\noindent The field of machine learning (ML) is concerned with the question of how to construct algorithms that automatically improve with experience. In recent years many successful ML applications have been developed, such as datamining programs, information-filtering systems, etc. Although ML algorithms allow the detection and extraction of interesting patterns of data for several kinds of problems, most of these algorithms are based on quantitative reasoning, as they rely on training data in order to infer so-called target functions. In the last years defeasible argumentation has proven to be a sound setting to formalize common-sense qualitative reasoning. This approach can be combined with other inference techniques, such as those provided by machine learning theory. In this paper we outline different alternatives for combining defeasible argumentation and machine learning techniques. We suggest how different aspects of a generic argument-based framework can be integrated with other ML-based approaches.
cs0402057.tex


%  Paper WICC 2003
%- fuente Time New Roman de 12 puntos.
%- simple espacio.
%Longitud: 3 a 5 p�ginas.
%   M�rgenes: superior 30 mm (1.2"); inferior,
%             derecho e izquierdo 20mm (0.7").
%   Formato del texto: Fuentes Times 12 para el texto.
%     sin n�mero de p�gina, ni encabezados, ni pie de p�gina.


\documentclass[12pt]{article}

%\usepackage{vmargin}
%\setpapersize{A4}
%\setmarginsrb{2cm}{3cm}{2cm}{2cm}{0pt}{0pt}{0pt}{0pt}

\usepackage{xspace}
\usepackage{latexsym}


\pagestyle{empty}

%
%  Adaptado para articulo a partir del archivo DEFPHD.TEX
%  usado en la Tesis
%
%


%=============== DEFINICIONES PARA LA TESIS DOCTORAL ============
% (C) Carlos I. Ches�evar, 1998 - U.N.S.
% Ultima actualizacion: 18 octubre 1999
%
%===============================================================
% 0) Convenciones
% 1) Unidades de medida, hyphenations y abreviaturas
% 2) Comandos y entornos varios
% 3) Comandos y entornos tecnicos
%===============================================================

% ================================================================
%                         0) Convenciones
% ================================================================
% a) Todas las referencias tienen prefijos que identifican
%    su origen:
%    Ejem = referencia para ejemplos  (ej: EjemVehiculos)
%    Fig  = referencia para figuras   (ej: FigArbolDialectico)
%    D    = referencia para definicion (ej: DEspecificidad)
% b) Toda figura est\'a antecedida por
%    ----- Comienzo de figura -----
%    y termina con
%    ----- Fin de figura -----
%




%\newcommand{\Hipot}{\mbox{${\cal H}$}}

\newcommand{\chesne}{Ches{\~n}evar, C.I.}

\newcommand{\warranted}{\mbox{\emph{warranted}}\xspace}
\newcommand{\warrant}{\mbox{\emph{warrant}}\xspace}
\newcommand{\Warrant}{\mbox{\emph{Warrant}}\xspace}



\newcommand{\UnaSecFrames}{\mbox{$\Lambda$}\xspace}

\newcommand{\SecFrames[1]}{\mbox{$\Lambda_{#1}$}\xspace}


%
% Comandos auxiliares del capitulo 5
%



\newcommand{\citahip}[1]{~(\ref{#1})}

\newcommand{\Thsld}{\mbox{\textsl{Th}$_{_{sld}}$}\xspace}

\newcommand{\Clarg}{\mbox{\textsl{C}$_{_{arg}}$}\xspace}
\newcommand{\Clwar}{\mbox{\textsl{C}$_{_{war}}$}\xspace}

\newcommand{\Depth}[1]{\ensuremath{\mbox{\textsf{Depth}}(#1)}}

\newcommand{\sld}{\mbox{\textsc{Sld}}\xspace}

\newcommand{\War}[1]{\ensuremath{#1^{\textsl{U}}}\xspace}









%
% Comandos auxiliares para pruebas de si y solo si
%

\newcommand{\ParaUnLado}{\noindent$(\Longrightarrow)$\xspace}

\newcommand{\ParaElOtroLado}{\noindent$(\Longleftarrow)$\xspace}



%
%  Comandos capitulo 3
%


\newcommand{\Arx}[2]{\mbox{\du{\ArgSeti{A}{#1}}{#2}}}

\newcommand{\Marked}[2]{\mbox{$#1^{#2}$}}

\newcommand{\Undefeated}[2]{\mbox{$U(#1)$}}
\newcommand{\Defeated}[2]{\mbox{$D(#1)$}}

\newcommand{\Pruned}[1]{$Pruned(#1)$}



%============================================================
%
% SISTEMAS LOGICOS definibles a partir como SDEA
%
%============================================================


\newcommand{\InferCred} %{\mbox{$\mid\hspace{-2pt}\sim_{_{cred}}\ $}}
 {\mbox{${\Infer}_{_{\vspace*{6mm}{\hspace*{-9pt}cred}}}$}}


%============================================================

\newcommand{\InferSL} %{\mbox{$\mid\hspace{-2pt}\sim_{_{SL}}\ $}}
  {\mbox{${\Infer}_{_{\vspace*{6mm}{\hspace*{-9pt}SL}}}$}}

\newcommand{\MPenSL}{\mbox{{\sf MP-\SDEsl}}}
%============================================================

\newcommand{\InferMTDR} %{\mbox{$\mid\hspace{-2pt}\sim_{_{SL}}\ $}}
  {\mbox{${\Infer}_{_{\vspace*{6mm}{\hspace*{-9pt}\textsl{MTDR}}}}$}}

\newcommand{\EquivMTDR}{\mbox{{\sf Contraposition-\MTDR}}}
%============================================================



\newcommand{\IntroAss}{\mbox{{\sf Intro-assumption}}}

%============================================================

\newcommand{\InferDelp} %{\mbox{$\mid\hspace{-2pt}\sim_{_{SL}}\ $}}
  {\mbox{${\Infer}_{_{\vspace*{6mm}{\hspace*{-9pt}\textsl{LP}}}}$}}





%============================================================



\newcommand{\InferNeg} %{\mbox{$\mid\hspace{-2pt}\sim_{_{SL}}\ $}}
  {\mbox{${\Infer}_{_{\vspace*{6mm}{\hspace*{-9pt}\textsl{neg}}}}$}}

\newcommand{\InferNot} %{\mbox{$\mid\hspace{-2pt}\sim_{_{SL}}\ $}}
  {\mbox{${\Infer}_{_{\vspace*{6mm}{\hspace*{-9pt}\textsl{not}}}}$}}

\newcommand{\InferNlp} %{\mbox{$\mid\hspace{-2pt}\sim_{_{SL}}\ $}}
  {\mbox{${\Infer}_{_{\vspace*{6mm}{\hspace*{-9pt}\textsl{NLP}}}}$}}




\newcommand{\ProgNLP}{\mbox{$\textsl{Prog}_\mathcal{L}$}\xspace}
%============================================================




\newcommand{\SDEar}{\textsl{LDS}$_{AR}$\xspace}

\newcommand{\SDEx}{\textsl{AS}$_{_{\mathsf{x}}}$\xspace}

\newcommand{\SDEcred}{\textsl{AS}$_{_{\mathsf{cred}}}$\xspace}
\newcommand{\SDEskep}{\textsl{AS}$_{_{\mathsf{LP}}}$\xspace}
\newcommand{\SDEdelp}{\textsl{AS}$_{_{\mathsf{LP}}}$\xspace}
\newcommand{\SDEmtdr}{\textsl{AS}$_{_{\mathsf{MTDR}}}$\xspace}
  \newcommand{\SDEsl}{\textsl{AS}$_{_{\mathsf{SL}}}$\xspace}
 \newcommand{\SDEneg}{\textsl{AS}$_{_{\mathsf{neg}}}$\xspace}
 \newcommand{\SDEnot}{\textsl{AS}$_{_{\mathsf{not}}}$\xspace}
 \newcommand{\SDEnlp}{\textsl{AS}$_{_{\mathsf{NLP}}}$\xspace}  % Kakas-Toni

%============================================================


\newcommand{\simsim}{\sim\hspace{-1em}\vspace{1pt}\sim}
\newcommand{\InferX}{\mbox{$\mid\hspace{-2pt}\simsim\ $}}


% ============ COMANDOS EN GENERAL ==============================
%                 PARA ENTORNOS


\newtheorem{definition}{Definition}[section]
\newtheorem{example}[definition]{Example}
\newtheorem{proposition}[definition]{Proposition}
\newtheorem{theorem}[definition]{Theorem}
\newtheorem{lemma}[definition]{Lemma}
\newtheorem{corollary}[definition]{Corollary}
\newtheorem{observation}{Note}[section]

\newcommand{\email}[1]{\texttt{#1}}
\newcommand{\qed}{\rule{2mm}{2mm}}
\newenvironment{proof}{\noindent {\bf Demostraci\'on:}}{\hfill \qed}



% =================== SEMANTICA =======================================
%\newcommand{\MM}{\mbox{\underline{$\cal M$}}}



%%% Some new macros;  27.11

\newcommand{\AssLiteral}[1]{\ensuremath{\mathsf{assume}\,#1}\xspace}
\newcommand{\assume}[1]{\ensuremath{\srule{\mathsf{assume}#1}{}}\xspace}
\newcommand{\definedas}{\ensuremath{{=}_{_{\mathit{def}}}}\xspace}

%%% Some other new macros;  3.12

\newcommand{\HerbrandBaseNot}{\ensuremath{\mathcal{HB}_{\mathsf{ass}}}\xspace}
\newcommand{\Asm}[1]{\ensuremath{\textsl{Asm}(#1)}\xspace}
\newcommand{\Drules}[1]{\ensuremath{\mathcal{R}_{#1}}\xspace}



\newcommand{\comi}[1]{`#1'}




%%%%%%%%%%%%%%%%%%%%%  Semantica - Comandos para reglas de transformaci\'on

\newcommand{\NLP}{\textsl{NLP}\xspace}
\newcommand{\progP}{\ensuremath{\mathcal{P}}\xspace}
\newcommand{\prog}[1]{\ensuremath{\mathcal{P}_{\mathit{#1}}}\xspace}
\newcommand{\lpnot}{\ensuremath{\mathsf{not}\,}\xspace}
\newcommand{\Lang}{\mathcal{L}\xspace}
%\newcommand{\skippar}[1]{}


\newcommand{\SEM}{\ensuremath{\text{SEM}_{\text{min}}}\xspace}
\newcommand{\sem}{\text{SEM}\xspace}
\newcommand{\wfs}{\text{WFS}\xspace}
\newcommand{\undef}{\textrm{undef}\xspace}
\newcommand{\semdelp}{\ensuremath{\text{SEM}_{\textsl{DeLP}}}\xspace}


\newcommand{\semlp}{\ensuremath{\text{SEM}_{\textsl{LP}}}\xspace}


\newcommand{\normwfs}[1]{\ensuremath{\mathit{norm}_{\wfs}(#1)}\xspace}
\newcommand{\HEAD}{\textsf{Head}\xspace}
\newcommand{\transf}{\ensuremath{\mapsto}\xspace}
\newcommand{\isimpl}{\ensuremath{\,\gets\,}\xspace}


\newcommand{\Argum}[2]{\ensuremath{\langle #1, #2 \rangle}\xspace}

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



\newcommand{\PiModelo}{$\Pi$-modelo\xspace}
\newcommand{\PiModelos}{$\Pi$-modelos\xspace}

\newcommand{\PiFrame}{$\Pi$-frame\xspace}
\newcommand{\PiFrames}{$\Pi$-frames\xspace}




\newcommand{\FFa}{\mbox{\underline{${\cal F}_1$}}}
\newcommand{\FFb}{\mbox{\underline{${\cal F}_2$}}}


\newcommand{\CoFinal}{\mbox{$CoFinal$}}


\newcommand{\VTrue}{\textbf{True}}
\newcommand{\VFalse}{\textbf{False}}
\newcommand{\VUndef}{\textbf{Undef}}


