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    <article-meta>
      <title-group>
        <article-title>An Extension of Datalog for Modelling and Solving Complex Combinatorial Problems</article-title>
      </title-group>
      <contrib-group>
        <aff id="aff0">
          <label>0</label>
          <institution>University of Calabria</institution>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <fpage>7</fpage>
      <lpage>9</lpage>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>
        Datalog is a well-known language that served as a solid theoretical
foundation for many studies in the area of databases [
        <xref ref-type="bibr" rid="ref27">27</xref>
        ]. Although Datalog has been
overtaken by the more appealing SQL language in the software development
market, there has been a renewal of interest in the Datalog language [
        <xref ref-type="bibr" rid="ref25">25</xref>
        ] both in
academia and in industry in the last few years. Two of the main areas in which
Datalog has been adopted as base language include ontological reasoning [
        <xref ref-type="bibr" rid="ref21 ref6">21, 6</xref>
        ]
and logic programming [
        <xref ref-type="bibr" rid="ref22 ref8">8, 22</xref>
        ]. In particular, Datalog is the base language of a
powerful logic programming formalism that is called Answer Set Programming
(ASP) [
        <xref ref-type="bibr" rid="ref20 ref7">20, 7</xref>
        ]. ASP extends Datalog with unrestricted usage of negation in the
body of rules, disjunction in the head of rules, aggregate atoms, hard and weak
constraints, and more.
      </p>
      <p>
        Computational problems, even of high complexity [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ], can be solved in ASP
by specifying a logic program, i.e., a set of logic rules, such that its answer
sets correspond to solutions, and then, using an answer set system to nd such
solutions [
        <xref ref-type="bibr" rid="ref23">23</xref>
        ]. It is worth noting that ASP allows one to solve problems not
even polynomially rewritable to SAT [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. Importantly, a xed ASP program
can be used to model the solution of a problem over varying instances. The
availability of e cient implementations [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ] for such an expressive language made
ASP appealing for the development of applications in several areas [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ], including
deductive databases [
        <xref ref-type="bibr" rid="ref24">24</xref>
        ] and combinatorial problem solving [
        <xref ref-type="bibr" rid="ref11 ref13 ref14 ref18 ref2 ref4 ref5">11, 14, 13, 5, 4, 2, 18</xref>
        ].
      </p>
      <p>
        In our tutorial of the 3rd International Workshop on the Resurgence of
Datalog in Academia and Industry (Datalog 2.0), we present ASP starting from
Datalog, and discussing the role of the main language extension present in the
standard ASPCore2 language [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ]. We also discuss the impact of the constructs
in terms of computational complexity and evaluation procedures. Importantly,
we illustrate the usage of ASP for knowledge representation and reasoning. We
present the Guess-Check-Optimize programming methodology, and show its
application in a number of real-world applications of ASP (developed using DLV [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ],
and WASP [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]). Among these we mention a tool for the automatic generation of
the teams of employees [
        <xref ref-type="bibr" rid="ref26">26</xref>
        ], which has been employed in the sea port of Gioia
Tauro for intelligent resource allocation; and a tool for travel agents that allows
for the intelligent allotment of touristic packages [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ]. Finally, we overview some
programming tools [
        <xref ref-type="bibr" rid="ref12 ref16">12, 16</xref>
        ] provided by the ASPIDE IDE for ASP [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ] that make
more friendly the development of ASP programs and the extension of existing
implementations [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ].
      </p>
    </sec>
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