\documentclass[landscape]{slides}
\usepackage[dvips]{color}
\usepackage{amssymb,amsmath}
\usepackage{qtree}
\title{\textcolor{red}{Introduction to Head-Driven Phrase Structure Grammar [Sag and Wasow, 1999]}}
\author{Ariadna Font Llitj\'{o}s and Katharina Probst}
\date{\today}

\begin{document}
\maketitle

%%%%---------------------------------------------%%%%
%%%%%%%%%%%%%%%%%%%%% NOTES %%%%%%%%%%%%%%%%%%%%%%%%%

%%%%---------------------------------------------%%%%

\begin{slide}
\begin{center}
\textcolor{red}{\textbf{Basic Design Choices of HPSG\/}}
\end{center}
\begin{small}
\begin{itemize}
\item Emphasis on the lexicon:  The lexical entries are very complex
\item Few grammar rules: Grammar rules apply to all phrase types
\item The constructed parse tree�s nodes are feature structures
\end{itemize}
\end{small}
\end{slide}

%------------------------------------

\begin{slide}
\begin{center}
\textcolor{red}{\textbf{Outline\/}}
\end{center}
\begin{small}
\begin{itemize}
\item Lexical Entries: How are words represented in the lexicon?
\item Lexical hierarchy and inheritance: How can we limit the complexity of the lexical entries?
\item Lexical Rules: How do we obtain derived word forms?
\item Grammar Rules: How do we combine nodes in a parse tree?
\item Principles: What principles guide the parse tree construction?
\item Sample Parse: \textit{Ann likes the boy.}
\end{itemize}
\end{small}
\end{slide}

%------------------------------------

\include{HPSGLexicon}


%------------------------------------

\begin{slide}
\begin{center}
\textcolor{red}{\textbf{Grammar Rules\/}}\\
\end{center}
\begin{tiny}
\begin{itemize}

\item \textbf{Head-Complement Rule}
\begin{displaymath}
\left \lbrack \begin{array}{ll}
phrase & \\
COMPS & \langle \rangle
\end{array} \right \rbrack
\rightarrow
H \left \lbrack \begin{array}{ll}
word & \\
COMPS & \langle \boxed{1},\dots,\boxed{n}\rangle
\end{array} \right \rbrack \boxed{1},\dots,\boxed{n}
\end{displaymath}

\item \textbf{Head-Specifier Rule}
\begin{displaymath}
\left \lbrack \begin{array}{ll}
phrase & \\
SPR & \langle \rangle
\end{array} \right \rbrack
\rightarrow
\boxed{1} \ \ \ \  H \left \lbrack \begin{array}{ll}
phrase & \\
SPR & \langle \boxed{1}\rangle
\end{array} \right \rbrack 
\end{displaymath}

\item \textcolor{blue}{\textbf{Head-\textit{Pre}Modifier Rule }
\begin{displaymath}
\lbrack phrase \rbrack 
\rightarrow
\left \lbrack \begin{array}{ll}
phrase & \\
MOD & \langle \boxed{1}\rangle
\end{array} \right \rbrack 
H \boxed{1} \lbrack phrase \rbrack\ \ \  
\end{displaymath}}

\item \textbf{Head-\textit{Post}Modifier Rule }
\begin{displaymath}
\lbrack phrase \rbrack 
\rightarrow
H \boxed{1} \lbrack phrase \rbrack\ \ \  
\left \lbrack \begin{array}{ll}
phrase & \\
MOD & \langle \boxed{1}\rangle
\end{array} \right \rbrack 
\end{displaymath}
\end{itemize}
\end{tiny}
\end{slide}

%------------------------------------

\begin{slide}
\begin{center}
\textcolor{red}{\textbf{Grammar Rules cont.\/}}\\
\end{center}
\begin{tiny}
\begin{itemize}

\item \textbf{Coordination Rule}
\begin{displaymath}
\left \lbrack \begin{array}{ll}
SYN & \boxed{0}\\
IND & s_{0}
\end{array} \right \rbrack
\rightarrow
\left \lbrack \begin{array}{ll}
SYN & \boxed{0}\\
IND & s_{0}
\end{array} \right \rbrack \dots 
\end{displaymath}
\begin{displaymath}
\left \lbrack \begin{array}{ll}
SYN & \boxed{0}\\
IND & s_{n-1}
\end{array} \right \rbrack
\left \lbrack \begin{array}{ll}
HEAD & conj\\
IND & s_{0}\\
RESTR & \langle \lbrack \begin{array}{ll}
ARGS & \langle s_{1}\dots s_{n}\rangle 
\end{array} \rbrack \rangle 
\end{array} \right \rbrack
\left \lbrack \begin{array}{ll}
SYN & \boxed{0}\\
IND & s_{n}
\end{array} \right \rbrack 
\end{displaymath}