%
%   CAPITULO 4: Comandos auxiliares para la semantica
%
%

\newcommand{\ClaseModelo}[1]{\ensuremath{{\protect\mathfrak{M}_{\scriptsize #1}}}\xspace}
\newcommand{\Modelo}[1]{\ensuremath{{\protect\EuScript{M}_{#1}}}\xspace}


% Modelo
\newcommand{\MM}{\ensuremath{{\protect\EuScript{M}}}\xspace}

% Clase de modelos
\newcommand{\ClaseMM}{\ensuremath{{\protect\mathfrak{M}}}\xspace}

\newcommand{\ClaseMMa}{\ensuremath{{\protect\mathfrak{M}_{1}}}\xspace}
\newcommand{\ClaseMMb}{\ensuremath{{\protect\mathfrak{M}_{2}}}\xspace}
\newcommand{\ClaseMMc}{\ensuremath{{\protect\mathfrak{M}_{2}}}\xspace}


% Clase de modelos finales
\newcommand{\ClaseFFa}{\ensuremath{{\protect\mathfrak{F}_{1}}}\xspace}
\newcommand{\ClaseFFb}{\ensuremath{{\protect\mathfrak{F}_{2}}}\xspace}

% Clase de modelos de acuerdo

\newcommand{\ClaseAAa}{\ensuremath{{\protect\mathfrak{Agree}_{1}}}\xspace}
\newcommand{\ClaseAAb}{\ensuremath{{\protect\mathfrak{Agree}_{2}}}\xspace}

\newcommand{\ClaseAgree}[1]{\ensuremath{{\protect\mathfrak{Agree}_{#1}}}\xspace}



% Clase de modelos de justificaci\'on

\newcommand{\ClaseJJa}{\ensuremath{{\protect\mathfrak{Agree}_{1}}}\xspace}
\newcommand{\ClaseJJb}{\ensuremath{{\protect\mathfrak{Agree}_{2}}}\xspace}

\newcommand{\ClaseJus}[1]{\ensuremath{{\protect\mathfrak{Jus}_{#1}}}\xspace}
\newcommand{\ClaseWar}[1]{\ensuremath{{\protect\mathfrak{Warrant}_{#1}}}\xspace}



\newcommand{\MMa}{\Modelo{1}}
\newcommand{\MMb}{\Modelo{2}}
\newcommand{\MMc}{\Modelo{3}}



% Clase de arbol de frames

\newcommand{\FrameTree}[1]{\ensuremath{{\protect\mathfrak{Tree}(#1)}}\xspace}






% =============================================================
%   DELPneg, y variantes
% =============================================================

\newcommand{\DELP}{\textsl{DeLP}\xspace}
\newcommand{\DLP}{\DELP}
\newcommand{\DELPneg}{\ensuremath{\textsl{DeLP$_{neg}$}}\xspace}
\newcommand{\DELPnot}{\ensuremath{\textsl{DeLP$_{\textsf{not}}$}}\xspace}
\newcommand{\WDELPnot}{\ensuremath{\textsl{DeLP$_{\textsf{not*}}$}}\xspace}
\newcommand{\dlp}{\textsl{dlp}\xspace}
\newcommand{\nlp}{\textsl{nlp}\xspace}





% =============================================================
%   Transformation names for DELPneg
% =============================================================


\newcommand{\TPlusNeg}{\ensuremath{\mapsto_{Pneg}}\xspace}
\newcommand{\TMinusNeg}{\ensuremath{\mapsto_{Mneg}}\xspace}
\newcommand{\TSubNeg}{\ensuremath{\mapsto_{Sneg}}\xspace}
\newcommand{\TUnfoldNeg}{\ensuremath{\mapsto_{Uneg}}\xspace}
\newcommand{\TTautNeg}{\ensuremath{\mapsto_{Tneg}}\xspace}

% Unfolding in one step for DELPneg
\newcommand{\TUONEneg}[1]{\ensuremath{\mapsto_{Uneg}^{#1}}\xspace}



% =============================================================
%
%   Transformation names for DELPnot
%
% =============================================================


\newcommand{\TPlusNot}{\ensuremath{\mapsto_{R^{+}not}}\xspace}
\newcommand{\TMinusNot}{\ensuremath{\mapsto_{R^{-}not}}\xspace}
\newcommand{\TSubNot}{\ensuremath{\mapsto_{Snot}}\xspace}
\newcommand{\TUnfoldNot}{\ensuremath{\mapsto_{Unot}}\xspace}
\newcommand{\TTautNot}{\ensuremath{\mapsto_{Tnot}}\xspace}

% Unfolding in one step for DELPnot
\newcommand{\TUONEnot}[1]{\ensuremath{\mapsto_{Unot}^{#1}}\xspace}


%  Note:
%  \TUONEneg  and \TUONEnot are one-step-unfolding
%  for DELPneg and DELPnot, resp.
%  But they can be denoted with the same symbol, since they
%  do not differ.





% transformation rules

\newcommand{\REDplus}{\ensuremath{\textbf{RED}^{+}}\xspace}
\newcommand{\REDminus}{\ensuremath{\textbf{RED}^{-}}\xspace}
\newcommand{\SUB}{\ensuremath{\textbf{SUB}}\xspace}
\newcommand{\UNFOLD}{\ensuremath{\textbf{UNFOLD}}\xspace}
\newcommand{\TAUT}{\ensuremath{\textbf{TAUT}}\xspace}







% transformation names for DELPneg and DELPnot
%%% DELPneg

\newcommand{\REDplusneg}{\ensuremath{\textbf{RED}^{+}_{neg}}\xspace}

\newcommand{\REDminusneg}{\ensuremath{\textbf{RED}^{-}_{neg}}\xspace}

\newcommand{\SUBneg}{\ensuremath{\textbf{SUB}_{neg}}\xspace}

\newcommand{\UNFOLDneg}{\ensuremath{\textbf{UNFOLD}_{neg}}\xspace}

\newcommand{\UONEneg}[1]{\ensuremath{\textbf{UNFOLD}_{neg}^{#1}}\xspace}

\newcommand{\TAUTneg}{\ensuremath{\textbf{TAUT}_{neg}}\xspace}

%%% DELPnot

\newcommand{\REDplusnot}{\ensuremath{\textbf{RED}^{+}_{not}}\xspace}

\newcommand{\REDminusnot}{\ensuremath{\textbf{RED}^{-}_{not}}\xspace}

\newcommand{\SUBnot}{\ensuremath{\textbf{SUB}_{not}}\xspace}

\newcommand{\UNFOLDnot}{\ensuremath{\textbf{UNFOLD}_{not}}\xspace}
\newcommand{\UONEnot}[1]{\ensuremath{\textbf{UNFOLD}_{not}^{#1}}\xspace}

\newcommand{\TAUTnot}{\ensuremath{\textbf{TAUT}_{not}}\xspace}




\newcommand{\Undecided}{\ensuremath{\mathsf{Undefined}}\xspace}
\newcommand{\Unknown}{\ensuremath{\mathsf{Unknown}}\xspace}
\newcommand{\Positive}{\ensuremath{\mathsf{Positive}}\xspace}
\newcommand{\Negative}{\ensuremath{\mathsf{Negative}}\xspace}
\newcommand{\Justified}{\ensuremath{\mathsf{Justified}}\xspace}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FIN SEMANTICA












\newcommand{\from}[3]{\marginpar{\textbf{\tiny From #1 to #2:}}\textsc{(#3)}}








\newcommand{\negacion}{$/\hspace*{-0.5em}$}
\newcommand{\negation}{$/\hspace*{-0.5em}$}

\newcommand{\Negacion}{/\hspace*{-0.5em}}



\newcommand{\comentario}[1]{}
\newcommand{\skippar}[1]{}


% ================================================================
%    1) Unidades de medida, hyphenations y abreviaturas
% ================================================================


\newcommand{\clearemptydoublepage}{\newpage{\pagestyle{empty}\cleardoublepage}}

% Unidad de longitud para figuras:  1 mm

\setlength{\unitlength}{1mm}

% Variables de entorno para longitudes
% (usadas en comandos para definicion de reglas de infer)

\newlength{\EA}  % Espacio Adicional
\newlength{\MEA} % Medio Espacio Adicional
\newlength{\parametro}
\newlength{\premisas}
\newlength{\consec}
\newlength{\rotulo}
\newlength{\largoregla}

\setlength{\EA}{8mm}
\setlength{\MEA}{4mm}


\hyphenation{usan-do  gra-dual-men-te}
\hyphenation{in-tui-ti-va in-tui-ti-vas in-tui-ti-vos in-tui-ti-vo}
\hyphenation{in-ter-ac-ti-va}
\hyphenation{pro-ce-di-mien-to}
\hyphenation{ge-ne-ral Si-guien-do de-rro-ta-do  pro-pues-ta}
\hyphenation{pro-ble-ma pro-ble-mas}
\hyphenation{re-cha-za-ble  re-cha-za-bles}
\hyphenation{in-de-pen-dien-te  in-de-pen-dien-tes}
\hyphenation{cons-tru-ir  cons-tru-ible  cons-tru-ibles}
\hyphenation{va-ria-ble va-ria-bles}
\hyphenation{re-fe-ren-cia re-fe-ren-cias}
\hyphenation{ite-ra-ti-vo ite-ra-ti-vos}
\hyphenation{res-tric-cio-nes}
\hyphenation{exis-te}
\hyphenation{ca-rac-te-ri-za ca-rac-te-ri-zan}
\hyphenation{Su-pon-ga-mos}
\hyphenation{ma-ne-ra ma-ne-ras}
\hyphenation{mo-de-lo mo-de-lar}
\hyphenation{in-fe-rior in-fe-rio-res}
\hyphenation{Pos-te-rior-men-te  an-te-rior  an-te-rior-men-te}
\hyphenation{re-pre-sen-tar re-pre-sen-ta}
\hyphenation{di-men-sio-nes}
\hyphenation{asu-mien-do asu-mir}
\hyphenation{for-mal for-ma-les for-ma-lis-mo for-ma-lis-mos}
\hyphenation{re-ba-ti-ble re-ba-ti-bles}
\hyphenation{in-me-dia-tos in-me-dia-to}
\hyphenation{so-por-te in-ter-fe-ren-cia}
\hyphenation{in-fe-ren-cia}
\hyphenation{acep-ta-ble  acep-ta-bles  acep-ta-bi-li-dad}
\hyphenation{li-te-ral li-te-ra-les}
\hyphenation{de-rro-ta-dor de-rro-ta-dor-es de-rro-ta}
\hyphenation{aso-cia-da aso-cia-do aso-cia-das aso-cia-dos}
\hyphenation{de-sa-rro-lla  de-sa-rro-llo  de-sa-rro-llan  de-sa-rro-lla-do}
\hyphenation{abs-trac-to}
\hyphenation{mo-de-lo mo-de-los}
\hyphenation{acer-ca  acer-ca-mien-tos}
\hyphenation{co-rres-pon-de   co-rres-pon-da}
\hyphenation{co-rres-pon-den  co-rres-pon-dien-te co-rres-pon-der}
\hyphenation{ra-zo-na ra-zo-nan ra-zo-na-mien-to}
\hyphenation{exis-ta  exis-ten}
\hyphenation{re-le-van-te re-le-van-tes}
\hyphenation{teo-re-ma teo-re-mas}
\hyphenation{apro-pia-da-men-te en-te-ra-men-te}
\hyphenation{di-fe-ren-te ca-rac-te-ri-za}
\hyphenation{ori-gi-nal ori-gi-nal-men-te ori-gi-na-ria-men-te}
\hyphenation{de-no-mi-na-da  de-no-mi-na-das  de-no-mi-na-do de-no-mi-na-dos}
\hyphenation{pre-fe-ren-cia  va-rian-te va-rian-tes}
\hyphenation{ins-tan-cia ins-tan-cias}

