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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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%%%%%%%%%% macros %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% General Math
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\def\E{{\cal E}} \def\F{{\cal F}} \def\G{{\cal G}} \def\H{{\cal H}}
\def\I{{\cal I}} \def\J{{\cal J}} \def\K{{\cal K}} \def\L{{\cal L}}
\def\M{{\cal M}} \def\N{{\cal N}} \def\O{{\cal O}} \def\P{{\cal P}}
\def\Q{{\cal Q}} \def\R{{\cal R}} \def\S{{\cal S}} \def\T{{\cal T}}
\def\U{{\cal U}} \def\V{{\cal V}} \def\W{{\cal W}} \def\X{{\cal X}}
\def\Y{{\cal Y}} \def\Z{{\cal Z}}

\newcommand{\ALE}{{\cal ALE}}
\newcommand{\Dom}[1]{{\sf Dom(}#1{\sf )}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\semtitle{Description Logics}
\semsubject{Designing Knowledge Bases}
\semauthor{Enrico Franconi}
\sememail{franconi@cs.man.ac.uk}
\semwebpage{http://www.cs.man.ac.uk/\~{}franconi}
\seminstitution{Department of Computer Science, University of Manchester}

\begin{document}

\makesemtitle

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{The Royal Family}

{\footnotesize 

$
\begin{array}{rcl}
{\tt Male } & \doteq & {\tt \Not Female}  \\
{\tt Woman } & \doteq & {\tt Human \And Female}  \\
{\tt Man } & \doteq & {\tt Human \And Male}  \\
{\tt Mother } & \doteq & {\tt Woman \And \some{CHILD}{Human}}  \\
{\tt Father } & \doteq & {\tt Man \And \some{CHILD}{Human}}  \\
{\tt Parent } & \doteq & {\tt Father \Or Mother}  \\
{\tt Grandmother } & \doteq & {\tt Woman \And \some{CHILD}{Parent}}  \\
{\tt Mother{-}w/o{-}doughter } & \doteq & {\tt Mother \And \all{CHILD}{Male}}  \\
{\tt Super{-}mother } & \doteq & {\tt Mother \And \atleast 3 CHILD}  \\
\end{array}
$

\vspace{1em}

\MiniPage
{\tt
Woman(elisabeth), Woman(diana),\\
Man(charles), Man(edward), \\
Man(andrew),\\
Mother{-}w/o{-}doughter(diana),}%
{\tt CHILD(elisabeth,charles),\\
CHILD(elisabeth,edward),\\
CHILD(elisabeth,andrew),\\
CHILD(diana,william),\\
CHILD(charles,william)}

}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Taxonomy}

      \includegraphics[width=.9\textwidth]{royal.eps}
%\epsfxsize=\textwidth
%\epsfbox{royal.eps}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Questions}

\begin{itemize}

\item What happens if we add to the knowledge base:

\vspace{1em}

{\tt CHILD(diana,margaret), Female(margaret)}

\vspace{2em}

\item $\Sigma\stackrel ? \models $ {\tt Super{-}mother(elisabeth)}

\item $\Sigma\stackrel ? \models\Not ${\tt Female(william)}

\item $\Sigma\stackrel ? \models $ {\tt Mother{-}w/o{-}doughter(elisabeth)}

\vspace{1em}

\item Which are the most specific concepts of which {\tt elisabeth} is
  instance (realization problem)?

\vspace{1em}

\item Retrieve all the instances of {\tt Male}.

\end{itemize}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Inclusion Axioms}

{\footnotesize 

$
\begin{array}{rcl}
{\tt \some{TEACHES}{Course}} & \IsSubs & 
  {\tt (Student\And\some{DEGREE}{Bs})\Or Prof} \\
{\tt Prof} & \IsSubs & {\tt \some{DEGREE}{Ms}} \\
{\tt \some{DEGREE}{Ms}} & \IsSubs & {\tt \some{DEGREE}{Bs}} \\
{\tt Ms\And Bs} & \IsSubs & {\tt \bot} \\
\end{array}
$

\vspace{3em}

{\tt

TEACHES(john,cs156),\\
($\atmost 1 {\tt DEGREE}$)(john),\\
Course(cs156)