\item \textbf{Imperative Rule}
\begin{displaymath}
\left \lbrack \begin{array}{ll}
phrase & \\
HEAD & \left \lbrack \begin{array}{ll}
verb & \\
FORM & fin
\end{array} \right \rbrack \\
SPR & \langle \rangle \\ 
COMPS & \langle \rangle \\ 
SEM & \left \lbrack \begin{array}{ll}
MODE & dir \\
INDEX & s 
\end{array} \right \rbrack 
\end{array} \right \rbrack
\rightarrow
\left \lbrack \begin{array}{ll}
phrase & \\
HEAD & \left \lbrack \begin{array}{ll}
verb & \\
FORM & inf
\end{array} \right \rbrack \\
SPR & \langle NP \left \lbrack \begin{array}{ll}
PER & 2nd
\end{array} \right \rbrack \rangle \\
SEM & \left \lbrack \begin{array}{ll}
INDEX & s 
\end{array} \right \rbrack \\
\end{array} \right \rbrack
\end{displaymath}

\end{itemize}
\end{tiny}
\end{slide}

%------------------------------------

\begin{slide}
\begin{center}
\textcolor{red}{\textbf{Only a few Grammar Rules, but...\/}}\\
\end{center}

\begin{small}
\begin{itemize}
\item Grammar rules are very general (they don't depend on the POS of the head nor the complements and specifier), except for the \textcolor{red}{linear ordering of the constraints}.

\item For attributive adjectives (\textit{`the tall boy'}), we already would need to introduce a new rule, the Head-PreModifier Rule above.

\end{itemize}
\end{small}
\end{slide}

%------------------------------------

\begin{slide}
\begin{center}
\textcolor{red}{\textbf{Parsing \textit{`Ann likes the boy'}}}\\

\textcolor{red}{\textbf{Applying the Head-Complement Rule to \textit{`Ann'}}}\\
\end{center}
\begin{tiny}\begin{tiny}

%! Missing $ inserted.
%<inserted text> 
%                $
%l.168 \end
%          {tiny}

%\begin{tiny}
%\Tree [ .{\left {\lbrack {\begin{array}{ll} phrase & \\
%COMPS & {\langle {\rangle }} {\end{array}}} {\rbrack}} {\right}} [ .N ]]
%\end{tiny}
%\end{slide}

%------------------------------------
 
%\begin{slide}
%\begin{tiny}

%\def\FS{{\left {\lbrack {\begin{array}{ll}
%phrase & \\
%COMPS & {\langle {\rangle}}
%\end{array}} {\right} {\rbrack}}}}

%\Tree 
%[ .\FS [ N ]]

%\end{tiny}
%\end{slide}

%------------------------------------
\begin{displaymath}
\left \lbrack \begin{array}{ll}
phrase & \\
COMPS & \langle \rangle
\end{array} \right \rbrack
\rightarrow
H \left \lbrack \begin{array}{ll}
word & \\
COMPS & \langle \boxed{1},\dots,\boxed{n} \rangle
\end{array} \right \rbrack \boxed{1},\dots,\boxed{n}
\end{displaymath}

\begin{tiny}
\begin{displaymath}
NP \left \lbrack \begin{array}{ll}
\textcolor{red}{phrase} & \\
SYN & \left \lbrack \begin{array}{ll}
HEAD & \boxed{1} \\
SPR  & \langle \rangle \\
\textcolor{red}{COMPS} & \textcolor{red}{\langle \rangle} \\
\end{array} \right \rbrack \\
ARG-ST & \langle \rangle \\
SEM & \left \lbrack \begin{array}{ll}
INDEX & i \\
MODE & ref \\
RESTR & \boxed{a}\\
\end{array} \right 
\rbrack 
\end{array} \right
\rbrack
\rightarrow
\left \lbrack \begin{array}{ll}
\textcolor{red}{word}& \\
SYN & \left \lbrack \begin{array}{ll}
HEAD & \boxed{1} \left \lbrack \begin{array}{ll}
noun &\\
ANA & - \\
CASE & {\lbrace nom,acc\rbrace}\\
AGR & \left \lbrack \begin{array}{ll}
NUM & sg \\
PER & 3rd \\
\end{array} \right \rbrack
\end{array} \right \rbrack\\
SPR  & \langle \rangle \\
\textcolor{red}{COMPS} & \textcolor{red}{\langle \rangle} \\
\end{array} \right \rbrack \\
ARG-ST & \langle \rangle \\
SEM & \left \lbrack \begin{array}{ll}
INDEX & i \\
MODE & ref \\
RESTR & \langle \boxed{a} \left \lbrack \begin{array}{ll}
RELN & name \\
SIT & s \\
NAME & Ann \\
NAMED & i  
\end{array} \right \rbrack \rangle
\end{array} \right 
\rbrack 
\end{array} \right
\rbrack
\end{displaymath} 