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\newcommand{\farg}{forma argumental}
\newcommand{\fargs}{formas argumentales}
\newcommand{\fpr}{forma de prueba rebatible}
\newcommand{\fcarg}{forma contraargumental}

\newcommand{\estialgo}{\sf }


% ================================================================
%                    2) Comandos y entornos varios
% ================================================================

\newcommand{\cqd} {como quer\'{\i}amos demostrar}
\newcommand{\grad} {$^{\circ}$\ }
\newcommand{\Theorist}{\mbox{{\sc Theorist}}}
\newcommand{\etal}{\mbox{$et\ al.$}}
\newcommand{\ej}{ej.:\xspace}
\newcommand{\True}{\mbox{{\sc true}}}
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\newcommand{\eg}{\mbox{$e.g.$}\xspace}
\newcommand{\etc}{\mbox{$etc.$}}
\newcommand{\Eg}{\mbox{$E.g.$}}
\newcommand{\y}{\mbox{ $\wedge$ }}
\newcommand{\imp}{\mbox{ $\Rightarrow$ }}

\newcommand{\ALPHA}{\mbox{\large$\alpha$}}
\newcommand{\BETA}{\mbox{\large$\beta$}}
\newcommand{\DELTA}{\mbox{$\Delta$}}
\newcommand{\GAMMA}{\mbox{$\Gamma$}}


% Letras en estilo caligrafico
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\newcommand{\Ccal}{\mbox{${\cal C}$}}
\newcommand{\Dcal}{\mbox{${\cal D}$}}

\newcommand{\Fcal}{\mbox{${\cal F}$}}

\newcommand{\Pcal}{\mbox{${\cal P}$}}


% tab me deja el espacio en mm que le doy como parametro

\newcommand{\tab}[1]{\hspace*{#1mm}}

% Entorno para citas
\newenvironment{cita}{\begin{sl}\begin{quotation}}{\end{quotation}\end{sl}}

% Estilo de letra para citas
\newcommand{\esticita}{\sl}
\newcommand{\unacita}{\sl}

%  ENTORNOS VARIOS: Definiciones, lemas, ejemplos
%
%

% ====================
% Entorno para definiciones
% ====================
%\newenvironment{DefB}{\vspace*{-3mm}\begin{Definicion}{\em } \em }{$\Box$ \end{Definicion}\vspace*{-3mm}}

\newenvironment{DefB}{\vspace*{-2mm}\begin{Definicion}{ } }{$\Box$ \end{Definicion}\vspace*{-2mm}}
\newtheorem{Definicion}{{\sc Definici\'on}}[section]

% ojo! Defi es equivalente a DefB
\newenvironment{Defi}{\vspace*{-2mm}\begin{Definicion}{\em } \em}{$\Box$ \end{Definicion}\vspace*{-2mm}}

% .........En ingles..........
\newenvironment{Definition}{\vspace*{-2mm}\begin{DefinitionText}{\em }\em }{$\Box$ \end{DefinitionText}\vspace*{-2mm}}
\newtheorem{DefinitionText}{{\sc Definition}}[section]

% ====================
% Entorno para ejemplos
% ====================
\newenvironment{Ejem}{\begin{Ejemplo}{\em } \em }{$\Box$\end{Ejemplo}}
\newtheorem{Ejemplo}{{\sc Ejemplo}}[section]

% ..........En ingles..........
\newenvironment{Example}{\begin{ExampleText}{\em } \em}{$\Box$\end{ExampleText}}
\newtheorem{ExampleText}{{\sc Example}}[section]
% ====================

% Entorno para proposiciones
\newenvironment{Prop}{\begin{Proposicion}{\em } \em }{$\Box$ \end{Proposicion}}
\newtheorem{Proposicion}{{\sc Proposici\'on}}[section]

% .........En ingles........
\newenvironment{Proposition}{\begin{PropositionText}{\em } \em }{$\Box$ \end{PropositionText}}
\newtheorem{PropositionText}{{\sc Proposition}}[section]


% ====================
% Entorno para corolarios
\newenvironment{Coro}{\begin{Corolario}{\em } \em }{$\Box$ \end{Corolario}}
\newtheorem{Corolario}{{\sc Corolario}}[section]
% ........ En ingles .......
\newenvironment{Corollary}{\begin{CorollaryText}{\em } \em }{$\Box$ \end{CorollaryText}}
\newtheorem{CorollaryText}{{\sc Corollary}}[section]
% ====================
% Entorno para lemas
\newenvironment{Lema}{\begin{Lemax}{\em}\em}{$\Box$ \end{Lemax}}
\newtheorem{Lemax}{{\sc Lema}}[section]
% ........ En ingles .......

\newenvironment{Lemma}{\begin{LemmaText}{\em}\em}{$\Box$\end{LemmaText}}
\newtheorem{LemmaText}{{\sc Lemma}}[section]

% ====================
% Entorno para teoremas
\newenvironment{Teo}{\begin{Teox}{\em } \em }{$\Box$ \end{Teox}}
\newtheorem{Teox}{{\sc Teorema}}[section]
% ........  En ingles ......
\newenvironment{Theorem}{\begin{TheoremText}{\em } \em }{$\Box$\end{TheoremText}}
\newtheorem{TheoremText}{{\sc Theorem}}

% ====================

% Entorno para notas
\newenvironment{Nota}{\begin{Notax}{\em } \em }{\end{Notax}}
\newtheorem{Notax}{{\bf Observaci\'on}}[section]


% Entorno para observaciones
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\newtheorem{obsx}{{\bf Observaci\'on}}[section]

% Entorno para algoritmos
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\newtheorem{Algox}{{\sc Algoritmo}}[section]

% Entorno para demostraciones
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\newtheorem{demox}{{\sc Demostraci\'on:}}

\newenvironment{Proof}{\noindent{\sc Proof:}}{$\Box$}
\newtheorem{ProofText}{{\sc Demostraci\'on:}}



% ========= Entorno para bloques de estructuras algoritmicas ====

\newcommand{\paracada}{{\bf Para cada}}
\newcommand{\repetir}{{\bf Repetir}}
\newcommand{\hastaque}{{\bf Hasta que}}
\newcommand{\Si}{{\bf Si}}
\newcommand{\entonces}{{\bf entonces}}
\newcommand{\sino}{{\bf sino}}
%\Si{ a = b}{c = d}{jkfd}
%\newcommand{\Si}[2] {{\bf \begin{tabular}{ll}
%                          {\bf Si} & \begin{tabular}[c]{ #1 \ \\ }
%                                     \end{tabular} \\
%                                   & {\bf entonces}  \\
%                                   &


\newlength{\blk}
\setlength{\blk}{5mm}

% Bloque definible por el usuario (sangria es parametro)
% \newenvironment{bl}[1]{\hspace*{#1} \begin{tabular}{|l}}{\end{tabular} }
\newenvironment{bl}[1]{\hspace*{#1} \begin{tabular}{l}}{\end{tabular} \\ }

% Bloque comun (sangria de 5mm)
\newenvironment{blc}{\hspace*{\blk} \begin{tabular}{l}}{\end{tabular}\\}

% Acotacion
\newenvironment{acotacion}{\begin{quotation}\begin{sl}}{\end{sl}\end{quotation}}


% ================================================================
%                    2) Comandos y entornos varios
% ================================================================


% STRONG AND DEFEASIBLE CLAUSES (Prolog-like)
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\newcommand{\defleftarrow}{ {\tiny \defleft} }

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\newcommand{\iclause}[2]{{#1 @---- #2}}

\newcommand{\Rsrule}[2]{{\sf #2 $\leftarrow$ #1}}
\newcommand{\Rdrule}[2]{{\sf #2 \defleftarrow\  #1}}


% STRONG AND DEFEASIBLE RULES (RIGHT)

% OJO! Redefinimos \srule[2]  y \drule[2]
\newcommand{\srule}[2]{\ensuremath{\mathit{#1}\;\gets\;\mathit{#2}}\xspace}
\newcommand{\drule}[2]{\ensuremath{\mathit{#1}\;\defleftarrow\;\mathit{#2}}\xspace}

\newcommand{\Srule}[2]{\ensuremath{(\mathit{#1}\;\gets\;\mathit{#2})}\xspace}
\newcommand{\Drule}[2]{\ensuremath{(\mathit{#1}\;\defleftarrow\;\mathit{#2})}\xspace}




%\newcommand{\srule}[2]{#1 \mbox{$\rightarrow$}\ #2}
\newcommand{\defrightarrow}{\mbox{$\,\succ -\hspace{-10pt}- \,$ }}
\newcommand{\defarrow}{ {\tiny \defrightarrow} }
%\newcommand{\drule}[2]{#1 \defarrow\ #2}
\newcommand{\fact}[1]{\mbox{#1}}

\newcommand{\siValeQue}{\mbox{$\longleftarrow$}}
\newcommand{\siNormalmente}{\defleftarrow}


% ============= Sistema de Vreeswijk (1993) ===============

% VreInfer: igual que \Infer pero subindicado
\newcommand{\VreInfer}[1]{\mbox{$\Infer_{_{\hspace*{-10pt} #1}}$}}

\newcommand{\limite}{lim}
\newcommand{\prem}{prem}
\newcommand{\sent}{sent}
\newcommand{\asm}{asm}
\newcommand{\conc}{conc}
\newcommand{\sub}{sub}
\newcommand{\info}{info}
\newcommand{\enable}{enable}
%% \newcommand{\warrant}{warrant}
\newcommand{\saa}{saa}

% ============= Sistema de Nute (1987) ===============
\newcommand{\derivaNute}{\mbox{$\vdash\hspace{-7pt}\vdash$}}
\newcommand{\xpar}[2]{\mbox{$\langle #1,#2 \rangle$}}

% ============= Sistema de Prakken-Sartor (1995) ===============
% El simbolo ~ (\sim en LaTex) para negacion debil debe ir cerca del literal (ej: ~A)
% Por eso el \hspace...
\newcommand{\mysim}{\sim\hspace{-2pt}}



% =========== Sistema multilenguaje para arg. rebatible ========


%\newcommand{\srule}[2]{\mbox{#1 $\rightarrow$ #2}}
%\newcommand{\defrightarrow}{\mbox{$\,\succ -\hspace{-10pt}- \,$ }}
%\newcommand{\defarrow}{ {\tiny \defrightarrow} }
%\newcommand{\drule}[2]{\mbox{#1\defarrow #2}}

\newcommand{\SFM}{\mbox{SFM}}
\newcommand{\MLAR}{\mbox{MLAR}}
\newcommand{\MLderives}[1]{\mbox{$\vdash_{#1}$}}
\newcommand{\LKK}{\mbox{$L_{\cal K}$}}
\newcommand{\LDelta}{\mbox{$L_{\Delta}$}}
\newcommand{\LInfer}{\mbox{$L_{\mid\hspace{-2pt}\sim}$}}
\newcommand{\LArbit}{\mbox{$L_{Arbit}$}}
\newcommand{\LParte}{\mbox{$L_{Party}$}}
\newcommand{\LPro}{\mbox{$L_{Pro}$}}
\newcommand{\LOpp}{\mbox{$L_{Opp}$}}
\newcommand{\LDebate}{\mbox{$L_{Debate}$}}

\newcommand{\CPro}{\mbox{$C_{Pro}$}}
\newcommand{\COpp}{\mbox{$C_{Opp}$}}
\newcommand{\CParty}{\mbox{$C_{Party}$}}
\newcommand{\CArbit}{\mbox{$C_{Arbit}$}}

\newcommand{\Pro}{\mbox{$Pro$}}
\newcommand{\Opp}{\mbox{$Opp$}}
\newcommand{\Party}{\mbox{$Party$}}
\newcommand{\Adversary}{\mbox{$\overline{Party}$}}

