
equivalence of physical actions
•  ∶ AtmA ×  ⟶ 2   is a function describing a partition o f in equivalence classes (i .e.,
associates each physical action with its equivalence class), such tha t∈foArgetaacnhd ,  ∈  , it
holds that:
(I1) if     then(  ,  ) = (</p>
          <p>,  ) ;
•  ∶ Agt ×  × ℒ ACT ⟶ ℒACT is a selector function for physical actions tha t,agnidve n,selects
one physical actio (n,  ,   ) from the equivalence clas s of. Namely, it holds th a(t, ,   ) ∈
(  ,  ) ∧ ∀  ′ ∈ (  ,  )  ′ ⪯,   . For each ∈ Agt and ,  ∈  , it holds that:
(I2) if     then (,  , 
 ) =  (,  ,</p>
          <p>).</p>
        </sec>
        <sec id="sec-2-2-14">
          <title>Let us briefly describe the intended features shaped by the packages introduced by Def. 2.2. Notice</title>
          <p>that the concrete implementation, in a real MAS, the specification of some packages might depend on
other packages (for example, in what follows we will describe a possible implementation of  that relies
on the function  ).</p>
        </sec>
        <sec id="sec-2-2-15">
          <title>For an agent  , (,  ) is the set of mental actions that  can execute at world  . To execute a mental</title>
          <p>action,  has to pay the cost  1(, ,  ) .  1(,  ) is the budget that  has (in  ) to perform mental actions.
As mentioned, concerning physical actions, we are interested in modeling situations where performing
an action may require multiple resources. Hence, the cost  2(,   ,  ) of an action   (for agent  in
world  ) is a tuple in Amounts, while the available budget is described by  2(,  ) . For an agent  , the set
of physical actions it can execute at  is (,  ) . Equivalence between physical actions is determined
by function  . That is, (  ,  ) is the set of physical actions that are equivalent to   in  . Roles of
agents (that, as we will see, afects the capability of agents in a group to execute actions) is described
through  . Namely,  (,  ) is the set of physical actions that agent  is enabled by its group to perform
(recall that, at each time instant, an agent belongs to a single group). Agent’s preference on execution
of physical actions is determined by the function  . For an agent  , and a physical action   , the value of
 (,  ,   ) should be intended as a degree of willingneosfsagent  to execute   at world  . Analogously
to property (C2) imposed in Def. 2.1, the constrain (D1) imposes that agent  always knows which mental
actions it can perform and those it cannot, but if two situations/worlds are equivalent as concerns
background knowledge, then they cannot be distinguished through the executability of actions. Similar
“indistinguishability’ requirements are imposed for each package by conditions (E1), (F1), (F2), (G1),
(H1), (G2), (E2), (I1), and (I2).</p>
        </sec>
        <sec id="sec-2-2-16">
          <title>Let us give some hints on how the functions  and  might be actually implemented in a concrete MAS.</title>
          <p>
            As concerns  , we assume defined (e.g., by the MAS designer) a preference relation among (equivalent)
actions, for any agent  . In practice, this relation might be obtained by exploiting some specific reasoning
module. Some possibilities in this sense are described in [
            <xref ref-type="bibr" rid="ref22">22, 23</xref>
            ]. Similarly, as for all packages, a specific
module in the MAS implementation may be devoted to realize the selector function  . Here we outline
a simple option in defining  , relying on the availability of functions  2,  2, and  . Given an agent  , a
world  , and an action   , let  = { ′ | ′ ∈ (  ,  ) ∧  2(,  ′ ,  ) ≤  2(,  )} and  ′ ⊆  such that
for each  ′ ∈  ′ the value sum( 2(,  ′ ,  )) is minimal among the elements of  . Finally, select the
preferred element to be the ⪯, -maximal element of  ′ (i.e., the action  ″ with the larger value of
 (,  ,  ″). In case of multiple options, any deterministic criterion can be applied).
