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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Logic and Answer Set Programming in High School: Two Learning Unit Experiences</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Kristian Reale</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Mathematics and Computer Sciences, University of Calabria</institution>
          ,
          <addr-line>Rende (CS)</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>This paper presents the design and implementation of two learning units for teaching Answer Set Programming (ASP) to high school students, with a focus on deductive Artificial Intelligence models. These units were carried out in classroom settings at two diferent schools, aiming to develop logical reasoning and problem-solving skills through declarative programming. The paper discusses the teaching methods employed and the outcomes observed in both educational contexts. The findings provide practical information for educators who are interested in considering the integration of logic programming into high school curricula.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Answer Set Programming</kwd>
        <kwd>High School</kwd>
        <kwd>Logic Programming</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>technological and conceptual bridge between diferent disciplines: scientific, classical, and professional.
The educational experiences were implemented through two Italian distinct educational activities
carried out as part of National-Level projects for high school institutions. Both projects aimed to delve
into topics that are typically not covered in standard high school curricula and explore new advanced
scientific subjects often reserved for university courses or based on scientific research findings.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Overview of the Conducted Activities</title>
      <p>The target institutions for the activities were two high schools of the province of Reggio Calabria, Italy.
In particular, the first high school is known as “IIS Francesco La Cava” (IIS La Cava) located in Bovalino
(Reggio Calabria). This school ofers distinct fields of study: Vocational Institute for Commercial
Services, Classical High School, and Scientific High School. The second institution is known as “IIS
Pietro Mazzone” (IIS Mazzone) located in Roccella Ionica (Reggio Calabria). This institution provides
various fields of study, including Scientific High School.</p>
      <p>The first educational activity, conducted at the “IIS Mazzone”, is titled “The Logic of Artificial
Intelligence" and is part of the Piano Lauree Scientifiche 1, a national initiative aimed at generating
interest and enthusiasm for science. The activity was designed to introduce high school students to
the fundamentals of Logic-Based Artificial Intelligence, with a particular focus on deductive reasoning
through the use of Answer Set Programming. The course combined theoretical instruction with practical
lab sessions, encouraging students to work in groups to apply what they had learned by designing
simple deductive AI systems. The final challenge consisted of developing a logic-based AI agent capable
of playing a card game, ofering students a hands-on opportunity to engage with key concepts in
computational reasoning.</p>
      <p>The second education activity, conducted at the “IIS La Cava”, is called “Smart Village: Planning
the Paths of Thought in a Digital Town" and is part of a government-funded educational program for
student skill development2. The activity was designed around the idea of developing a tourist navigation
system for the town of Bovalino, integrating various technologies and programming approaches suitable
for high school learners. The final part of the activity focused on Answer Set Programming, with the
aim of teaching students how to use the language to build the intelligent reasoning component of the
system. This allowed them to experience how logic-based AI works in practice, and how declarative
programming can solve real-world problems like finding the best route in a town while avoiding
roadblocks.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Learning Plan Design and Implementation</title>
      <p>In this Section, the learning units developed for each educational activity are introduced. Particular
attention was given to the academic background of the students and prior knowledge, which were
analyzed to design appropriate and meaningful learning experiences for each specific school context.</p>
      <sec id="sec-3-1">
        <title>3.1. The Logic of Artificial Intelligence Learning Unit</title>
        <p>For the “The Logic of Artificial Intelligence” educational activity, the following Learning Unit was
proposed and carried out.</p>
        <sec id="sec-3-1-1">
          <title>Learning Unit: The Logic of Artificial Intelligence</title>
          <p>1https://www.istruzione.it/dg_studente/piano_nazionale_lauree_scientifiche.shtml
2PON Project “Smart Village: Un Paese Nel Digitale" Module “Pianifichiamo i Percorsi del Pensiero" codice identificativo