%\newcommand{\Rules}{\mbox{${\cal R}$}}

\newcommand{\dead}{\mbox{$dead$}}
\newcommand{\alive}{\mbox{$alive$}}
\newcommand{\TheOtherParty}{\mbox{$\overline{Party}$}}
\newcommand{\status}[2]{{\tt status(#1,#2)}}
\newcommand{\linked}[3]{{\tt linked\_defeater(#1,#2,#3)}}
\newcommand{\defeater}[3]{{\tt defeater(#1,#2,#3)}}
\newcommand{\cudef}[3]{{\tt curr\_defeat(#1,#2,#3)}}
\newcommand{\debate}[4]{{\tt debate(#1,#2,#3,#4)}}
%\newcommand{\Defeats}[2]{{\tt defeats(#1,#2)}}
\newcommand{\preferred}[2]{{\tt preferred(#1,#2)}}
\newcommand{\nonminimal}[1]{{\tt nonminimal(#1)}}
\newcommand{\subarg}[2]{{\tt subarg(#1,#2)}}
\newcommand{\subproof}[2]{{\tt subproof(#1,#2)}}
\newcommand{\counterargues}[2]{{\tt counterargues(#1,#2)}}
\newcommand{\disagrees}[2]{{\tt disagree(#1,#2)}}
\newcommand{\justif}[1]{{\tt justified(#1)}}
\newcommand{\incon}[1]{{\tt inconsistent(#1)}}
\newcommand{\istrue}[2]{\mbox{#1}:\mbox{#2}}
\newcommand{\argu}[2]{{\tt {arg(\mbox{$#1$},\mbox{$#2$})}}}
\newcommand{\dproof}[2]{{\tt {dproof(\mbox{$#1$},\mbox{$#2$})}}}

\newcommand{\true}{\textbf{true}}
%\newcommand{\true}{\textbf{false}}


\newcommand{\ter}[1]{{\tt #1}}
\newcommand{\ntr}[1]{{\tt<}{\em #1}{\tt>}}
\newcommand{\isa}{\tt::=}
\newcommand{\obien}{\mbox{$\mid$}}


% =========================== SIMBOLOS =========================
\newcommand{\nn}{\mbox{$\tilde{n}$}}
\newcommand{\ac}{\mbox{$\acute{a}$}}
\newcommand{\ec}{\mbox{$\acute{e}$}}
\newcommand{\ic}{\mbox{$\acute{\imath}$}}
\newcommand{\oc}{\mbox{$\acute{o}$}}
\newcommand{\uc}{\mbox{$\acute{u}$}}

\newcommand{\funcion}[3]{#1:\{#2\} $\longrightarrow$ \{#3\}}
\newcommand{\cruz}{\dagger}
\newcommand{\adv}{$\overline{Party}$}
\newcommand{\cp}{$C_{prop}$}
\newcommand{\co}{$C_{opp}$}
\newcommand{\ca}{$C_{arbiter}$}
\newcommand{\cparty}{$C_{Party}$}
\newcommand{\cotherparty}{$C_{\overline Party}$}
\newcommand{\ccurrent}{$C_{current}$}
\newcommand{\ccommon}{$C_{commit}$}
\newcommand{\carbiter}{$C_{arbiter}$}


% Titulo de definicion
\newcommand{\titudefi}[1]{{(#1).}}

% Titulo de ejemplo
\newcommand{\tituejem}[1]{{({\sl  #1}).}}



% Remark
\newcommand{\remark}[1]{\noindent {\rm /*} {\em #1} {\rm */}}

% Conjunto comun y corriente
\newcommand{\cjto}[1]{\mbox{$\{#1\}$}}

% Tamanio del arbol dialectico
\newcommand{\Tam}[1]{$Size$(#1)}

% Profundidad del arbol dialectico
\newcommand{\Prf}[1]{$Depth$(#1)}

\newcommand{\cpl}[1]{\mbox{$\overline{#1}$}}

\newcommand{\FLAMBDA}{\mbox{$F\hspace*{-2pt}\lambda$}}
\newcommand{\flambda}{F\hspace*{-2pt}\lambda}

\newcommand{\talque}{{\mid}}
\newcommand{\Prolog}{{\sc Prolog}}
\newcommand{\nega}{{\em neg}}
%\newcommand{\cneg}{\mbox{$\neg$}}  % negacion clasica
\newcommand{\pneg}{\mbox{{\sf neg}}}  % negacion en Horn clauses
\newcommand{\alfabeta}{$\alpha$-$\beta$}

% Consecuentes de un conjunto de reglas rebatibles
\newcommand{\Co}[1]{\mbox{$Co(#1)$}}

% Antecedentes de un conjunto de reglas rebatibles
\newcommand{\An}[1]{\mbox{$An(#1)$}}

% Literales en un argumento excepto la cabeza
\newcommand{\Lit}[1]{\mbox{$Lit(#1)$}}


% Implicacion material e implicacion rebatible
\newcommand{\Implies}{\mbox{$\rightarrow$}}
\newcommand{\Rimplies}{\mbox{$\leftarrow$}}
% \newcommand{\defimp}{\mbox{${\scriptstyle \,>\hspace{-2pt}-\hspace{-4pt}-\,}$}}
%\newcommand{\Rdefimp}{\mbox{${\scriptstyle\,-\hspace{-2pt}-\hspace{-4pt}<\,}$}}

% Implicacion rebatible (\defimp) e implicacion fuerte (\strimp)
\newcommand{\defimp}{\defarrow}
\newcommand{\Rdefimp}{\defleftarrow}
\newcommand{\strimp}{\mbox{$\rightarrow$}\ }

% Conjunto Delta
\newcommand{\DD}{\mbox{$\Delta$}\xspace}

% Conjunto K
\newcommand{\KK}{\mbox{$\mathcal{K}$}\xspace}
\newcommand{\KKag}{\mbox{${\cal K}^{Ag}$}}
\newcommand{\DELTAag}{\mbox{$\Delta^{Ag}$}}
\newcommand{\KDag}{$\Pair{\KK}{\DELTA}^{Ag}$}

% Conjuntos K particular y K general
\newcommand{\KKp}{\mbox{$\KK_{P}$}}
\newcommand{\KKg}{\mbox{$\KK_{G}$}}

% Base de conocmiento
\newcommand{\KB}{\mbox{{\rm KB}}}

% Clausura de algun conjunto
\newcommand{\clausura}[1]{\mbox{$ #1^{^{\vdash}}$}}

% Inferencia Rebatible y su negacion
\newcommand{\Infer}{\mbox{$\mid\hspace{-2pt}\sim\ $}}
\newcommand{\notInfer}{\mbox{$\:\not\mid\hspace{-2pt}\sim\ $}}

% Inferencia en formas argumentales
%% viejo \newcommand{\syInfer}{\mbox{$\mid\hspace{-2pt}\stackrel{\sim}{\sim}\ $}}
%% viejo \newcommand{\SyInfer}{\mbox{$\mid\hspace{-2pt}\approx\ $}}
%% viejo \newcommand{\notSyInfer}{\mbox{$\:\not\mid\hspace{-2pt}\approx\ $}}

\newcommand{\SyInfer}{\mbox{$\Infer_{_{\hspace*{-11pt}\mbox{\tiny FP}}}$}}
\newcommand{\notSyInfer}{\mbox{$\notInfer_{_{\hspace*{-11pt}\mbox{\tiny FP}}}$}}


% Relacion ``Mas informado que''
\newcommand{\Sinfo}{\mbox{$\succ_{_{\! {\bf info}}}$}}
% Relacion ``Mas especifico que que''
\newcommand{\Sspec}{\mbox{$\succ_{_{\! {\bf spec}}}$}}
\newcommand{\spec}{\mbox{$\succ$}}
\newcommand{\speceq}{\mbox{$\succeq$}}


%  Relacion ``Mas especifico que''
\newcommand{\morespec}{\mbox{$\succ_{_{\! {\bf spec}}}$}}

%  Relacion ``No comparable por especificidad''
\newcommand{\nocompspec}{\mbox{$\asymp_{_{\! {\bf spec}}}$}}

%  Relacion ``Derrota en base a especificidad''
% \newcommand{\defeatspec}{\mbox{${\succ}_{_{\! {\bf spec}}}^{^{\sim} }$}}





% Relaciones de desacuerdo, derrota y contraargumentacion
\newcommand{\disag}[1]{\mbox{$\bowtie_{_{\! #1}}$}}
\newcommand{\defeats}{\mbox{$\gg_{_{\bf def}}$}}
\newcommand{\counter}[1]{\mbox{$\stackrel{\hspace{2pt}#1}{\otimes\hspace{-5pt}\rightarrow}$}}
\newcommand{\mydefeats}[1]{\mbox{$\stackrel{\hspace{2pt}#1}{\gg_{_{\bf def}}}$}}

\newcommand{\Pair}[2]{\mbox{$( #1, #2 )$}}
\newcommand{\Tree}[1]{\mbox{${\cal T}_{\scriptsize #1}$}}



\newcommand{\TSS}[2]{\mbox{$\langle #1, #2 \rangle $}}
\newcommand{\ARG}[2]{\mbox{$\langle #1, #2 \rangle $}}

% ===================   Argumentos varios  ==============================

\newcommand{\BSa}{\mbox{$\TSS{B_{1}}{j_{1}}$}}
\newcommand{\BSb}{\mbox{$\TSS{B_{2}}{j_{2}}$}}
\newcommand{\BSi}{\mbox{$\TSS{B_{i}}{j_{i}}$}}
\newcommand{\BSn}{\mbox{$\TSS{B_{n}}{j_{n}}$}}

\newcommand{\ASCero}{\mbox{$\TSS{A_{0}}{h_{0}}$}}
\newcommand{\ASa}{\mbox{$\TSS{A_{1}}{h_{1}}$}}
\newcommand{\ASb}{\mbox{$\TSS{A_{2}}{h_{2}}$}}
\newcommand{\ASc}{\mbox{$\TSS{A_{3}}{h_{3}}$}}
\newcommand{\ASd}{\mbox{$\TSS{A_{4}}{h_{4}}$}}
\newcommand{\ASe}{\mbox{$\TSS{A_{5}}{h_{5}}$}}
\newcommand{\ASi}{\mbox{$\TSS{A_{i}}{h_{i}}$}}
\newcommand{\ASiProx}{\mbox{$\TSS{A_{i+1}}{h_{i+1}}$}}
\newcommand{\ASj}{\mbox{$\TSS{A_{j}}{h_{j}}$}}
\newcommand{\ASnMinus}{\mbox{$\TSS{A_{n-1}}{h_{n-1}}$}}
\newcommand{\ASn}{\mbox{$\TSS{A_{n}}{h_{n}}$}}
\newcommand{\ASh}{\mbox{$\TSS{A}{h}$}}
\newcommand{\BSq}{\mbox{$\TSS{B}{q}$}}
\newcommand{\BSj}{\mbox{$\TSS{B}{j}$}}
\newcommand{\SSj}{\mbox{$\TSS{S}{j}$}}

%===============================Miscel==============================
% Linea de argumentacion Lambda
\newcommand{\linarg}{\mbox{\large$\lambda$}}
\newcommand{\LAMBDA}{\mbox{\large$\lambda$}}


% Delta Grounded
\newcommand{\GDELTA}{\mbox{$\Delta^{^{\hspace{-2pt}\downarrow}}$}}

% Lenguaje L
%\newcommand{\Lp}{\mbox{{\large$\cal L$}}}

%% ojo!!!! comentado


% Lenguaje L para el agente
\newcommand{\Lpag}{\mbox{{\large${\cal L}^{^{Ag}}$}}}

% Sistema Formal L
\newcommand{\LLL}{\mbox{${\bf I \hspace{-2pt} L}$}}

% Agente A
\newcommand{\Agent}{\mbox{$\cal A$}}

% Sistema MTDR
\newcommand{\MTDR}{\mbox{\textsl{MTDR}}\xspace}

% Sistema SL
\newcommand{\SL}{\mbox{$\textsl{SL}$}\xspace}





%....................Nuevas definiciones para Chile 95............