          </p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Motivation for the Integration</title>
      <p>The decision to integrate Blueprint Personas with the L-DINF framework stems from both theoretical
and practical considerations. While Blueprint Personas provide a powerful abstraction for representing
patient profiles within ASP-based scheduling systems, their utility is limited by their inherently static
and declarative nature. Once instantiated, these personas remain fixed, unable to evolve or adapt in
response to contextual changes. ASP solvers, though highly eficient in producing globally optimized
schedules, operate in a centralized and one-shot manner. As a result, they struggle to accommodate the
frequent and often unpredictable disruptions that characterize real-world healthcare environments.</p>
      <p>The introduction of the L-DINF framework is not intended to replace ASP, but rather to augment
it. L-DINF conceptualizes patients (and other agents) as cognitively capable entities endowed with
beliefs, intentions, and the ability to engage in ongoing deliberation. These agents are capable of
dynamically perceiving environmental changes, such as a clinic becoming unavailable, and updating
their internal states accordingly. This agent-based reasoning adds a layer of adaptability and proactivity
that complements ASP’s static optimization, enabling systems to respond in real time without requiring
full recomputation. So, the ASP program may be scheduled for periodic execution to ensure overall
optimization, whereas the L-DINF framework can be utilized to manage run-time changes.</p>
      <p>More specifically, L-DINF enriches the scheduling process through the following capabilities:
• Dynamic Adaptation: Agents revise beliefs and intentions on the fly, enabling local adjustments
without re-running the entire ASP program.
• Enhanced Explainability: Agent decisions are grounded in explicit reasoning chains involving
beliefs, preferences, and inferred intentions.
• Personalized Scheduling: Cognitive profiles support individualized, goal-directed planning
beyond rule-based parameter matching.
• Social Coordination: Through formal group dynamics, agents can coordinate, delegate, and
share resources, capabilities that are dificult to express declaratively in ASP alone.</p>
      <sec id="sec-3-1">
        <title>While the integration of L-DINF introduces challenges, including increased logical complexity</title>
        <p>and computational cost in large-scale deployments, its advantages in flexibility, responsiveness, and
transparency make it particularly valuable in dynamic settings. Importantly, in scenarios where
scheduling constraints are stable and well-defined, ASP remains the most eficient and suitable choice.</p>
      </sec>
      <sec id="sec-3-2">
        <title>Thus, our proposal is not to abandon ASP, but to extend it. The incorporation of L-DINF ofers a synergistic enhancement, leveraging ASP’s optimization strengths while overcoming its limitations in adaptivity and reasoning. This hybrid approach enables more resilient, explainable, and patient-centered scheduling solutions that are better aligned with the complex demands of modern healthcare systems.</title>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Why the Substitution from Blueprint Personas to L-DINF Agents Is</title>
    </sec>
    <sec id="sec-5">
      <title>Possible</title>
      <p>In this section, we argue that the substitution of Blueprint Personas with L-DINF agents in appointment
scheduling systems is not only feasible but also conceptually coherent. This is due to the fact that the
fundamental components of a persona, such as preferences, constraints, and goals, can be structurally
and semantically mapped into the epistemic constructs provided by the L-DINF framework. However,
while some elements map easily, others require non-trivial adaptation due to the shift from static
declarative models to autonomous cognitive agents.</p>
      <sec id="sec-5-1">
        <title>4.1. Components That Map Easily</title>
        <p>• Declarative Attributes → Beliefs (  )</p>
        <sec id="sec-5-1-1">
          <title>Blueprint Personas include static descriptors such as location, disability status, or sensory preferences. These are analogous to explicit beliefs in L-DINF. Since these attributes are not meant to evolve during execution but form the basis for reasoning, they can be directly encoded as agent beliefs. This mapping is straightforward because the semantics in both models are declarative.</title>
          <p>Example:
1 ASP: disabled(p1).
2 L-DINF: B_i(disabled(p1)). i is an agent who manages the reservations
• Preferences → Preference Functions (pref _do ,  (,  ,   ))</p>
          <p>Preferences in ASP (e.g., for doctors, time slots, or clinics) are modeled as weighted rules or
soft constraints. In L-DINF, preferences are formalized using pref _do and scored by a function
 (,  ,   ) that quantifies the desirable action of a particular agent  in the world  . This allows
agents to rank alternatives in a principled way, much like ASP optimizers—but grounded in agent
beliefs. Example:
• Constraints → Feasibility Rules (can_do )</p>
          <p>Constraints in ASP, such as distance limits or accessibility conditions, are often specified as hard
constraints. In L-DINF, these are interpreted as feasibility conditions that determine whether
an agent can perform a given action. This mapping is logical and local: it preserves the original
semantics while embedding it in agent-specific reasoning. Example:
1 can_do_p1(slot(c3, t1)) &lt;--accessible(c3) and distance(c3)&lt;20.
4.2. Components that Require Adaptation
• Soft Optimization → Local Intentional Reasoning: In ASP, soft constraints are globally
optimized via solvers like Clingo, producing a solution that minimizes a cost function. In L-DINF
instead, agents must reason locally over their preferences and constraints to select the most
suitable action. This requires restructuring the optimization logic into modular, distributed
reasoning procedures.