}

\vspace{3em}

{\tt
$\Sigma\stackrel ? \models$ Student(john)
}

}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Cardinality and sub-roles}

{\footnotesize 

$
\begin{array}{rcl}
{\tt Man} & \IsSubs & {\tt Human} \\
{\tt Woman} & \IsSubs & {\tt Human \And \Not Man}\\
{\tt Team} & \doteq & {\tt Set \And \all{MEMBER}{Human}\And \atleast 2 {MEMBER}} \\
{\tt LEADER} & \IsSubs & {\tt MEMBER} \\
{\tt Modern{-}team} & \doteq & \parbox[t]{\textwidth}{$
{\tt Team \And \atmost 4 {MEMBER}\ \And} \\{\tt 
\atleast 1 {LEADER} \And \all{LEADER}{Woman}}$} \\
\end{array}
$

\vspace{1em}

{\tt

Modern{-}team(gamma),\\
Man(tom), Man(dick), Human(mary),\\
MEMBER(gamma, tom), \\
MEMBER(gamma, dick), \\
MEMBER(gamma, mary), \\
($\atmost 3 {\tt MEMBER}$)(gamma)

}

\vspace{1em}

{\tt
$\Sigma\stackrel ? \models$ Woman(mary)
}

}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Cardinality and sub-roles - II}

$
\begin{array}{rcl}
{\tt DAUGHTER} & \IsSubs & {\tt CHILD}\\
{\tt SON} & \IsSubs & {\tt CHILD}\\
{\tt Female} & \IsSubs & \Not{\tt Male}\\
\end{array}
$

\vspace{3em}

$\atleast 2 {\tt  SON} \And
 \atleast 2 {\tt DOUGHTER}\ \And $\\
$ \all{\tt SON}{\tt Male} \And \all{\tt DAUGHTER}{\tt Female}
$

\vspace{1em}

\tab\tab{$\stackrel ? \IsSubs$}

\vspace{1em}

$\atleast 4 {\tt CHILD}$



\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Cardinality, sub-roles, and functional roles}

{\footnotesize 

$
\begin{array}{rcl}
{\tt DAUGHTER} & \IsSubs & {\tt CHILD}\\
\end{array}
$

\vspace{3em}


$\hspace{-4em}\begin{array}{rl}

\mbox{\overlay{1}NO} & {\tt \Sigma\stackrel ? \models 
 \some{CHILD}{Rich}\IsSubs\some{DAUGHTER}{Rich}} \\

\mbox{\overlay{1}YES} & {\tt \Sigma\stackrel ? \models 
 \some{DAUGHTER}{Rich}\IsSubs\some{CHILD}{Rich}} \\

\mbox{\overlay{1}YES} & {\tt \Sigma\stackrel ? \models 
 \all{CHILD}{Rich}\IsSubs\all{DAUGHTER}{Rich}} \\

\mbox{\overlay{1}NO} & {\tt \Sigma\stackrel ? \models 
 \all{DAUGHTER}{Rich}\IsSubs\all{CHILD}{Rich}} \\

\mbox{\overlay{1}NO} & {\tt \Sigma\stackrel ? \models
  \all{CHILD}{Rich}\And\usome{CHILD}\IsSubs\all{DAUGHTER}{Rich}\And
  \usome{DAUGHTER}} \\

\mbox{\overlay{1}NO} & {\tt \Sigma\stackrel ? \models
  \all{DAUGHTER}{Rich}\And\usome{DAUGHTER}\IsSubs\all{CHILD}{Rich}
  \And\usome{CHILD}} \\

\end{array}$

\vspace{3em}

What if the roles are functional?

}


\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{}

${\tt \Sigma\models 
 \all{CHILD}{Rich}\IsSubs\all{DAUGHTER}{Rich}}$

\vspace{3em}

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\end{center}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{}

  {\footnotesize ${\tt
      \all{CHILD}{Rich}\And\usome{CHILD}\not\sim\all{DAUGHTER}{Rich}\And\usome{DAUGHTER}}$}

\vspace{3em}

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\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Tests}

\begin{itemize}

\item In order to allow {\em procedures} to be used in specifying concepts,
  the {\tt TEST-C} operator is used.

\item A test restriction requires that an individual must pass the test to
  satisfy the restriction.

\end{itemize}

\vspace{1em}

{\em Example:}

${\tt Even{-}integer \doteq Integer \And (\mbox{:TEST{-}C } {\sc evenp})}$

where {\sc evenp} is a function in the host language.

\vspace{1em}

The reasoning procedures are changed in a way that individuals {\em passing}
some test function ``{\sf f}'' will be in the extension of the concept
$(\mbox{\tt :TEST{-}C } {\sf f})$. The individual to be tested is passed as
an argument to the function.

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Test functions}

Test functions return one of three values when applied to an individual:

\begin{itemize}

\item {\sc false}: the individual is inconsistent with the restriction.