\newcommand{\Deriva}{\vdash}
\newcommand{\syDeriva}{\stackrel{a}{\vdash}}

%\newcommand{\SyInfer}{\mbox{$\mid\hspace{-2pt}\stackrel{a}{\sim}\ $}}
%\newcommand{\notSyInfer}{\mbox{$\:\not\mid\hspace{-2pt}\stackrel{a}{\sim}\ $}}

\newcommand{\ASchema}[2]{\mbox{$\langle\hspace{-2pt}\langle #1, #2 \rangle\hspace{-2pt}\rangle $}}
%..old: \newcommand{\ASchema}[2]{\mbox{$\langle\langle #1, #2 \rangle\rangle $}}
\newcommand{\ASchemaG}[3]{\mbox{$\ll #1, #2 \gg^{\hspace{-2pt}\downarrow #3}$}}

\newcommand{\KD}{\Pair{\KK}{\DELTA}}
\newcommand{\ARS}[2]{\mbox{$\langle\hspace{-2pt}\langle #1, #2 \rangle\hspace{-2pt}\rangle $}}
\newcommand{\ED}[1]{\mbox{${\cal ED}(#1)$}}
\newcommand{\FP}[1]{\mbox{${\cal FP}(#1)$}}
\newcommand{\Sch}{\mbox{${\cal S}$}}

%..............Algunos Conjuntos
\newcommand{\AScero}{\mbox{$\TSS{A_{0}}{h_{0}}$}}
\newcommand{\Ta}{\mbox{$T_{1}$}}
\newcommand{\Tb}{\mbox{$T_{2}$}}
\newcommand{\Tc}{\mbox{$T_{3}$}}
\newcommand{\ha}{\mbox{$h_{1}$}}
\newcommand{\hb}{\mbox{$h_{2}$}}
\newcommand{\hc}{\mbox{$h_{3}$}}
\newcommand{\Aa}{\mbox{$A_{1}$}}
\newcommand{\Ab}{\mbox{$A_{2}$}}
\newcommand{\Ac}{\mbox{$A_{3}$}}

%........... Definiciones referidas a estructuras dial�cticas......



\newcommand{\xx}[1]{\hspace*{#1 mm}}




% ============== Definicion de Regla de Inferencia ==================
% COMANDO para reglas de inferencia
% \regla{$a$}{$b$}{$c$}
% Entrada #1 = premisas, #2, = conclusion, #3 = rotulo
% Salida:
%
%   a
% -----  c
%   b
%
%
%

\newcommand{\regla}[3]{\settowidth{\premisas}{#1}
\settowidth{\consec}{#2}
\setlength{\largoregla}{\premisas}
\addtolength{\largoregla}{\EA}
\settowidth{\rotulo}{\hspace*{2mm}{\scriptsize #3}}
\begin{tabular}{c}
\hspace*{\MEA}#1\hspace*{\MEA}\hspace*{-\largoregla}\rule[-1.5mm]{\largoregla}{0.3mm}\raisebox{-2mm}
{\hspace*{2mm}{\scriptsize #3}}\hspace*{-\rotulo}\\
\hspace*{\MEA}#2\hspace*{\MEA}\\
\end{tabular}}
% ==================================================================

\newcommand{\caja}[1]{\raisebox{2mm}[2mm][2mm]{\fbox{#1}}}
\newcommand{\paso}[1]{\mbox{#1}}
\newcommand{\angles}[2]{\mbox{$\langle #1,#2 \rangle$}}


% ==================================================================
% Definiciones para paper de Bondarenko et al.
\newcommand{\blanco}{\mbox{\textcolor{white}{$\cdot$}}}
\newcommand{\mapeo}{\mbox{$\overline{\blanco}$}}
\newcommand{\miregla}[2]{\mbox{$\frac{#1}{#2}$}}




%           |=====================================|
%      ====<   � F i n    d e    DEFTESIS.TEX !    >====   :)
%           |=====================================|

\renewcommand{\ARG}[2]{\mbox{$\langle #1, #2 \rangle $}}


% =====================================================================
%   Aqui viene OTHERDEF.TEX
% =====================================================================


\newcommand{\cali}[1]{\mbox{${\cal #1}$}}

%\newcommand{\Argum}[1]{\mbox{$\langle {\cal A}_{#1}, h_{#1} \rangle$}}

\newcommand{\ArgumGeneral}[1]{\mbox{$\rangle {\cal A}, h \langle$}}

%\input{misdefs}

\newcommand{\argum}[1]{\mbox{${\cal A}_{#1}$}}


\newcommand{\arbol}[1]{\mbox{${\cal T}_{#1}$}}
\newcommand{\GUM}[1]{\mbox{\dosupla{\argum{#1}}{h_{#1}} }}
\newcommand{\InferD}{\mbox{$\Infer_{_{\hspace*{-3mm} D}}$}}
\newcommand{\notInferD}{\mbox{$\not\hspace*{-1mm}\InferD$}}
\newcommand{\InferM}{\mbox{$\Infer_{_{\hspace*{-3mm} A}}$}}
\newcommand{\notInferM}{\mbox{$\not\hspace*{-1mm}\InferM$}}
\newcommand{\lds}{\mbox{{\sc lds}}}

% ===============================================
%
%        SISTEMA ARGUMENTATIVO ETIQUETADO
%
% ===============================================

% ----------------------------------------------
% 1) Definiciones de utilidad general
% ----------------------------------------------

% comandos antecedidos por "m" no necesitan $ para ser usados
\newcommand{\mbot}{\mbox{$\bot$}}
\newcommand{\mcup}{\mbox{$\cup$}}
\newcommand{\mwedge}{\mbox{$\wedge$}}
\newcommand{\mgamma}{\mbox{$\gamma$}}
\newcommand{\mGamma}{\mbox{$\Gamma$}}
\newcommand{\mPhi}{\mbox{$\Phi$}}
\newcommand{\malpha}{\mbox{$\alpha$}}
\newcommand{\memptyset}{\mbox{$\emptyset$}}
\newcommand{\msubseteq}{\mbox{$\subseteq$}}

\newcommand{\mequiv}{\mbox{$\equiv$}}
\newcommand{\mnotequiv}{\mbox{$\negacion\equiv$}}


\newcommand{\isin}{\mbox{$\in$}}
\newcommand{\suchthat}{\mbox{$\mid$\ }}
\newcommand{\deriva}{\mbox{$\vdash$}}

% conjunto
\newcommand{\set}[1]{$\{#1\}$}
% conjunto sin pesos
\newcommand{\conjunto}[1]{\{#1\}}
\newcommand{\cto}[1]{\{#1\}}

% ----------------------------------------------
% 2) Definiciones de conjuntos auxiliares
% ----------------------------------------------

% Orden de preferencia
\newcommand{\OrdenPref}{\mbox{$\preceq$}}

% Conjunto de argumentos minimales construidos desde Gamma
\newcommand{\Args}{{\sf Args}}


% Strong(Gamma), o S(Gamma)
\newcommand{\Strict}{{\sf Strict}}

% Defeasible(Gamma), o D(Gamma)
\newcommand{\Defeasible}{{\sf Defeasible}}

% WffsStrong(Gamma), o WffsS(Gamma)
\newcommand{\WffsS}{\mbox{{\sf Wffs-S}}}

% WffsDefeasible(Gamma), o WffsD(Gamma)
\newcommand{\WffsD}{\mbox{{\sf Wffs-D}}}

% Wffs(Gamma)
\newcommand{\Wffs}{{\sf Wffs}}

% Labels(Gamma)
\newcommand{\Labs}{{\sf Labels}}

% LabelNames(Gamma)
\newcommand{\LabNames}{\mbox{{\sf L-Names}}}

% LabelSupport(Gamma)
\newcommand{\LabSupport}{{\sf LabelSupport}}


% ----------------------------------------------
% 3)  Definiciones utiles para
% ----------------------------------------------

% ....estilo de letra para etiquetas
\newcommand{\etq}{\sf}



% ....lenguaje de representacion de conocimiento
\newcommand{\LengKR}{\mbox{$\mathcal{L}_{_\mathsf{KR}}$}\xspace}

% ....atomos en \LengKR
\newcommand{\Atoms}[1]{\ensuremath{\mbox{\textsf{Atoms}(#1)}}}

% ....atomos en \LengKR
\newcommand{\Literals}[1]{\ensuremath{\mbox{$\mathsf{Lit}(#1)$}}}


% ....Conjunto de todas las etiquetas atomicas
\newcommand{\Labels}{\mbox{$Labels$}}

% ....lenguaje de etiquetado
\newcommand{\LengLabel}{\mbox{$\mathcal{L}_{_\mathsf{Labels}}$}}

% ... lenguaje de inferencia rebatible etquetada
\newcommand{\LengArg}{\mbox{$\mathcal{L}_{_\mathsf{Arg}}$}\xspace}

% ....relacion de inferencia rebatible etquetada
\newcommand{\InferArg}
 {\mbox{${\Infer}_{_{\vspace*{6mm}{\hspace*{-9pt}Arg}}}$}}

\newcommand{\notInferArg}
 {\mbox{$\not\InferArg$}}

% ....relacion de inferencia rebatible con arboles
\newcommand{\InferTree}
  {\mbox{${\Infer}_{_{\vspace*{6mm}{\hspace*{-9pt}{\small\cal T}}}}$}}

\newcommand{\notInferTree}
 {\mbox{$\not\InferTree$}}

%
% .... relacion de inferencia con warrant (inferencia = clausura)
\newcommand{\InferW}
  {\mbox{${\Infer}_{_{\vspace*{6mm}{\hspace*{-9pt}{\small\sc w}}}}$}}

\newcommand{\notInferW}
 {\mbox{$\not\InferW$}}

%
% .... relacion de inferencia con justificacion
\newcommand{\InferJ}
  {\mbox{${\Infer}_{_{\hspace*{-9pt}*}}$}}

\newcommand{\notInferJ}
 {\mbox{$\not\InferJ$}}


%  Sistema Argumentativo Etiquetado
\newcommand{\SAE}{{\sc sae}}

% etiquetas n1, n2, n3, .. d1, d2, d3, ..
\newcommand{\nr}[1]{{\etq n_{#1}}}
\newcommand{\re}[1]{{\etq d_{#1}}}

% set of labels / Ojo! debe estar dentro de $$
\newcommand{\sol}[1]{{{\etq L}_#1}}

% tupla
\newcommand{\tupla}[2]{\mbox{$\langle #1,#2\rangle$}}



% etiqueta argumental (dos parametros)
%\newcommand{\etar}[2]{\mbox{$#1_{{\etq #2}}$}}

\newcommand{\etar}[2]{\mbox{$[#1,{\etq #2}]$}}

% etiqueta argumental (un parametro)
\newcommand{\etarX}[1]{\mbox{$#1$}}

% abrev-ud
\newcommand{\abrevud}{\mbox{$ud$}}


% Arbol dialectico
% antes era: \newcommand{\TREE}[2]{\mbox{${\cal T}_{#1}^{#2}$}}
\newcommand{\TREE}[2]{\mbox{${\mathbf T}_{#1}^{#2}$}}
\newcommand{\UnTREE}{\mbox{${\mathbf T}$}}


% Argumentos varios
\newcommand{\Argument}[1]{\mbox{${\cal A}_{#1}$}}

% Argumento Generico (ArgGen)
\newcommand{\ArgGen}[1]{\du{\Argument{#1}}{\alpha}}


% linea argumentativa
\newcommand{\Linarg}{\mbox{$\lambda$}}
\newcommand{\Linargi}[1]{\mbox{$\lambda_{#1}$}}
\newcommand{\SLinarg}{\mbox{$\lambda_{S}$}}
\newcommand{\ILinarg}{\mbox{$\lambda_{I}$}}


% -------------------------------------------
% Labelling language \LL
% Defeasible Language \LArg
% -------------------------------------------

% {sistema deductivo etiquetado}
\newcommand{\SDE}{\mbox{\textsl{SDE}}\xspace}
\newcommand{\SDEs}{\mbox{\textsl{SDEs}}\xspace}