\end{tiny}
\end{tiny}\end{tiny}
\end{slide}

%------------------------------------

\begin{slide}
\begin{center}
\textcolor{red}{\textbf{Principles applied to guarantee well-formedness}}
\end{center}
\begin{footnotesize}

\textbf{Head Feature Principle (HFP)}
\begin{tiny}
\begin{center}
\begin{displaymath}
\lbrack HEAD \boxed{1} \rbrack 
\end{displaymath}
\begin{displaymath}
/ \ \ \ \ \ \vert \ \ \ \ \ \backslash 
\end{displaymath}
\begin{displaymath}
\dots\ \ \ \ \ \ \ \ \  \delta_{h}\ \ \ \ \ \  \dots
\end{displaymath}
\begin{displaymath}
\lbrack HEAD \boxed{1} \rbrack
\end{displaymath}
\end{center}
\end{tiny}

\textbf{Semantic Inheritance Principle (SIP)}
\begin{tiny}
\begin{center}
\begin{displaymath}
\left \lbrack \begin{array}{ll}
MODE & \boxed{4}\\
INDEX & \boxed{5}
\end{array} \right
\rbrack
\end{displaymath}
\begin{displaymath}
/ \ \ \ \ \ \ \ \ \vert \ \ \ \ \ \ \ \ \backslash 
\end{displaymath}
\begin{displaymath}
\dots\ \ \ \ \ \ \ \ \ \ \ \ \ \  \delta_{h}\ \ \ \ \ \ \ \ \ \ \  \dots
\end{displaymath}
\begin{displaymath}
\left \lbrack \begin{array}{ll}
MODE & \boxed{4}\\
INDEX & \boxed{5}
\end{array} \right
\rbrack
\end{displaymath}
\end{center}

\end{tiny}\end{footnotesize}
\end{slide}

%------------------------------------

\begin{slide}
\begin{center}
\textcolor{red}{\textbf{{Effects of Head Feature Principle and Semantic Inheritance Principle application}}}\\
\end{center}

\begin{tiny}\begin{tiny}\begin{tiny}

\begin{displaymath}
NP \left \lbrack \begin{array}{ll}
\textcolor{red}{phrase} & \\
SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\boxed{1}} \\
SPR  & \langle \rangle \\
\textcolor{red}{COMPS} & \textcolor{red}{\langle \rangle} \\
\end{array} \right \rbrack \\
ARG-ST & \langle \rangle \\
SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{INDEX} & \textcolor{blue}{i} \\
\textcolor{blue}{MODE} & \textcolor{blue}{ref} \\
RESTR & \boxed{a}\\
\end{array} \right 
\rbrack 
\end{array} \right
\rbrack
\rightarrow
\left \lbrack \begin{array}{ll}
\textcolor{red}{word}& \\
SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\boxed{1} \left \lbrack \begin{array}{ll}
noun &\\
ANA & - \\
CASE & {\lbrace nom,acc\rbrace}\\
AGR & \left \lbrack \begin{array}{ll}
NUM & sg \\
PER & 3rd \\
\end{array} \right \rbrack
\end{array} \right \rbrack}\\
SPR  & \langle \rangle \\
\textcolor{red}{COMPS} & \textcolor{red}{\langle \rangle} \\
\end{array} \right \rbrack \\
ARG-ST & \langle \rangle \\
SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{INDEX} & \textcolor{blue}{i} \\
\textcolor{blue}{MODE} & \textcolor{blue}{ref} \\
RESTR & \langle \boxed{a} \left \lbrack \begin{array}{ll}
RELN & name \\
SIT & s \\
NAME & Ann \\
NAMED & i  
\end{array} \right \rbrack \rangle
\end{array} \right 
\rbrack 
\end{array} \right
\rbrack
\end{displaymath} 