\item {\sc unknown}: the individual is consistent with the restriction, but
  if information is added to the individual, the individual may become
  either inconsistent with or provably described by the restriction.

\item {\sc true}: the individual definitely passes the test, i.e., it
  provably satisfies it.

\end{itemize}

Test functions must be monotonic; that is, it should not be possible for the
same test function to return {\sc true} (or {\sc false}) for an individual
at one time, and {\sc false} (or {\sc true}) at a later time, when the
information regarding the individual has been refined.

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Forward-chaining Rules}

\begin{itemize}

\item A rule consists of an antecedent and a consequent.

\item An antecedent is always a concept name.

\item A consequent is a generic concept description.

\end{itemize}

\vspace{2em}

As soon as an individual is known to be in the extension of the antecedent
concept, the rule is triggered, and the individual is also known to satisfy
the consequent concept.

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Forward-chaining Rules}

\begin{itemize}

\item Intuitively, a rule $A \Longrightarrow C$ seems to have the same
  semantics as $A\IsSubs C$, in the sense that every individual in $A$
  should be also in $C$. 

\item However, a careful formal analysis shows that a rule is an
  autoepistemic statement, with a nonmonotonic behaviour.

\item Rules play a role only for individuals, and not for concept
  definitions.

\item They are mostly used for expressing contingent properties.

\end{itemize}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Integrity Checking}
  
\vspace{-1em}

\begin{itemize}

\item The aim of integrity checking is to support the activity of populating
  the KB with additional checks on the structures of the individuals w.r.t.
  to the concepts they are instances of.
  
\item This can not be obtained by adding extra restrictions (tests) to the
  definition of the concepts, because this would modify it (with problems
  for the classification).

\item The solution: Rule + Test.

\end{itemize}

%\vspace{1em}

{\em Example:}

  ${\tt Late{-}harvest{-}grape \Longrightarrow (\mbox{:TEST{-}C}\ 
    {\sc sugar{>}30})}$
  
  Where the test function {\sc sugar{>}30} provides (if it is the case) to
  remove the candidate instance from the {\tt Late-harvest-grape} concept,
  too.

%\vspace{1em}

Rule + Test can also emulate {\em methods}.

\end{slide}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Modelling a Museum}

      \includegraphics[width=.7\textwidth]{reif.eps}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Concept as Role}

\begin{itemize}

\item The painting {\em The Announcement} of Giotto's is in Florence.

\item The painting {\em The Announcement}, painted by Giotto in 1285 in
  Venice, is in Florence.

\end{itemize}

\vspace{2em}

${\tt Painter \IsSubs \all {PAINTING} {Painting}}$

${\tt Painting \IsSubs \all {AUTHOR} {Painter}}$

${\tt PaintEvent \IsSubs \some {WHO} {Painter} \And \some {WHAT}
  {Painting}}$

\vspace{2em}

\begin{itemize}

\item This TBox forces redundancy.

\item This TBox does not reveal inconsistencies.

\item This TBox is cyclic.

\end{itemize}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Redundant KB}

{\footnotesize
${\tt Painter \IsSubs \all {PAINTING} {Painting}}$

${\tt Painting \IsSubs \all {AUTHOR} {Painter}}$

${\tt PaintEvent \IsSubs \some {WHO} {Painter} \And \some {WHAT}
  {Painting}}$

\vspace{1ex}

{\tt
Painter(giotto),}

\begin{minipage}[t]{.55\hsize}
{\tt PAINTING(giotto, announcement),\\
Painting(announcement),\\
AUTHOR(announcement, giotto),
\vspace{1em}\\
PAINTING(giotto, escape),\\
Painting(escape),\\
AUTHOR(escape, giotto),}
\end{minipage}
\begin{minipage}[t]{.44\hsize}
{\tt PaintEvent(e1),\\
WHO(e1, giotto),\\
WHAT(e1, announcement),
\vspace{1em}\\
PaintEvent(e2),\\
WHO(e2, giotto),\\
WHAT(e2, escape)}
\end{minipage}
}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Reification}

\vspace{-1em}

${\tt \forall xy\per \parbox[t]{\textwidth}{${\tt {PAINTING}(x,y)
      \leftrightarrow {AUTHOR}(y,x)\leftrightarrow }$\\${\tt \exists z\per
      {PaintEvent}(z)\wedge {WHO}(z,x)\wedge {WHAT}(z,y)}$}}$

\vspace{1ex}

${\tt PaintEvent \IsSubs \some {WHO} \And \atmost 1 {WHO} \And \some
  {WHAT} \And \atmost 1 {WHAT} }$