% {sistema deductivo etiquetado para argumentacion}
\newcommand{\SDEA}{\mbox{SDEA}}

\newcommand{\LL}{\mbox{${\cal L}_{Label}$}}
\newcommand{\LArg}{\mbox{${\cal L}_{Arg}$}}
\newcommand{\ELL}{\mbox{$Ext(\LL, \LArg)$}}
\newcommand{\aldl}{\mbox{$\langle \LL, \LArg \rangle$}}

%\newcommand{\WffsK}[1]{\mbox{{\em Wffs}$_{K}(#1)$}}
%\newcommand{\WffsD}[1]{\mbox{{\em Wffs}$_{D}(#1)$}}
%\newcommand{\Wffs}[1]{\mbox{{\em Wffs}$(#1)$}}


\newcommand{\Arg}[1]{\mbox{${\cal A}_{#1}$}}
\newcommand{\Powerset}[1]{\mbox{${\cal P}(#1)$}}

\newcommand{\cfg}[1]{\mbox{${\cal C} \langle #1 \rangle$}}
\newcommand{\cfi}[1]{\mbox{${\cal C'} \langle #1 \rangle$}}
% cfi = configuracion inferida

\newcommand{\cfgaux}[1]{\mbox{${\cal C}_{aux} \langle #1 \rangle$}}
\newcommand{\cfgsup}[1]{\mbox{${\cal C} \langle [#1] \rangle$}}
\newcommand{\du}[2]{\mbox{$#1$:$#2$}\xspace}

%\renewcommand{\defeats}{\mbox{$Dft$}}
\newcommand{\attacks}{\mbox{$Atk$}}
\newcommand{\defends}{\mbox{$Def$}}

%\renewcommand{\true}{\mbox{{\sf T}}}
%\newcommand{\false}{\mbox{{\sf F}}}


\newcommand{\lista}[2]{\mbox{$\odot(#1,#2)$}}

\newcommand{\Arbol}[2]{\mbox{$\tau(#1,#2)$}}


\newcommand{\cbs}[1]{\mbox{$@#1$}}


% ======== otras definiciones / usadas en el trabajo para ASAI

\newcommand{\Hipot}{\mbox{${\cal H}$}}

\newcommand{\negafalla}{\mbox{$not$}}
\newcommand{\vdashLP}{\mbox{$\vdash_{\sc lp}$\ }}

\newcommand{\TreePrima}[1]{\mbox{${\cal T'}_{\tiny #1}$}}

\newcommand{\npp}{\mbox{$\sim$}}

\newcommand{\cneg}{\mbox{$\sim$}}










% ============================================================
%
% Capitulo 4: comandos auxiliares
%
% ============================================================


\newcommand{\GammaUno}{\mbox{$\Gamma_{1}$}\xspace}
\newcommand{\GammaDos}{\mbox{$\Gamma_{2}$}\xspace}

\newcommand{\Dua}{\du{\mathcal{A}_1}{Q_1}\xspace}
\newcommand{\Dub}{\du{\mathcal{A}_2}{Q_2}\xspace}

\newcommand{\Da}{\mbox{$\mathcal{A}_1$}\xspace}
\newcommand{\Db}{\mbox{$\mathcal{A}_2$}\xspace}

\newcommand{\Conca}{\mbox{$Q_1$}\xspace}
\newcommand{\Concb}{\mbox{$Q_2$}\xspace}


\newcommand{\TreeA}{\du{\UnTREE(\Da,\ldots)}{\Conca}\xspace}

\newcommand{\TreeB}{\du{\UnTREE(\Db,\ldots)}{\Concb}\xspace}

\newcommand{\TreeDial}[2]{\du{\UnTREE(#1,\ldots)}{#2}\xspace}




% ============================================================
%
% Nuevos comandos referidos a etiquetas y otras yerbas...
%
% ============================================================

% === manejo de contadores para reglas ===
\newcounter{nro-regla}
\setcounter{nro-regla}{0}

\newenvironment{regla-infer}{\begin{center}}{\end{center}
                         \addtocounter{nro-regla}{1}}


% comentario personal
\newcommand{\personal}[1]{}


% Abreviacion de declarative unit
\renewcommand{\abrevud}{\mbox{$du$}}
% Abreviacion de declarative units (plural)
\newcommand{\abrevuds}{\mbox{$du$s}}

% Derivacion en Prolog
\newcommand{\DeriProlog}{\mbox{$\vdash_{_{\textsc{sld}}}\hspace*{1mm}$}\xspace}
\newcommand{\NotDeriProlog}{\mbox{$\negacion\DeriProlog$}}
\newcommand{\notDeriProlog}{\mbox{$\negacion\DeriProlog$}}

% Argumento como formula etiquetada
\newcommand{\Argm}[2]{\du{{\cal #1}}{#2}}

% Argumento como conjunto
\newcommand{\ArgSet}[1]{\mbox{${\cal #1}$}}

\newcommand{\ArgSeti}[2]{\mbox{${\cal #1}_{\scriptstyle #2}$}}


% Arbol
%\newcommand{\BasicTREE}{\mbox{\TREE{}{}}}

% Conjunto de etiquetas atomicas
\newcommand{\ArgLabel}[1]{{\etq L}_{#1}}

% Arbol con subindice
\newcommand{\Baum}[1]{\mbox{${\cal T}(#1)$}}
\newcommand{\Baumi}[2]{\mbox{${\cal T}_{#1}(#2)$}}
\newcommand{\lBaumi}[3]{\mbox{${\cal T}_{#1}^{#2}(#3)$}}


% Referencia para regla de deduccion natural
\newcommand{\irule}[1]{R\ref{#1}}





% Implicacion Horn
\newcommand{\Rule}[2]{\mbox{$#1$ \Rimplies $#2$}}
% Implicacion Horn con parentesis
\newcommand{\RULE}[2]{\mbox{($#1$ \Rimplies $#2$)}}


\newcommand{\rinvertida}{@---}

% Implicacion Horn (Invertida)
\newcommand{\IRule}[2]{\mbox{$#1$ \rinvertida $#2$}}

% Implicacion Horn (Invertida) con parentesis
\newcommand{\IRULE}[2]{\mbox{($#1$ \rinvertida $#2$)}}



% Hecho Horn
\newcommand{\Fact}[1]{\mbox{$#1$}}



% Arbol de prueba  para \InferArg
%\newcommand{\ProofTree}{\mbox{${\cal PT}$}}
\newcommand{\ProofTree}{\mbox{$\clubsuit$}}

% Arbol de prueba  para \InferTree
%\newcommand{\TTree}{\mbox{${\cal PT}$}}
\newcommand{\TTree}{\mbox{$\spadesuit$}}


\newcommand{\Horn}{\mbox{{\sf Horn}}}

% Relacion "defeats"
\newcommand{\Derrota}{\mbox{{\sf defeats}}}


% Relacion "properly defeats"
\newcommand{\PDerrota}{\mbox{{\sf P-defeats}}}
\newcommand{\PDefeats}{\PDerrota}  % nombre alternativo

% Relacion "blocking defeats"
\newcommand{\BDerrota}{\mbox{{\sf B-defeats}}}
\newcommand{\BDefeats}{\BDerrota}  % nombre alternativo


% Conjunto de Literales
\newcommand{\Lits}{\mbox{{\sf Lit}}}

% Conjunto de hechos
\newcommand{\Facts}{\mbox{{\sf Facts}}}

% Conjunto de reglas
\newcommand{\Rules}{\mbox{{\sf Rules}}}

% Conjunto de metas
\newcommand{\Goals}{\mbox{{\sf Goals}}}

% Conclusiones (consistentes) derivables a partir de \Gamma
\newcommand{\ConcArg}{\mbox{{\sf ConcArg}}}

% Conjunto de clausulas de programa
\newcommand{\ProgClauses}[1]{\ensuremath{\mbox{\textsf{ProgClauses}(#1)}}}


% Conjunto de etiquetas argumentativas
\newcommand{\ArgumGen}{\mbox{{\sf ArgGen}}}

% Conjunto de etiquetas dialecticas
\newcommand{\DialecticalTrees}{\mbox{{\sf DialTrees}}}


% Subarbol valido
\newcommand{\ValidSubTree}{\mbox{\textsf{VSTree}}}

% Minimalidad
\newcommand{\Minimal}{\mbox{{\sf Minimal}}}


% Nombres de las reglas (para referenciarlas sin usar numeros)
%\newcommand{\IntroNR}{\mbox{Intro-NR}}
%\newcommand{\IntroRE}{\mbox{Intro-RE}}
%\newcommand{\IntroCO}{\mbox{Intro-$\wedge$}}
%\newcommand{\ElimIM}{\mbox{Elim-$\Rimplies$}}

% Longitud
\newcommand{\LongitudDibujo}[1]{\setlength{\unitlength}{#1 mm}}
% Centrado
\newcommand{\Centrado}[1]{\makebox(0,0){#1}}


% SEMANTICA con mundos posibles
\newcommand{\maybe}{\mbox{$\diamondsuit$}}
\newcommand{\Maybe}[1]{\diamondsuit(#1)}

\newcommand{\always}{\mbox{$\Box$}}
\newcommand{\Always}[1]{\Box(#1)}

\newcommand{\kmodels}{\mbox{$\mid\vdash$}}

\newcommand{\Kmodels}[1]{\mbox{$\mid\vdash_{\hspace*{-4pt}#1}\hspace*{1pt}$}}


\newcommand{\ValueTrue}{\mbox{\textbf{True}}}
\newcommand{\ValueFalse}{\mbox{\textbf{False}}}

\newcommand{\EntreAngulos}[1]{\mbox{$\langle #1 \rangle$}}
\newcommand{\BracketIzq}{[\hspace*{-0.2em}[}
\newcommand{\BracketDer}{]\hspace*{-0.2em}]}


\newcommand{\eval}[2]{\mbox{${\BracketIzq #1 \BracketDer}_{#2}$}}


% ======== Definiciones de prog. en logica y PLR ========


\newcommand{\DeLP}{\mbox{DeLP}}

\newcommand{\PLR}{\mbox{PLR}}

\newcommand{\Nclasica}{\mbox{$\neg$}}
\newcommand{\Nfalla}{\mbox{$not$}}
\newcommand{\Nfuerte}{\mbox{$\sim$}}

% antes era: \newcommand{\no}{\mbox{$\sim$}}
\newcommand{\no}{\ensuremath{\sim\!\!}\xspace}


\newcommand{\LengPL}{\mbox{${\cal L}_{_\mathsf{PL}}$}\xspace}
\newcommand{\LengPC}{\mbox{${\cal L}_{_\mathsf{PC}}$}\xspace}
\newcommand{\LengMTDR}{\mbox{${\cal L}_{_\mathsf{MTDR}}$}\xspace}


\newcommand{\StrictRules}{\mbox{$\Pi$}}
\newcommand{\DefeasibleRules}{\mbox{$\Delta$}}

% Conjuntos Pi y Delta (PLR)
\newcommand{\SetPi}{\mbox{$\Pi$}}
\newcommand{\SetDelta}{\mbox{$\Delta$}}

% Operadores Pi y Delta (SDE)
\newcommand{\OpPi}{\mbox{$\mathbf\Pi$}}
\newcommand{\OpDelta}{\mbox{$\mathbf\Delta$}}

\newcommand{\Inv}{\mbox{$\mathbf I$}}


\newcommand{\Oppi}{\mbox{$\mathbf\pi$}}
\newcommand{\Opdelta}{\mbox{$\mathbf\delta$}}


\newcommand{\mPi}{\OpPi}

% Programa P

%\newcommand{\Pcal}{\mbox{${\cal P}$}}


% Argumento en PLR
\newcommand{\ArgPLR}[2]{\mbox{$\langle {\cal #1}, #2 \rangle $}}
\newcommand{\ArgiPLR}[3]{\mbox{$\langle {\cal #1}_#2, #3 \rangle $}}