“10.2.2A-FSEPON-CL-2018-535"</p>
          <p>As shown in the learning unit, at “IIS Mazzone” High School, 14 students from the Scientific High
School field, aged 15-18, participated in this educational experience. All of them possessed programming
skills, particularly in C++, and some of them had some knowledge of Java.</p>
          <p>The contents were presented to the students as follow. The first part of this activity involved
an introduction to Artificial Intelligence, emphasizing the distinction between Deductive Reasoning
(Symbolic AI) and Inductive Reasoning (Machine/Deep Learning). Since the primary objective of the
activity focused on the utilization of Logic in Artificial Intelligence, the entire emphasis was placed on
the Deductive Reasoning approach, which typically utilizes Answer Set Programming. The activity
was divided into two components: a lecture and a laboratory session. During the lecture portion, slides
were presented to the students, providing an overview of Artificial Intelligence as a scientific field,
with a particular focus on the application of logic in AI. Specifically, Propositional Logic and a brief
introduction to First Order Logic were explained. Following that, an introduction to ASP was provided,
beginning with a distinction between procedural programming languages and declarative programming
languages, which is the underlying nature of ASP. The laboratory session involved dividing the students
into groups and assigning them the task of experimenting with the ASP language by creating an
Artificial Intelligence system capable of playing a card game of their choice.</p>
          <p>
            Prior to commencing the task, a practical demonstration was conducted to guide the students on how
to create an Artificial Intelligence system for the Seven and a Half [
            <xref ref-type="bibr" rid="ref11">11</xref>
            ] card game. In the Seven and a
Half game, the rules state that players draw cards trying to get as close as possible to 7.5 points without
going over. Picture cards like the King of Coins are special, and drawing too much can result in a bust.
In the following the ASP program of the Seven and a Half game proposed to the students is described.
7 : :- askCard, tableSum(S), not S &lt; 8.
8 : doNotAskCard :- owns(king, coins).
9 : doNotAskCard :- table(king, coins).
10 : askCard :- tableSum(S), fuzzy(Range), S &lt; Range, not doNotAskCard.
11 : fuzzy(Range) :- #rand(4, 6, Range).
          </p>
          <p>Rule 1 is a disjunctive rule allowing to either ask for another card or not ask: it expresses the possible
decision the the system must take a card or not. Rule 2 says that if there is at least one card on the
table, then   is true. Used later to determine whether the table is empty. Rule 3 and
4 calculate the total value of cards currently on the table by summing the value of each card. Rule 5
and 6 compute the total score the player would have if they added their card (owns) to the current
table sum (totalSum = value on table + value of card in hand). Rule 7 is a constraint that forbids asking
for a card if the table sum is 8 or more. Since 7.5 is the max, going over is a bust. Rules 8 and 9 state
that if the player owns the King of Coins or the King of Coins is already on the table, the system should
not ask for another card to avoid risking over 7.5. Rules 10 and 11 introduce a fuzzy element through
randomness by assigning a random threshold (between 4 and 6) to the fuzzy(Range) predicate. This
threshold is then used in rule 10 to determine whether the player should ask for a card, efectively
simulating variability in risk tolerance.</p>
          <p>
            For their project, some students chose to develop an AI system for the game Briscola [
            <xref ref-type="bibr" rid="ref12">12</xref>
            ], and one
group was able to create an AI that was able to beat the instructor in a game session. Finally, the last
group tried, without success, to create an ASP program capable of playing the game Scopa [
            <xref ref-type="bibr" rid="ref13">13</xref>
            ].
          </p>
        </sec>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Smart Village: Planning the Paths of Thought in a Digital Town Learning Unit</title>
        <p>For the “Smart Village: Planning the Paths of Thought in a Digital Town” educational activity, the
following Learning Unit was proposed and carried out.</p>
        <p>Learning Unit: Smart Village: Planning the Paths of Thought in a Digital Town
Scientific High School, Applied Sciences track:
4 students mainly skilled on Basic Logic and Object-Oriented Programming
with C++;
Classical High School:
12 students without any Computer Science background in their school
program;
Vocational Institute for Commercial Services:</p>
        <p>2 students mainly skilled with just Basic Computer Science.</p>
        <p>Build a navigator that calculates the route from point A to point B in the city
of Bovalino, avoiding closed roads.
- Introduction to both deductive and inductive Artificial Intelligence.