\end{tiny}\end{tiny}\end{tiny}
\end{slide}

%------------------------------------

\begin{slide}

\begin{footnotesize}

\textbf{Valence Principle (VP)}

\begin{itemize}
\item \textbf{A}
\begin{center}
\begin{tiny}
\begin{displaymath}
\lbrack COMPS \boxed{b} \rbrack 
\end{displaymath}
\begin{displaymath}
/ \ \ \ \ \ \vert \ \ \ \ \ \backslash 
\end{displaymath}
\begin{displaymath}
\dots\ \ \ \ \ \ \ \ \  \delta_{h}\ \ \ \ \ \  \dots
\end{displaymath}
\begin{displaymath}
\lbrack COMPS \boxed{b} \rbrack
\end{displaymath}
\end{tiny}
\end{center}
\item \textbf{B}
\begin{center}
\begin{tiny}
\begin{displaymath}
\lbrack SPR \boxed{c} \rbrack 
\end{displaymath}
\begin{displaymath}
/ \ \ \ \ \ \vert \ \ \ \ \ \backslash 
\end{displaymath}
\begin{displaymath}
\dots\ \ \ \ \ \ \ \ \  \delta_{h}\ \ \ \ \ \  \dots
\end{displaymath}
\begin{displaymath}
\lbrack SPR \boxed{c} \rbrack
\end{displaymath}
\end{tiny}
\end{center}
\end{itemize}
\end{footnotesize}

\end{slide}

%------------------------------------

\begin{slide}
\begin{center}
\textcolor{red}{\textbf{{+ Valence Principle (B) application}}}\\
\end{center}

\begin{tiny}\begin{tiny}\begin{tiny}

\begin{displaymath}
NP \left \lbrack \begin{array}{ll}
\textcolor{red}{phrase} & \\
SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\boxed{1}} \\
\textcolor{blue}{SPR}  & \textcolor{blue}{\langle \rangle} \\
\textcolor{red}{COMPS} & \textcolor{red}{\langle \rangle} \\
\end{array} \right \rbrack \\
ARG-ST & \langle \rangle \\
SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{INDEX} & \textcolor{blue}{i} \\
\textcolor{blue}{MODE} & \textcolor{blue}{ref} \\
RESTR & \boxed{a}\\
\end{array} \right 
\rbrack 
\end{array} \right
\rbrack
\rightarrow
\left \lbrack \begin{array}{ll}
\textcolor{red}{word}& \\
SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\boxed{1} \left \lbrack \begin{array}{ll}
noun &\\
ANA & - \\
CASE & {\lbrace nom,acc\rbrace}\\
AGR & \left \lbrack \begin{array}{ll}
NUM & sg \\
PER & 3rd \\
\end{array} \right \rbrack
\end{array} \right \rbrack}\\
\textcolor{blue}{SPR}  & \textcolor{blue}{\langle \rangle} \\
\textcolor{red}{COMPS} & \textcolor{red}{\langle \rangle} \\
\end{array} \right \rbrack \\
ARG-ST & \langle \rangle \\
SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{INDEX} & \textcolor{blue}{i} \\
\textcolor{blue}{MODE} & \textcolor{blue}{ref} \\
RESTR & \langle \boxed{a} \left \lbrack \begin{array}{ll}
RELN & name \\
SIT & s \\
NAME & Ann \\
NAMED & i  
\end{array} \right \rbrack \rangle
\end{array} \right 
\rbrack 
\end{array} \right
\rbrack
\end{displaymath} 

\end{tiny}\end{tiny}\end{tiny}
\end{slide}
%------------------------------------

\begin{slide}

\begin{center}
\textcolor{red}{\textbf{Result of applying the Head-Complement Rule\\ to \textit{`the'}}}
\end{center}

\begin{tiny}\begin{tiny}

\begin{displaymath}
DetP \left \lbrack \begin{array}{ll}
\textcolor{red}{phrase}& \\
PHON & the\\
ARG-ST & \langle \rangle\\

SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\left \lbrack \begin{array}{ll}
det &\\
COUNT & + \\
AGR & \left \lbrack \begin{array}{ll}
NUM & {sg,pl} \\
\end{array} \right \rbrack \\
\end{array} \right \rbrack} \\
\textcolor{blue}{SPR}  & \textcolor{blue}{\langle \rangle} \\
\textcolor{red}{COMPS} & \textcolor{red}{\langle \rangle} \\
\end{array} \right \rbrack \\

SEM & \left \lbrack \begin{array}{ll}
RESTR & \boxed{a} \\
\dots &
\end{array} \right \rbrack \\
\end{array} \right
\rbrack
\end{displaymath}

\end{tiny}\end{tiny}
\end{slide}

%------------------------------------

\begin{slide}
\begin{center}
\textcolor{red}{\textbf{Result of applying the Head-Complement Rule\\ to \textit{'boy'}}}
\end{center}
\begin{tiny}\begin{tiny}

\begin{displaymath}
NOM \left \lbrack \begin{array}{ll}
\textcolor{red}{phrase} & \\

SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\left \lbrack \begin{array}{ll}
noun &\\
AGR & \boxed{1} \left \lbrack \begin{array}{ll}
PERS & 3rd \\
NUM & sg\\
\end{array} \right \rbrack \\
ANA & - \\
CASE & {\lbrace nom,acc \rbrace}
\end{array} \right \rbrack} \\
\textcolor{blue}{SPR} & \textcolor{blue}{\left \langle \lbrack \begin{array}{ll}
DetP & \\
COUNT  & + \\
\lbrack AGR & \boxed{1} \rbrack 
\end{array} \right \rbrack \rangle} \\
\textcolor{red}{COMPS} & \textcolor{red}{\langle \rangle} \\
\end{array} \right \rbrack \\

SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{MODE} & \textcolor{blue}{ref} \\
\textcolor{blue}{INDEX} & \textcolor{blue}{i} \\
RESTR & \langle \boxed{b} \left \lbrack \begin{array}{ll}
RELN & boy \\
SIT & s \\
INSTANCE & i \\
\end{array}  \right \rbrack \rangle
\end{array} \right 
\rbrack 
\end{array} \right
\rbrack
\end{displaymath}

\end{tiny}\end{tiny}
\end{slide}

%------------------------------------

\begin{slide}

\begin{center}
\textcolor{red}{\textbf{Applying the Head-Specifier Rule to \textit{`the' and 'boy'}}} \\
\end{center}

\begin{footnotesize}
\begin{tiny}\begin{tiny}


\begin{displaymath}
%-----NP--------------
NP \left \lbrack \begin{array}{ll}
\textcolor{red}{phrase} & \\

SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\boxed{0}} \\
\textcolor{red}{SPR} & \textcolor{red}{\langle \rangle} \\
\textcolor{blue}{COMPS} & \textcolor{blue}{\langle \rangle} \\
\end{array} \right \rbrack \\

SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{MODE} & \textcolor{blue}{ref} \\
\textcolor{blue}{INDEX} & \textcolor{blue}{i} \\
RESTR & \langle \boxed{a} \bigoplus \boxed{b} \rangle \\
\end{array} \right 
\rbrack 
\end{array} \right
\rbrack
\rightarrow %-->>>>>>>>>>>>>>>>>>>>
%\end{displaymath}
%-----DET--------------
%\begin{displaymath}
DetP \textcolor{red}{\boxed{1}} \left \lbrack \begin{array}{ll}
phrase& \\
PHON & the\\
ARG-ST & \langle \rangle\\

SYN & \left \lbrack \begin{array}{ll}
HEAD & \left \lbrack \begin{array}{ll}
det &\\
COUNT & + \\
AGR & \boxed{2} \\
\end{array} \right \rbrack\\
SPR  & \langle \rangle \\
COMPS & \langle \rangle \\
\end{array} \right \rbrack \\

SEM & \left \lbrack \begin{array}{ll}
RESTR & \boxed{a} \\
\dots &
\end{array} \right \rbrack \\
\end{array} \right
\rbrack
\end{displaymath}

%-----NOM--------------
\begin{displaymath}
NOM \left \lbrack \begin{array}{ll}
\textcolor{red}{phrase} & \\

SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\boxed{0} \left \lbrack \begin{array}{ll}
noun &\\
COUNT & + \\
AGR & \boxed{2} \left \lbrack \begin{array}{ll}
PERS & 3rd \\
NUM & sg\\
\end{array} \right \rbrack \\
ANA & - \\
CASE & {\lbrace nom,acc \rbrace}
\end{array} \right \rbrack} \\
\textcolor{red}{SPR} & \textcolor{red}{\left \langle \boxed{1} \lbrack \begin{array}{ll}
DetP & \\
COUNT  & + \\
\lbrack AGR & \boxed{2} \rbrack 
\end{array} \right \rbrack \rangle} \\
\textcolor{blue}{COMPS} & \textcolor{blue}{\langle \rangle} \\
\end{array} \right \rbrack \\

SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{MODE} & \textcolor{blue}{ref} \\
\textcolor{blue}{INDEX} & \textcolor{blue}{i} \\
RESTR & \langle \boxed{b} \left \lbrack \begin{array}{ll}
RELN & boy \\
SIT & s \\
INSTANCE & i \\
\end{array}  \right \rbrack \rangle
\end{array} \right 
\rbrack 
\end{array} \right
\rbrack
\end{displaymath}