\newcommand{\StrictMoreEspec}{\mbox{$\succ$}}
\newcommand{\comentado}[1]{}


% ==========================================
% Pequenio picture con arbolito binario :)
%
\newcommand{\PasoDeriv}[3]{
  \begin{picture}(70,50)
      \put(0,0){}
      \put(35,45){\Centrado{#1 #2}}
      \put(35,10){\Centrado{#3}}
      \put(25,40){\line(1,-3){8}}
      \put(45,40){\line(-1,-3){8}}
  \end{picture}
}

% =========================================
% Nombres de las reglas de inferencia

% inferencia en \InferArg
\newcommand{\IntroNR}{\mbox{{\sf Intro-NR}}}
\newcommand{\IntroRE}{\mbox{{\sf Intro-RE}}}
\newcommand{\IntroConj}{\mbox{{\sf Intro-$\wedge$}}}
\newcommand{\ElimImp}{\mbox{{\sf Elim-$\Rimplies$}}}

% inferencia plain en warrant
\newcommand{\IntroAD}{\mbox{{\sf Intro-1D}}}
\newcommand{\IntroNAD}{\mbox{{\sf Intro-ND}}}

% marcado en warrant
\newcommand{\MarkAtomic}{\mbox{{\sf Mark-Atom}}}
\newcommand{\MarkD}{\mbox{{\sf Mark-1D}}}
\newcommand{\MarkND}{\mbox{{\sf Mark-ND}}}


% ..................................................................................
% CONVENCIONES DE NOTACION

% Utilizaremos ###### para anteceder a secciones
% Utilizaremos #====#====#====#====#====#=====# para subsecciones
% Utilizaremos #=========#=========#==========# para subsubsecciones

% Utilizaremos ====== para encerrar definiciones

% Utilizaremos ------ para encerrar proposiciones, lemas y teoremas

% Utilizaremos ~~~~~~ para encerrar ejemplos

% Utilizaremos ...... para separar areas de texto a distinguir entre si
% Definicion de \label en LaTeX
% Comenzaran con        Etiquetas asociadas a
%      Sec              secciones, subsecciones, etc.
%      Fig              figuras
%      Eq:              ecuaciones
%      Def              definiciones
% ..................................................................................



% =====================================================================
%
%  Notacion de defeat segun especificidad
%
% =====================================================================


% =====================================================================
% COMPARACION DE PREFERENCIA -- ESPECIFICIDAD / Comandos
% =====================================================================


% strict defeater
\newcommand{\Pdft}{\mbox{$\succ$}}

% blocking defeater
\newcommand{\Bdft}{\mbox{$\asymp$}}

% just defeats
\newcommand{\Dft}{\mbox{$\succeq$}}

%
\newcommand{\NotPdft}{\mbox{$\not\succ_{\mathbf spec}$}}



%\newcommand{\Bdft}{\mbox{$\succeq$}}
%\newcommand{\NotBdft}{\mbox{$\not\succeq$}}

% not comparable by specificity
\newcommand{\Eqdft}{\mbox{$\approx_{\mathbf spec}$}}
\newcommand{\NotEqdft}{\mbox{$\not\approx_{\mathbf spec}$}}


\newcommand{\completar}{\fbox{** completar **}}

\newcommand{\ojo}[1]{$\Longrightarrow$\ \framebox{\parbox{15cm}{{\small\sf #1}}}}


\newcommand{\nulo}{*}


\newcommand{\antec}{\mbox{$\sqsubset$ }}
\newcommand{\anteceq}{\mbox{$\sqsubseteq$ }}
\newcommand{\mantec}{\mbox{$\stackrel{{\footnotesize *}}{\sqsubseteq}$}}

\newcommand{\via}{\mbox{via }}
%\newcommand{\warranted}{\mbox{{\em warranted}}}



% dur permite definir unidades rebatibles atomicas
% el soporte #1 coincide con la conclusion #1
\newcommand{\dur}[2]{ \du{ \etar{\cto{#1}}{\cto{#2}}}{ #1 } }
% dun permite definir unidades no-rebatibles atomicas
% el soporte es \emptyset, la conclusion es #1
\newcommand{\dun}[2]{ \du{ \etar{\emptyset}{\cto{#2}}}{ #1 } }

\begin{document}

\begin{center}
     {\Large\bf      Integrating Defeasible Argumentation \\
                      and Machine Learning Techniques  \\
                                    \vspace{1mm}
                          %  \vspace*{2mm} \\
                         {\large (Preliminary Report)} }
\end{center}

\begin{center}
    { \large Sergio Alejandro G\'{o}mez \hspace{1.5cm}    Carlos Iv\'{a}n
    Ches\~{n}evar }
\end{center}

\begin{center}
% \ \\
\begin{tabular}{c}
% \ \\
{ Laboratorio de Investigaci\'on y Desarrollo en Inteligencia
Artificial}
\\
{Departamento de Ciencias e Ingenier\'{\i}a de la
Computaci\'on}  \\ {\sc Universidad Nacional del Sur}
\\ {Av.\ Alem 1253 -- B8000CPB Bah\'{\i}a Blanca -- {\sc Rep\'ublica
Argentina}} \\ {\sc Tel/Fax:} (+54) (291) 459 5135/5136 -- {\sc
Email:} {\tt \{sag, cic\}@cs.uns.edu.ar} \\
\end{tabular}

%----------------------------------------------------
% Sacar esto en caso de que se vaya a 6 paginas. sag.
 \vspace{2mm}
%----------------------------------------------------
\begin{footnotesize}
{\sc Key words:} {\sf Machine Learning, Defeasible Argumentation, Knowledge-based systems, Text mining.}
\end{footnotesize}
\end{center}


\nocite{ChesnePHD2001}
\nocite{Simari92}
%\nocite{Transfor2001}
\nocite{GarciaPHD2000}
\nocite{Survey2000}
\nocite{Tou2001}

% ==========================================

\begin{abstract}
\noindent The field of machine learning (ML) is concerned with the
question of how to construct algorithms that automatically improve
with experience. In recent years many successful ML applications
have been developed, such as datamining programs,
information-filtering systems, etc. Although ML algorithms allow
the detection and extraction of interesting patterns of data for
several kinds of problems, most of these algorithms are based on
\emph{quantitative} reasoning, as they rely on training data in
order to infer so-called target functions.

In the last years \emph{defeasible argumentation} has proven to be
a sound setting to formalize common-sense \emph{qualitative}
reasoning. This approach can be combined with other inference
techniques, such as those provided by machine learning theory.

In this paper we outline different alternatives for combining defeasible
argumentation and machine learning techniques. We suggest how different
aspects of a generic argument-based framework can be integrated with
other ML-based approaches.
\end{abstract}
% ===================================================================



% ===================================================================
\section{Introduction and motivations}
\label{sec:intro}

The ability to generate and collect data has increased exponentially in
the last years. Automatizing transactional databases has resulted in
an explosive growth of information, motivating the evolution of
several \emph{datamining} techniques.
Simply stated, datamining refers to \emph{extracting or mining knowledge
from large amounts of data}. This knowledge constitutes non-trivial
and potentially useful information that can be obtained in many cases
by applying \emph{machine learning} (ML) techniques.

The field of machine learning is concerned with the question of how
to construct algorithms that automatically improve with experience~\cite{mitchell}.
In recent years many successful ML applications have been developed,
such as datamining programs, information-filtering systems, etc.
Although ML algorithms allow the detection and extraction of
interesting patterns of data for several kinds of problems,
most of these algorithms provide an output based
on \emph{quantitative} evidence (i.e. training data), whereas
the inference process which  led to this output is commonly unknown
(i.e. `black-box' metaphor).

In the last years \emph{defeasible
argumentation}~\cite{Survey2000,PraVre99,Simari92} has proven to be
a sound setting to formalize common-sense \emph{qualitative}
reasoning. This approach can be combined with other inference
techniques, such as those provided by machine learning theory.

In this preliminary report we explore different alternatives for
developing applications which combine defeasible argumentation and
machine learning techniques. We
suggest how different aspects of a generic argument-based
framework can be integrated with other ML-based
approaches. The paper is structured as follows. First, we briefly
introduce the components of most argument-based framework and then
outline possible directions for the integration of ML techniques
and defeasible argumentation. Next, we describe a particular
setting suitable for the application of such approach, namely
text mining problems.
%Finally, we consider some future look at where this research can
%aim for in the future.
Finally, we discuss some promising research lines that are
currently being pursued.

% ===================================================================
\section{Integrating ML and argument-based frameworks}
\label{sec:framework}

Argument-based frameworks~\cite{Simari92,Survey2000,PraVre99}
provide a sound formalization of defeasible reasoning, and have
found a wide acceptance in many areas such as development of legal
reasoning applications, multiagent systems, etc. As pointed out
in~\cite{Carbogim00}, most argument-based frameworks share a number
of common notions, namely:

\begin{enumerate}
\item
  \textbf{Knowledge Base formalized in an underlying logical language}:
  Most argument-based frameworks involve
  a knowledge base $K=(\Pi,\Delta)$ which provides \emph{background knowledge}
  for an intelligent agent formalized in a first-order logical language $L$.
  This background knowledge typically involves a set $\Pi$ of \emph{strict rules}
  and \emph{facts}  and a set $\Delta$ of \emph{defeasible rules}.

\item
   \textbf{Argument}:
   An  \emph{argument} is a defeasible proof obtained from the knowledge
   base $K$ by applying suitable (defeasible) inference rules
   associated with the underlying logical language $L$.

\item \textbf{Dialectical reasoning}:
   Given two arguments $A$ and $B$, conflict (or attack) among arguments
   arises whenever  $A$ and $B$ cannot be simultaneously accepted (typically
   because of some kind of logical contradiction). Many argument systems provide a
   preference criterion which defines a partial order among arguments,
   allowing to determine whether $A$ should be preferred over $B$.
   This defines a \emph{defeat} relationship.
   Given the set $Args$ of arguments obtained from a knowledge base $K$,
   it holds that $attacks \subseteq Args \times Args$, and  $defeats \subseteq attacks$.
   In order to determine whether a given argument $A$ is ultimately
   undefeated (or \emph{warranted}), a dialectial process is recursively
   carried out, where defeaters for $A$, defeaters for these defeaters, and so on,
   are taken into account.
 \end{enumerate}


Next we will outline different approaches that we are currently considering
to model the above issues in the context of ML techniques.

\begin{itemize}

\item
   \textbf{Building a defeasible knowledge base from training data}:

% Towards the Application of Association Rules
% for Defeasible Rule Discovery
% by Guido Governatori and Andrew Stranieri
% JURIX 2001

Recently there have been some approaches to obtaining defeasible
rules from training data, particularly in the context of Inductive
Logic Programming (ILP). In~\cite{Inoue}, the authors present a
method to generate non-monotonic rules with exceptions from
positive/negative examples and background knowledge in Inductive
Logic Programming. The form of the programs to be learnt is the
one of \emph{extended logic programs}, which incorporates both
strict negation and negation as failure that can be effectively
used in the presence of incomplete information. Default rules are
generated as specializations of general rules that cover positive
examples, whereas exceptions to general rules are identified from
negative examples and are then generalized to rules for
cancellation of defaults. The resulting learning system LELP
allows also to learn hierarchical defaults by recursively calling
an exception identification algorithm.

% FLACH
%PhD Thesis: "Conjectures: An inquiry concerning the logic of induction"
%Peter Flach, 1998, Univ. of Bristol, UK

In~\cite{Guido}, the authors investigate
the feasibility of
Knowledge Discovery from Data-bases (KDD) in order to facilitate
the discovery of defeasible rules for legal decision making. In
particular they argue in favour of Defeasible Logic as an
appropriate formal system in which the extracted principles should
be encoded.

In the context of obtaining defeasible rules  by means of induction-based techniques,
the work of Peter Flach~\cite{Flach} provides an interesting survey of
several approaches to computational induction and provides a descriptive
theory of induction as a logical framework system.
Several rule systems for conjectural reasoning are axiomatized
and semantically characterized.