${\tt Painter \doteq \some {\inv{WHO}} {PaintEvent}}$

${\tt Painting \doteq \some {\inv{WHAT}} {PaintEvent}}$

${\tt PAINTING \doteq \restrict{\inv{WHO}}{PaintEvent}\comp{WHAT} }$

${\tt AUTHOR \doteq \restrict{\inv{WHAT}}{PaintEvent}\comp{WHO} }$

\vspace{1ex}

{\footnotesize
{\tt
PaintEvent(e1),
WHO(e1, giotto),
WHAT(e1, announcement)
}

\vspace{1ex}

$\models$\smalltab \parbox[c]{\textwidth}{\tt Painter(giotto),
  \\PAINTING(giotto, announcement),\\ Painting(announcement),\\ 
  AUTHOR(announcement, giotto) }
}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{}

{\footnotesize
{\tt

PAINTING(giotto, announcement)

}

\vspace{1em}

$\models$\smalltab \parbox[c]{\textwidth}{\tt Painter(giotto),\\ 
  Painting(announcement),\\ AUTHOR(announcement, giotto)}
}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Building Knowledge Bases}

  In order to build good KBs some choices must be done during its design. It
  is important to well understand some subtle distinctions:

\begin{itemize}
\item Primitive vs. Defined.
\item Definitional vs. Incidental.
\item Concept vs. Individual.
\item Concept vs. Role.
\end{itemize}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{When to Use Primitive Concepts?}

\begin{itemize}
\item some concepts can not be completely defined (e.g. natural kinds);
\item it can be not convenient/useful to completely define a concept;
\item sooner or later we must end up with something not completely defined
  ({\em encyclopedic knowledge} cannot be given).
\end{itemize}


Thus, primitive concepts must be used when:
\begin{itemize}
\item there is no other way;
\item even if it were defined, no (automatic) classification below it will
  be never required by the application.
\end{itemize}

Typically primitive concepts lie in the top region of the taxonomy.

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{When to Use Defined Concepts?}

\begin{itemize}
\item ontological reason: it is easy and natural (in the context of the
  application) to give a complete definition of the concept;
\item organisation of the antecedents of rules;
\item capturing complete descriptions used by rules for populating primitive
  concepts.
\end{itemize}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Definitional vs. Incidental}
  
  Are {\em incidental\/} all the properties that are contingent features for
  a concept, and thus must not be part of its definition. 

  \vspace{1em}

  {\em Examples:} 

  ${\tt (\all {SUGAR} {Dry})}$
  
  is incidental for the concept {\color{blue}{\tt RED-BORDEAUX-WINE}},
  while not

  ${\tt (\all {COLOR} {Red}) \smalltab\mbox{and}\smalltab (\all {REGION}
    {Bordeaux})}$

\vspace{1em}

${\tt (\all {INTELLIGENCE} {Stupid})}$ 

is incidental for {\color{blue}{\tt CHICKEN}}, while not

${\tt (\all {REPRODUCES{-}WITH} {Egg})}$ 



\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Concept vs. Individual}

\begin{itemize}
\item the set of individuals is a countable, discrete set;
\item the concept space is ideally continuous and infinite;
\item each individual has a clear identity: even if two individual have the
  same properties, they are distinct;
\item if two concepts have equivalent descriptions, they {\bf denote the
    same} concept;
\item individual descriptions can be modified;
\item concept descriptions can not be modified;
\item individual update does not (usually) change the concept hierarchy;
\item rules applies only to individuals.
\end{itemize}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Concept vs. Individual, cont.}

Nevertheless, it is not always easy to decide whether an object should be a
concept or an individual. The main issue to deal with is the ``granularity''
level.

\vspace{2em}


{\em Example:}

Consider the KB describing courses in a Computer Science department : is
``Introduction To Data Structures And Algorithms (503)'' course a concept or
an individual?
 
\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Individual vs. Concept}

Another example: if we have {\tt Wine} and {\tt White-wine}, what about:
\begin{itemize}
\item chardonay-wine
\item forman-chardonay
\item 1981-forman-chardonay
\item 1981-forman-chardonay-from-vineyard32
\item 1981-forman-chardonay-from-in-cask18
\item 1981-forman-chardonay-bottle\#1576
\end{itemize}

A key to solve the problem could be asking the domain/application expert:
``how many wines do you have?'', in order to understand the needed
granularity.  \vspace{1cm}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Concept vs. Role}

Is not always easy to decide what must be a concept and what a role.