\end{tiny}\end{tiny}
\end{footnotesize}

\end{slide}

%------------------------------------

\begin{slide}

Already seen the effects of Head Feature Principle, Valence Principle Part A and Semantic Inheritance Principle in blue.

\begin{center}
\textcolor{red}{\textbf{Other principles applied to guarantee well-formedness}}
\end{center}
\begin{footnotesize}


\textbf{Semantic Compositionality Principle (SCP)}
\begin{tiny}
\begin{center}
\begin{displaymath}
\begin{array}{ll}
\lbrack RESTR & \boxed{a} \oplus \dots  \oplus \boxed{n}\rbrack \end{array}
\end{displaymath}
\begin{displaymath}
/ \ \ \ \ \ \vert \ \ \ \ \ \backslash 
\end{displaymath}
\begin{displaymath}
\begin{array}{ll}
\lbrack RESTR & \boxed{a}\rbrack \end{array} \ \ \ \  \dots\ \ \ \begin{array}{ll}\lbrack RESTR & \boxed{n}\rbrack \end{array}
\end{displaymath}
\end{center}


\end{tiny}

Note: the \textbf{Nominal SPR Agreement (NSA)} says that nouns must be specified as:
\begin{tiny}
\begin{center}
\begin{displaymath}
\left \lbrack \begin{array}{ll}
HEAD & \left \lbrack \begin{array}{ll}
AGR & \boxed{1} \end{array} \right \rbrack \\
SPR & \left \langle (\lbrack \begin{array}{ll}
AGR & \boxed{1} \\
\end{array} \right \rbrack) \rangle \\
\end{array} \right \rbrack 
\end{displaymath}
\end{center}

\end{tiny}
\end{footnotesize}
\end{slide}

%------------------------------------
\begin{slide}


\begin{center}
\textcolor{red}{\textbf{Effects of having applied the Semantic Compositionality Principle during the rule application}} \\
\end{center}

\begin{footnotesize}
\begin{tiny}\begin{tiny}


\begin{displaymath}
%-----NP--------------
NP \left \lbrack \begin{array}{ll}
\textcolor{red}{phrase} & \\

SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\boxed{10}} \\
\textcolor{red}{SPR} & \textcolor{red}{\langle \rangle} \\
\textcolor{blue}{COMPS} & \textcolor{blue}{\langle \rangle} \\
\end{array} \right \rbrack \\

SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{MODE} & \textcolor{blue}{ref} \\
\textcolor{blue}{INDEX} & \textcolor{blue}{i} \\
\textcolor{blue}{RESTR} & \textcolor{blue}{\langle \boxed{a} \bigoplus \boxed{b} \rangle} \\
\end{array} \right \rbrack 
\end{array} \right \rbrack
\rightarrow %-->>>>>>>>>>>>>>>>>>>>
%\end{displaymath}
%-----DET--------------
%\begin{displaymath}
DetP \textcolor{red}{\boxed{1}} \left \lbrack \begin{array}{ll}
phrase& \\
PHON & the\\
ARG-ST & \langle \rangle\\

SYN & \left \lbrack \begin{array}{ll}
HEAD & \left \lbrack \begin{array}{ll}
det &\\
COUNT & + \\
AGR & \boxed{2} \\
\end{array} \right \rbrack\\
SPR  & \langle \rangle \\
COMPS & \langle \rangle \\
\end{array} \right \rbrack \\

SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{RESTR} & \textcolor{blue}{\boxed{a}} \\
\dots &
\end{array} \right \rbrack \\
\end{array} \right
\rbrack
\end{displaymath}

%-----NOM--------------
\begin{displaymath}
NOM \left \lbrack \begin{array}{ll}
\textcolor{red}{phrase} & \\

SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\boxed{10} \left \lbrack \begin{array}{ll}
noun &\\
COUNT & + \\
AGR & \boxed{2} \left \lbrack \begin{array}{ll}
PERS & 3rd \\
NUM & sg\\
\end{array} \right \rbrack \\
ANA & - \\
CASE & {\lbrace nom,acc \rbrace}
\end{array} \right \rbrack} \\
\textcolor{red}{SPR} & \textcolor{red}{\left \langle \boxed{1} \lbrack \begin{array}{ll}
DetP & \\
COUNT  & + \\
\lbrack AGR & \boxed{2} \rbrack 
\end{array} \right \rbrack \rangle} \\
\textcolor{blue}{COMPS} & \textcolor{blue}{\langle \rangle} \\
\end{array} \right \rbrack \\

SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{MODE} & \textcolor{blue}{ref} \\
\textcolor{blue}{INDEX} & \textcolor{blue}{i} \\
\textcolor{blue}{RESTR} & \textcolor{blue}{\langle \boxed{b} \left \lbrack \begin{array}{ll}
RELN & boy \\
SIT & s \\
INSTANCE & i \\
\end{array}  \right \rbrack \rangle}
\end{array} \right \rbrack 
\end{array} \right \rbrack
\end{displaymath}

\end{tiny}\end{tiny}
\end{footnotesize}

\end{slide}
%------------------------------------

\begin{slide}


\begin{center}
\textcolor{red}{\textbf{Applying the Head-Complement Rule to \textit{`likes NP[the boy]'}}}
\end{center}
\begin{tiny}\begin{tiny}


\begin{footnotesize}
\begin{tiny}\begin{tiny}

%\Tree [.VP [.V like] NP ]

%\Tree [ .{VP\\phrase\\HEAD \boxed{0}\\SPR \boxed{1}\\COMPS <>\\MODE prop\\INDEX p\\ RESTR \boxed{c} \oplus \boxed{d}} [ .{V\\word\\HEAD \boxed{0}} like ] .{NP\\the boy} ] 

%---VP----------------------------------
\begin{displaymath}
VP \left \lbrack \begin{array}{ll}
\textcolor{red}{phrase} & \\
SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\boxed{0} \left \lbrack \begin{array}{ll}
verb &\\
FORM & fin
\end{array} \right \rbrack}\\
\textcolor{blue}{SPR} & \textcolor{blue}{\langle \lbrack NP_i\boxed{1} \left \lbrack \begin{array}{ll}
CASE & nom \\
AGR & 3sing \end{array} \right \rbrack \rbrack \rangle} \\   
\textcolor{red}{COMPS} & \textcolor{red}{\langle \rangle} 
\end{array} \right \rbrack \\

SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{MODE} & \textcolor{blue}{prop} \\
\textcolor{blue}{INDEX} & \textcolor{blue}{s} \\
\textcolor{blue}{RESTR} & \textcolor{blue}{ \langle \boxed{e} \oplus \boxed{f} \rangle}
\end{array} \right \rbrack
\end{array}\right  \rbrack
\rightarrow %-->>>>>>>>>>>>>>>>>>>>
\end{displaymath}
%---V----------------------------------
\begin{displaymath}
V \left \lbrack \begin{array}{ll}
word & \\

SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\boxed{0}\left \lbrack \begin{array}{ll}
verb &\\
FORM & fin
\end{array} \right \rbrack} \\
\textcolor{blue}{SPR} & \textcolor{blue}{\langle \lbrack NP_i\boxed{1} \left \lbrack \begin{array}{ll}
CASE & nom \\
AGR & 3sing \end{array} \right \rbrack \rangle} \\   
\textcolor{red}{COMPS} & \textcolor{red}{\langle NP_j\boxed{2} \left \lbrack \begin{array}{ll}
CASE & acc 
\end{array} \right \rbrack \rangle} 
\end{array} \right \rbrack \\

ARG-ST & \langle \lbrack NP_i \left \lbrack \begin{array}{ll}
CASE & nom \\
AGR & 3sing \end{array} \right \rbrack \rbrack 
\lbrack NP_j \left \lbrack \begin{array}{ll}
CASE & acc 
\end{array} \right \rbrack \rangle \\

SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{MODE} & \textcolor{blue}{prop} \\
\textcolor{blue}{INDEX} & \textcolor{blue}{s} \\
\textcolor{blue}{RESTR} & \textcolor{blue}{\boxed{e} \langle \left \lbrack \begin{array}{ll}
RELN & like \\
SIT & s \\
LIKER & i \\
LIKED & j  
\end{array} \right \rbrack} ,\\
 & \left \lbrack \begin{array}{ll}
RELN & t-overlap \\
ARG1 & s \\
ARG2 & now 
\end{array} \right \rbrack \rangle
\end{array} \right \rbrack \\
\end{array} \right \rbrack
\end{displaymath}

%-----NP--------------
\begin{displaymath}
NP \textcolor{red}{\boxed{2}} \left \lbrack \begin{array}{ll}
phrase & \\

SYN & \left \lbrack \begin{array}{ll}
HEAD & \boxed{10} \textcolor{blue}{\left \lbrack \begin{array}{ll}
CASE & acc 
\end{array} \right \rbrack}  \\
SPR & \langle \rangle \\
COMPS & \langle \rangle \\
\end{array} \right \rbrack \\