\item
%   \textbf{Using ML techniques for building arguments}:
\textbf{Building arguments}:
%--------------------
\newcommand{\argument}[2]{\langle #1, #2 \rangle}

Finding hypotheses which explain unseen instances is
central to most ML algorithms. Interestingly, in argument-based
frameworks an argument is also understood as
providing ``a hypothesis supporting a given conclusion''~\cite{Simari92}.
We contend that argument-based reasoning and
many ML techniques share this common notion. Many theoretical
results from argument theory could therefore be applied in a ML context.

\emph{Analytical learning} methods~\cite{mitchell}
(like explanation-based learning) offer the advantage of
generalizing more accurately from less data by using prior
knowledge to guide learning.  However, they can be misled when
given incorrect or insufficient prior knowledge.  On the other
hand, \emph{inductive learning} methods (like neural nets, decision tree
learning, inductive logic programming) offer the advantage that
they require no explicit prior knowledge and learn regularities
based solely on the training data. However, they can fail when
given insufficient training data, and can be misled by the
implicit inductive bias they must adopt in order to generalize
beyond the observed data.
A combined analytical and inductive ML method that overcomes the pitfalls
associated with each separate approach (yet conserving their
individual advantages) should be as follows: given a set of
training examples $D$ of some target function $f$ (possibly
containing errors), a domain theory $B$ (possibly containing
errors), and a space of candidate hypothesis $H$, determines which
hypothesis $h$ fits best the training examples and domain theory.

We think that defeasible argumentation can be used to improve ML
approaches as the one described above  as it provides a sound
formalization for both expressing and reasoning with uncertain and
incomplete information. From the set of examples $D$ and theory
$B$, a knowledge base $(\Pi, \Delta)$ can be induced as explained
above. The hypothesis $h$ can be expressed as an argument structure
$\argument{A}{h}$ where $A$ stands for both the relevant part of
the background theory and relevant features of $D$.
%Besides, a prediction of $f$ over a previously
%unseen instance $x$ will be justified by the  defeasible
%entailment $h \wedge x \vdash f(x)$.

%--------------------
\item
%   \textbf{Using ML techniques in dialectical reasoning}:
\textbf{Dialectical reasoning and ML}:

The process of defeasible argumentation always involves the
analysis of conflicting arguments in a dialectical setting. As
explained before, such setting relies on a \emph{defeat}
relationship for comparing conflicting arguments. Determining
whether an argument is ultimately accepted requires a recursive
analysis in which defeaters, defeaters for these defeaters, and so
on, are taken into account~\cite{Survey2000}.

In many formalizations of argumentation the notion of defeat is
considered as an abstract relationship (i.e. a partial order $\preceq$
among  arguments). Some approaches (e.g.~\cite{Simari92})
rely on the notion of \emph{specificity} for defining defeat.
In this context, ML techniques provide sound alternatives for
considering \emph{numeric attributes} or \emph{probabilistic values}
for deciding between conflicting hypotheses~\cite{mitchell}.
We think that such approaches could provide the basis for defining
new comparison criteria in the context of argument-based frameworks.
In the same line of reasoning, contrasting conflicting hypotheses is
a common situation in many ML algorithms.
In this setting defeasible argumentation provides a useful theoretical background
for contrasting such hypotheses,
making easier to identify \emph{fallacious} patterns of reasoning
which might lead to incorrect results.

%In a ML setting, classifying a previously unseen instance involves
%using some criteria to decide on the classification of that
%instance.
%A dialectical reasoning can be carried out to balance
%or contrast the evidence for and against the predicted
%classification.
%------------------------------

\end{itemize}


% ===================================================================
\section{Text mining: a case study}
\label{sec:textmining}

%  \subsection{Problem definition}

Datamining is the process of discovering interesting patterns
from large amounts of data \cite{han}. In \emph{textual datamining} the needs
of the user may vary from looking for a specific piece of text
to getting familiarized with a subject area \cite{honkela}.
Basic approaches for information retrieval and
data mining involve the following strategies:
\begin{itemize}
     \item
     \emph{Searching using keywords:} This is done by
    automatically indexing the documents by frequency of term
    appearance.
   %Each query is converted into a list of terms. Then the query
   % is compared to the document representations.
    This approach is used by web crawlers \cite{brin}
     and traditional information retrieval systems \cite{frakes}.
    \item
     \emph{Exploration of the document collection supported by
    organizing the documents in some manner:} For each document,
    an internal representation is obtained
    % \cite{salton}
    and then the documents are
    arranged into clusters by some similarity measure \cite{rasmussen}.
    This process can be done by using ML
    techniques such as neural networks \cite{gomez1, gomez2, honkela,
    kohonen} or bayesian classifiers \cite{billsus, pazzani}.
     \item
     \emph{Filtering:}  It refers to discarding uninteresting
    documents from an incoming document flow \cite{mostafa}.
 \end{itemize}

Each approach has its pros and cons. Searching using keywords is
easy to implement but can lead to retrieve unrelated documents or,
even worse, to not discover related documents (this can be
measured using some metric such as precision and recall
\cite{frakes}). Clustering of documents can be efficiently
implemented by neural nets but may require retraining in the
presence of new examples; besides, in this case the model is not
understandable by a human programmer because it is compiled as a
set of numerical weights.  Filtering is difficult because of the
dynamic nature of user interests and document flow \cite{gomez1}.

Some recent approaches propose using argumentation to analyze
structured text in the form of XML documents~\cite{besnard-hunter,
hunter1}. As explained in the previous section, we feel that the
integration of defeasible argumentation and ML can tackle many of
the problems described above, thus enhancing existing algorithms
for text mining.

% ==========================================
\section{Conclusions and future work}
\label{sec:conclu}

The success of argumentation-based approaches is partly due to the
sound setting it provides for \emph{qualitative reasoning}.
Although numeric attributes offer an useful source of information
for \emph{quantitative reasoning} in several knowledge domains,
they have been mostly neglected  in the defeasible argumentation
community. This is maybe due to the historical origins of
argumentative reasoning, which were more related to legal
(qualitative) reasoning rather than to number-based attributes as
those used in rule-based production systems.

We think that integrating ML techniques with argumentation
frameworks would be highly desirable, as it would provide a
combination of both analytical and inductive ML methods capable of
tackling the pitfalls of each separately yet conserving their
advantages, making them more attractive and suitable for other
research and application areas. Part of our current research work
is focused on these aspects.

% ==========================================
% Referencias

% \begin{scriptsize}
\begin{footnotesize}
\bibliographystyle{giia}
%\bibliography{papers}
\newcommand{\etalchar}[1]{$^{#1}$}
\begin{thebibliography}{MMLP97}

\bibitem[BH01]{besnard-hunter}
{\sc Besnard, P., and Hunter, A.}
\newblock A logic-based theory of deductive arguments.
\newblock {\em Artificial Intelligence 128\/} (2001), 203--235.

\bibitem[BP97]{billsus}
{\sc Billsus, D., and Pazzani, M.}
\newblock Learning probabilistic user models.
\newblock {\em Workshop notes of Machine Learning for User Modeling, Sixth
  International Conference on User Modeling, Chia Laguna, Sardinia, 2-5 June
  1997\/} (1997).
\newblock Available at http://www.ics.uci.edu/\~{
  }pazzani/Publications/ProbUserModels.ps.

\bibitem[BP00]{brin}
{\sc Brin, S., and Page, L.}
\newblock The anatomy of a large-scale hypertextual web search engine., 2000.
\newblock Available at
  http://www7.scu.edu.au/programme/fullpapers/1921/com1921.htm.

\bibitem[CML00]{Survey2000}
{\sc Ches{\~n}evar, C.~I., Maguitman, A., and Loui, R.}
\newblock {L}ogical {M}odels of {A}rgument.
\newblock {\em ACM Computing Surveys 32}, 4 (December 2000), 337--383.

\bibitem[CRL00]{Carbogim00}
{\sc Carbogim, D., Robertson, D., and Lee, J.}
\newblock Argument-based applications to knowledge engineering.
\newblock {\em The Knowledge Engineering Review (to appear)\/} (2000).

\bibitem[FBY92]{frakes}
{\sc Frakes, W., and Baeza-Yates, R.}
\newblock {\em Information Retrieval. Data Structures and Algorithms}.
\newblock Prentice Hall, 1992.

\bibitem[Fla98]{Flach}
{\sc Flach, P.}
\newblock {\em Conjectures: An inquiry concerning the logic of induction}.
\newblock PhD thesis, University of Bristol, UK, 1998.

\bibitem[GL01a]{gomez1}
{\sc G\'{o}mez, S.~A., and Lanzarini, L.}
\newblock Aplicaci\'on de redes neuronales al filtrado de documentos.
\newblock {\em III Workshop de Investigadores en Ciencias de la Computaci\'on.
  WICC 2001, San Luis\/} (2001), 131--133.

\bibitem[GL01b]{gomez2}
{\sc G\'{o}mez, S.~A., and Lanzarini, L.}
\newblock Querando!: Un agente de filtrado de documentos web.
\newblock {\em CACIC 2001 (VII Congreso Argentino de Ciencias de la
  Computaci\'on, El Calafate, Argentina\/} (2001), 1205--1217.

\bibitem[GS01]{Guido}
{\sc Governatori, G., and Stranieri, A.}
\newblock Towards the application of association rules for defeasible rule
  discovery.
\newblock In {\em JURIX\/} (2001).

\bibitem[HK00]{han}
{\sc Han, J., and Kamber, M.}
\newblock {\em Datamining. Concepts and Techniques.}
\newblock Morgan Kaufmann, 2000.

\bibitem[Hon97]{honkela}
{\sc Honkela, T.}
\newblock {\em Self-organizing maps in Natural Language Processing.}
\newblock PhD thesis, Helsinky University of Technology, 1997.

\bibitem[Hun01]{hunter1}
{\sc Hunter, A.}
\newblock Hybrid argumentation systems for structured news reports, 2001.

\bibitem[IK97]{Inoue}
{\sc Inoue, K., and Kudoh, Y.}
\newblock {L}earning {E}xtended {L}ogic {P}rograms.
\newblock In {\em Proc. of the 15th Int. Conf. on Artificial Intelligence\/}
  (1997), Morgan Kaufmann.

\bibitem[KKL{\etalchar{+}}00]{kohonen}
{\sc Kohonen, T., Kaski, S., Lagus, K., Saloj\"{a}rvi, J., Honkela, J.,
  Paatero, V., and Saarela, A.}
\newblock Self organization of a massive document collection.
\newblock {\em IEEE Transactions on Neural Networks, Vol. 11, No. 3, May
  2000\/} (2000).

\bibitem[Mit97]{mitchell}
{\sc Mitchell, T.}
\newblock {\em Machine Learning}.
\newblock Mc Graw Hill, 1997.

\bibitem[MMLP97]{mostafa}
{\sc Mostafa, J., Mukhopadhyay, S., Lam, W., and Palakal, M.}
\newblock A multilevel approach to intelligent information filtering: Model,
  system, and evaluation.
\newblock {\em ACM Transactions on Information Systems, Vol. 15, No. 4.\/}
  (October 1997), 368--399.

\bibitem[PB97]{pazzani}
{\sc Pazzani, M., and Billsus, D.}
\newblock Learning and revising user profiles: The identification of
  interesting web sites.
\newblock {\em Machine Learning 27\/} (1997), 313--331.

\bibitem[PV99]{PraVre99}
{\sc Prakken, H., and Vreeswijk, G.}
\newblock {L}ogics for {D}efeasible {A}rgumentation.
\newblock In {\em Handbook of Philosophical Logic}, D.~Gabbay, Ed. Kluwer
  Academic Publisher, 1999.

\bibitem[Ras92]{rasmussen}
{\sc Rasmussen, E.}
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\end{thebibliography}

\end{footnotesize}
% \end{scriptsize}

\end{document}

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