- Smart Devices and IoT systems.
- Computational thinking and basic programming in Scratch (for Classical
High School students).
- Microsoft Access.
- App Inventor.</p>
        <p>- Logic and Answer Set Programming
Conducted at: IIS “La Cava”
Duration at: 30 hours
Number of students: 18
Age range: 15–18 years
Institutes of origin
and background:</p>
        <sec id="sec-3-2-1">
          <title>Objective:</title>
        </sec>
        <sec id="sec-3-2-2">
          <title>Course Topics:</title>
          <p>Evaluation Method: Final multiple-choice questionnaire covering the concepts explained in the
course.</p>
          <p>Group work focused on the development of a mini project. The division into
groups is based on their skills (one group for each Institute):</p>
          <p>Scientific High School, Applied Sciences track:</p>
          <p>building the ASP program to determine the best route;
Classical High School:
importing Maps coordinates of Points of Interest (POI) into Microsoft</p>
          <p>Access;
Vocational Institute for Commercial Services:</p>
          <p>designing the app using App Inventor.</p>
          <p>Final Results: Final questionnaire with more than 75% correct answers.</p>
          <p>The students from the Classical High School learned to read ASP programs, but
were not able to build one from scratch.</p>
          <p>The students from the Vocational Institute for Commercial Services showed
significant gaps in their understanding of logic.</p>
          <p>The students from the Scientific High School wrote the ASP program for
calculating the route, although with some errors.</p>
          <p>The proposed Learning Unit involved 18 students aged 15 to 18, including 12 from a Classical High
School, 4 from a Scientific High School, and 2 from a Vocational Institute for Commercial Services, all
of whom participated in this educational experience. Among them, only the Scientific High School
students had some advanced computer science skills, particularly in programming with C++. The
Vocational Institute for Commercial Services students had basic computer science skills, and, finally, the
Classical High School students had no computer science background due to the absence of this subject
in their curriculum.</p>
          <p>
            The learning unit began with an introduction to Artificial Intelligence and emphasized the significance
of equipping devices like smartphones (smart devices) with AI capabilities. The attention then shifted
to laboratory activities regarding practical application of Answer Set Programming, where the students
collaboratively, and with my guidance, had to build an Intelligent Android App Navigator to assist users
in navigating the town of Bovalino. Specifically, the Navigator aimed to provide users with the shortest
route from point A to point B within the town while considering road closures and diversions. During
the laboratory session, the concept of algorithms was first introduced, along with exercises utilizing the
tool Scratch [
            <xref ref-type="bibr" rid="ref14">14</xref>
            ] . The introduction of Scratch served as a valuable foundation for understanding the
tool App Inventor [
            <xref ref-type="bibr" rid="ref15">15</xref>
            ], which allows the creation of real Android apps using a similar methodology to
Scratch. The focus then transitioned to Java programming, and finally, to the utilization of the ASP
language for the development phase of the navigation algorithm.
          </p>
          <p>For the definition of the ASP program that calculates the best route, some explanations of the ASP
language, as well as examples like the well known 3-coloring problem, were shown to the students.
Since ASP is a self-documenting declarative language, all students were able to understand the meaning
of the logic rules. Only the students from the Scientific High School, Applied Sciences track were able to
understand how to express a constraint given in natural language as a new ASP rule. The ASP program
for the navigator was built under my guidance: all the students understood the ASP program, but only
those from the Scientific High School proposed a small possible variant of some rules. In the following,
the ASP program developed during the activity is described.
1 : start(1).
2 : end(7).
1 : path(X, Y) | noPath(X, Y) :- arc(X, Y).
2 : visited(X) :- start(X).
3 : visited(Y) :- path(X, Y), visited(X).
4 : :- end(X), not visited(X).
5 : :- interruption(X), visited(X).