• Static Personas → Dynamic Agents: Blueprint Personas are static input structures. Once
declared, they do not change during runtime. In L-DINF, agents can update beliefs based on
environmental perception and modify their intentions accordingly. This demands the modeling
of inference rules that govern how belief updates propagate through the agent’s decision process.
• One-shot Decision Making → Ongoing Deliberation: ASP computes a single solution per
run. L-DINF, by contrast, supports ongoing deliberation and dynamic replanning. This means
that agents can abandon intentions if conditions change or generate new ones in response to
updated knowledge. This shift requires modeling the agent’s decision lifecycle, including intend,
drop, and replace operations.
• No Social Context → Group Reasoning and Negotiation: Personas in ASP are individual and
isolated. L-DINF allows agents to join groups, share beliefs, and coordinate actions.
Implementing this requires defining group membership rules, shared knowledge bases, and collaborative
preference negotiation mechanisms. While powerful, this introduces a layer of complexity not
present in ASP.</p>
          <p>Persona Element
Static attributes (e.g., location)
Preferences (doctor, time)
Access/distance constraints
Soft constraints
Behavioral adaptation
Multi-agent behavior</p>
          <p>L-DINF Equivalent
Beliefs (  )
pref _do , (,  ,   )
Feasibility rules (can_do )
Local reasoning and selection
Intention updates, inference
Group dynamics (joinA,   )</p>
          <p>Efort to Adapt</p>
          <p>Easy
Easy</p>
          <p>Easy
Moderate</p>
          <p>High
High</p>
          <p>L-DINF provides a more expressive and adaptive framework that retains the strengths of the original
personas while extending their functionality into autonomous, intelligent scheduling agents.
Synthesizing we can think of using for translation of all the modules this pseudo code:
1 forall patient P:
2 B_P(prefers_clinic = C) &lt;-- preference(P, C)
3 pref_do_P(slot(C, T), D) &lt;-- appointment_preference(P, C, S, E) and T in [S, E]
4 B_P(sensory_sensitive(S)) &lt;-- sensory_preference(P, S)
5 B_P(doctor_preference(T, S, Y)) &lt;-- doctor_preference(P, T, S, Y)
6 B_P(distance_to_clinic(C, D)) &lt;-- distance(P, C, D)</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>5. General Schema for Translating Blueprint Personas into L-DINF</title>
    </sec>
    <sec id="sec-7">
      <title>Agents</title>
      <sec id="sec-7-1">
        <title>The following schema outlines how elements from a Blueprint Persona defined in ASP can be translated into formal components of the L-DINF framework. Each transformation associates declarative or preference-based information from the persona with a corresponding logical construct in the agent’s epistemic model.</title>
        <p>Blueprint Persona (ASP)
patient(P, …)
disabled(P)
preference(P, C)
appointment_preference(P, C,
S, E)
sensory_preference(P,
``noise'')
doctor_preference(P, T, S,
Y)
distance(P, C, D)
need(P, V, N)
availability(C, T)
alternative(C1, T1, C2, T2)
L-DINF Representation
agent identity
  (disabled(P )) i is an agent who manages the
reservations
  (prefers_clinic = )
  (appointment_time_preference(, , ))
  (sensory_noise_sensitive)
  (doctor _preference( , ,  ))
  (distance_to_clinic(, ))
intend (n_sessions( )) ∧ constraint( )
can_do (slot(,  ))
Cl(slot(1,  1), slot(2,  2))</p>
      </sec>
    </sec>
    <sec id="sec-8">
      <title>6. Use Case: Mario, a proactive patient Agent</title>
      <sec id="sec-8-1">
        <title>We consider a patient named Mario, who sufers from a chronic condition and is sensitive to noise.</title>
        <p>Initially, Mario prefers morning appointments at Clinic C1, which is located near his home. His
medical profile and preferences are encoded as a traditional ASP-style persona in section 2.1. In
transitioning to an L-DINF-based representation, Mario is modeled as a cognitive agent endowed with
epistemic capabilities, specifically, beliefs, preferences, and intentions,which allow for autonomous and
context-aware reasoning. The initial mental state of the agent is represented through the following
beliefs:
1 B_mario(prefers_clinic = c1).
2 B_mario(appointment_time_preference(c1, 0800, 1000)).
3 B_mario(sensory_noise_sensitive).
4 B_mario(doctor_preference("GP", "chronic_diseases", 10)).
5 B_mario(distance_to_clinic(c1, 12)).</p>
      </sec>
      <sec id="sec-8-2">
        <title>Preferred time slots are expressed using preference functions:</title>
        <p>1 B_mario(pref_do_mario(slot(c1, 0830), 9)).</p>
      </sec>
      <sec id="sec-8-3">
        <title>Mario is able to attend this slot if the clinic is accessible and within his mobility budget:</title>
        <p>1 B_mario(can_do_mario(slot(c1, 0830)) &lt;-- accessible(c1) and distance(c1)&lt; 20).</p>
      </sec>
      <sec id="sec-8-4">
        <title>A key advantage of the L-DINF framework emerges when environmental changes are introduced.</title>
      </sec>
      <sec id="sec-8-5">
        <title>Suppose Mario perceives that Clinic C1 has become inaccessible, expressed as a perceptual update:</title>
        <p>+¬  (1) . Based on an epistemic inference rule, he is able to derive a revised belief about his
action feasibility: ⊢(¬  (1),¬ _ _ ((1, 0830))) . This triggers a goal revision process.
Recognizing the infeasibility of his original plan, Mario searches for alternative, equivalent actions: he
knows that (1, 0830) and (2, 0930) are equivalent action and his degree of willingness for the
second action is 8 ( ( ,  , (2, 0930)) = 8. ); we also know that he prefers the second action so as
to form the fact   _ ((2, 0930)) . This is expressed as follows:</p>
        <p>Initially, Mario belongs to a singleton group: 1 = { } and  1 = ∅. Anna,
another patient agent, is part of a group scheduled for Clinic C2: 2 = {} and  2 =
{  (2),   _(2, 0930),  _  (2)} . Mario joins Anna’s group using the group
action primitive  _ (( , )) and after this operation 2 = {,  }. Mario now
has access to the shared group knowledge base, and he can revise his beliefs and confirm his new
intention:
1 B_mario(accessible(c2)).
2 B_mario(can_do_mario(slot(c2, 0930))).
3 B_mario(do_mario(slot(c2, 0930))).</p>
      </sec>
      <sec id="sec-8-6">
        <title>Mario has autonomously revised his beliefs, intentions, and group membership in response to environmental changes. He selects an equivalent action, joins a relevant group, and executes a feasible alternative. This proves the flexibility and expressiveness of the L-DINF agent model.</title>
      </sec>
    </sec>
    <sec id="sec-9">
      <title>7. Conclusions</title>
      <sec id="sec-9-1">
        <title>In this work, we have explored the integration of the L-DINF epistemic logic framework into medical</title>
        <p>appointment scheduling systems originally based on ASP and Blueprint Personas. Rather than replacing</p>
      </sec>
      <sec id="sec-9-2">
        <title>ASP, our goal is to enhance its declarative and optimization-oriented strengths with the capacity of L</title>
        <p>DINF for cognitive reasoning, agent-level deliberation, and adaptive behavior. This integration addresses
the limitations of static persona models by enabling agents to revise beliefs, reformulate intentions, and
coordinate with others in response to real-time contextual changes. By embedding cognitive constructs
such as beliefs, preferences, and intentions into scheduling agents, the L-DINF framework introduces
significant advantages in terms of dynamic adaptability, personalized decision making, and transparent
reasoning. Agents modeled in L-DINF are not only responsive to environmental disruptions but also
capable of proactively participating in collaborative planning through shared group knowledge and
structured delegation mechanisms.</p>
        <p>We have proposed a structured translation methodology that transforms Blueprint Personas into
epistemic agent models; while this extension introduces additional modeling and computational
complexity, particularly in large-scale deployments, the resulting increase in system intelligence, flexibility,
and robustness demonstrates its value in realistic and dynamic healthcare environments. We have
also shown that the ability to reason dynamically and deliberate continuously allows L-DINF agents
to operate efectively within uncertain and evolving clinical scenarios. Future work will involve
implementing this hybrid ASP + L-DINF architecture in real-world systems, validating its performance
through empirical studies, and demonstrating its practical feasibility across diverse scheduling contexts.</p>
      </sec>
    </sec>
    <sec id="sec-10">
      <title>Declaration on Generative AI</title>
      <sec id="sec-10-1">
        <title>The author(s) have not employed any Generative AI tools to generate content. They have used tools to correct minor mistakes.</title>
        <p>[23] S. Costantini, A. Formisano, Augmenting weight constraints with complex preferences, in: Logical</p>
      </sec>
      <sec id="sec-10-2">
        <title>Formalizations of Commonsense Reasoning, Papers from the 2011 AAAI Spring Symposium, AAAI</title>
        <p>Press, USA, 2011.</p>
      </sec>
    </sec>
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