E.g.:
\begin{itemize}
\item {\sc Person}: it is a concept.
\item {\sc Mother}: 
\begin{itemize}
\item consider ``Sue is a new mother'' and ``Sue is the mother of Tom''
\item {\tt Mother} as a concept does not exist if we don't consider the
  ``role she plays'' in a parental relation, i.e., if ``Sue is a new
  mother'' she must be the {\tt MOTHER} of somebody!
\end{itemize}
\end{itemize}

\vspace{1em}

Thus:

${\tt
  Mother \doteq (Woman \And (\some {\tt MOTHER} {\tt Person}))
}$

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{Concept vs. Role}

\begin{itemize}

\item But when the role is not the only important component of the
  definition, this dual use is not so neat (consider {\tt VINTAGE}, {\tt
    GRAPE}).


\item Another problem is the {\sl reading direction}: in the above example
  the role could be, {\tt MOTHER} or {\tt CHILD}.


\item A clear convention must be stated, possibly creating long, non
  ambiguous names for roles, as, e.g.: {\tt HAS-CHILD, IS-THE-PARENT-OF,
    HAS-VINTAGE, HAS-GRAPE}.

\item As an alternative, the adoption of long names for concepts can be also
  suggested: e.g., {\tt WINE-GRAPE}.

\end{itemize}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{How to design a KB in steps (1-3)}

  \begin{itemize}
  \item {\bf Enumerate Objects}. As a bare list of elements of the KB; they
    will became individuals, concepts, or role.
  \item {\bf Distinguish Concepts from Roles}. Make a first decision about
    what object must be considered role; remember that some could have a
    ``natural'' concept associated. The remaining objects will be concepts
    (or maybe individuals). Also, try to distinguish roles from attributes.
  \item\label{taxonomy} {\bf Develop Concept Taxonomy}. Try to decide a
    classification of all the concepts, imagining their extensions. This
    taxonomy will be used as a first reference, and could be revised when
    definition will be given. It will be used also to check if definition
    meet our expectations (sometime, interesting, unforeseen
    (re)classifications are found).

  \end{itemize}
\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{How to design a KB in steps (4-5)}

  \begin{itemize}
  \item {\bf Devise partitions}. Try to make explicit all the disjointness
    and covering constraints among classes, and reclassify the concepts.
  \item {\bf Individuals}. Try to list as many as possible {\sl generally\/}
    useful individuals . Some could have been already listed in step 1. Try
    to describe them (classify).

  \end{itemize}
\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{How to design a KB in steps (6)}

  \begin{itemize}
  \item {\bf Properties and Parts}. Begin to define the internal structure
    of concepts (this process will continue in the next steps). For each
    concept list:
    \begin{itemize}
    \item {\em intrinsic\/} properties, that are part of the very nature
      of the concept;
    \item {\em extrinsic\/} properties, that are contingent or external
      properties of the object; they can sometime change during the time;
    \item {\em parts}, in the case of structured or collective objects.
      They can be physical (e.g., ``the components of a car'', ``the casks
      of a winery'', ``the students of a class'', ``the members of a
      group'', {\sl ``the grape of a wine''\/}) or abstract (e.g., {\sl
        ``the courses of a meal''}, ``the lessons of a course'', {\sl ``the
        topics of a lesson''\/}).
    \end{itemize}

  \end{itemize}

\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{slide}{How to design a KB in steps (6)}

  \begin{itemize}
  \item In some cases some relationships between individuals of
    classes can be considered too accidental to be listed above (e.g.,
    ``the employees of a winery''; but the matter could change if we
    consider {\tt Winery} as a subconcept of {\tt Firm}).
    
  \item In general, the above distinctions depend on the level of
    detail adopted.
    
  \item Some of the listed roles will be later considered
    definitional, and some incidental.
    
  \item After this and the next steps check/revision of the taxonomy
    could be necessary.

  \end{itemize}
\end{slide}

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\begin{slide}{How to design a KB in steps (7-12)}

  \begin{itemize}
  \item {\bf Cardinality Restrictions.} For the relevant roles for each
    concept.
  \item {\bf Value Restriction.} As above. Also, chose the right
    restriction.
  \item {\bf Propagate Value Restrictions.} If some value
    restrictions stated in the previous step does not correspond to already
    existing concepts, they must be defined.
  \item {\bf Inter-role Relationship.} Even if hardly definable in DL, they
    can be useful during the populating and debugging phases.
  \item {\bf Definitional and Incidental.} It is important distinguish
    between definitional and incidental properties, w.r.t. to the particular
    application.
  \item {\bf Primitive and Defined.} As above.
  \end{itemize}
  
\end{slide}

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\end{document}