6 : :~ path(X, Y). [1@1, X, Y]</p>
          <p>The fact 1 and 2 define the starting node (node 1) and the ending node (node 7) of the desired
shortest path where a node is a Point of Interest (POI). Rule 1 states that for every arc (connection)
between nodes X and Y, the program nondeterministically, chooses whether to include it in the path
(path(X, Y)) or exclude it (noPath(X, Y)). Rule 2 and 3 state that the starting node is considered visited
and if there is a path from node  to node  and  has been visited, then  is also marked as visited.
This rule recursively marks all reachable nodes along the selected path as visited. The constraint 4 states
that the end node must be visited. The constraint 5 prevents visiting nodes marked as interruptions.
Finally, the weak constraint 6 tries to minimize the total occurence of the predicate path in order to
obtain the shortest path.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Discussion and Conclusions</title>
      <p>The outcomes of both educational activities were highly satisfactory, as students enthusiastically
participated and achieved remarkable results. All students quickly grasped the principles of logical
reasoning thanks to the self-documenting nature of ASP, which facilitated their understanding and
application of the language. This experience not only enhanced their computational thinking skills
but also significantly strengthened their critical thinking abilities. By distinguishing between classical
imperative programming paradigms and logic-based declarative languages, students developed a more
structured and analytical mindset essential for problem-solving.</p>
      <p>The guidance provided during the initial laboratory phase gradually diminished as students became
proficient in logical thinking within a few hours. Final questionnaires revealed positive feedback,
showing that even students without prior computer science experience could efectively engage with
logical reasoning through ASP. Furthermore, using ASP to develop an intelligent automatic navigator
and an agent capable of playing a card game helped students appreciate the central role of deductive,
logic-based approaches in advancing Artificial Intelligence. This logical foundation ofers a valuable
alternative to traditional, more complex inductive AI methods reliant on neural networks.</p>
      <p>These outcomes highlight how prior knowledge and active engagement influence performance of
students. The ones with stronger backgrounds, such as those from Scientific High Schools, were able to
create functional AI programs with impressive results, while others faced challenges with fundamental
concepts like logic and program construction. This underscores the importance of targeted support and
tailored teaching strategies when introducing complex subjects like Artificial Intelligence and Answer
Set Programming. The success of some students in developing an AI system capable of playing Briscola
and defeating also the instructor in a game session, demonstrates how hands-on, project-based learning
fosters deeper understanding, critical thinking, and motivation.</p>
      <p>This experience confirms that subjects initially perceived as dificult by high school students can
become accessible through practical, hands-on activities. Providing opportunities for students to create
their own games (such as the card games developed in this project) and real-world tools like the App
Navigator (familiar from their daily smartphone use) served as powerful motivators. This approach
enabled students to actively engage with complex concepts by building tangible products, thereby
reinforcing their logical and critical thinking skills. Moreover, the rapid acquisition of a declarative logic
language like ASP by the students suggests its strong potential for inclusion in high school computer
science curricula, where fostering logic and critical thinking is essential for preparing students to
navigate the challenges of the digital age.</p>
    </sec>
    <sec id="sec-5">
      <title>Acknowledgments</title>
      <p>The school experiences have been partially supported by: (i) PON Project “Smart Village: Un Paese
Nel Digitale” Module “Pianifichiamo i Percorsi del Pensiero” codice identificativo
“10.2.2A-FSEPONCL-2018-535”; (ii) Piano Lauree Scientifiche 2017/18 previsto dal D.M. 1047/2017 con l’"Accordo di
Partenariato” in via di definizione tra l’Università degli Studi di Pavia/Università di Milano e l’Università
della Calabria. Other thanks: Caterina Autelitano, the School Principal of “IIS La Cava” High School in
Bovalino, played a crucial role in enabling the PON project; Francesco Bonaparte provided support in
the definition of the project and its successful continuation; Rosita Fiorenza, the School Principal of “IIS
Mazzone” High School in Roccella Ionica, who made possible the collaboration with the University of
Calabria for the PLS project.</p>
    </sec>
    <sec id="sec-6">
      <title>Declaration on Generative AI</title>
      <p>During the preparation of this work, the author used ChatGPT in order to: Grammar and spelling check.
After using this tool, the authors reviewed and edited the content as needed and take full responsibility
for the publication’s content.</p>
    </sec>
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