SEM & \left \lbrack \begin{array}{ll}
MODE & ref \\
INDEX & i \\
\textcolor{blue}{RESTR} & \textcolor{blue}{\boxed{f} \langle \boxed{a} \bigoplus \boxed{b} \rangle} \\
\end{array} \right \rbrack 
\end{array} \right \rbrack
\end{displaymath}

\end{tiny}\end{tiny}
\end{footnotesize}
\end{tiny}\end{tiny}
\end{slide}

%------------------------------------

\begin{slide}
\begin{center}
\textcolor{red}{\textbf{Other Well-Formedness conditions that were applied in the rule application above}}
\end{center}

\textbf{Lexical Satisfaction} \\
\\
\begin{tiny}
A word structure:
\begin{displaymath}
\textit{F} 
\rightarrow
\textit{w}
\end{displaymath}

satisfies a lexical entry 
\begin{displaymath}\langle \textit{w},\textit{d} \rangle \end{displaymath}
 just in case:\\
1. F is of type word and F satisfies \textit{d},\\
2. \textbf{Argument Realization Principle}\\
F satisfies the following FSD:

\begin{displaymath}
\left \lbrack \begin{array}{ll}
SYN & \left \lbrack \begin{array}{ll}
SPR & \boxed{a}\\
COMPS & \boxed{b}
\end{array} \right \rbrack \\
ARG-ST & \boxed{a} \oplus \boxed{b} 
\end{array} \right \rbrack 
\end{displaymath}

and\\
3. \textbf{Case Constraint}\\
Any NP in a noninitial position of F's ARG-ST list is \begin{displaymath}
\left \lbrack \begin{array}{ll} CASE & acc \end{array} \right \rbrack \end{displaymath}

\end{tiny}

\end{slide}
%------------------------------------

\begin{slide}
\begin{center}
\textcolor{red}{\textbf{Applying the Head-Specifier Rule\\ to \textit{`NP[Ann] VP[likes the boy]'}}}\\
\end{center}

%---S----------------------------------
\begin{displaymath}
S \left \lbrack \begin{array}{ll}
\textcolor{red}{phrase} & \\

SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\boxed{0} \left \lbrack \begin{array}{ll}
verb &\\
FORM & fin
\end{array} \right \rbrack}\\
\textcolor{red}{SPR} & \textcolor{red}{\langle \rangle} \\   
\textcolor{blue}{COMPS} & \textcolor{blue}{\langle \rangle} \\
\end{array} \right \rbrack \\

SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{MODE} & \textcolor{blue}{prop} \\
\textcolor{blue}{INDEX} & \textcolor{blue}{s} \\
\textcolor{blue}{RESTR} & \textcolor{blue}{ \langle \boxed{g} \oplus \boxed{h} \rangle}
\end{array} \right \rbrack
\end{array} \right \rbrack
\rightarrow %-->>>>>>>>>>>>>>>>>>>>
\end{displaymath}

%---NP Subj----------------------------
\begin{tiny}
\begin{displaymath}
NP \textcolor{red}{\boxed{1}} \left \lbrack \begin{array}{ll}
phrase & \\
SYN & \left \lbrack \begin{array}{ll}
HEAD & \textcolor{blue}{\left \lbrack \begin{array}{ll}
CASE & nom \\
AGR & 3sing 
\end{array} \right \rbrack} \\ 
SPR  & \langle \rangle \\
COMPS & \langle \rangle \\
\end{array} \right \rbrack \\
ARG-ST & \langle \rangle \\
SEM & \left \lbrack \begin{array}{ll}
INDEX & i \\
MODE & ref \\
\textcolor{blue}{RESTR} & \textcolor{blue}{\boxed{g}}\\
\end{array} \right 
\rbrack 
\end{array} \right \rbrack 
\end{displaymath}
%---VP----------------------------------
\begin{displaymath}
VP \left \lbrack \begin{array}{ll}
\textcolor{red}{phrase} & \\

SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\boxed{0} \left \lbrack \begin{array}{ll}
verb &\\
FORM & fin
\end{array} \right \rbrack}\\
\textcolor{red}{SPR} & \textcolor{red}{\langle \lbrack NP_i\boxed{1} \left \lbrack \begin{array}{ll}
CASE & nom \\
AGR & 3sing \end{array} \right \rbrack \rbrack \rangle} \\   
\textcolor{blue}{COMPS} & \textcolor{blue}{\langle \rangle}
\end{array} \right \rbrack \\


SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{MODE} & \textcolor{blue}{prop} \\
\textcolor{blue}{INDEX} & \textcolor{blue}{s} \\
\textcolor{blue}{RESTR} & \textcolor{blue}{\boxed{h} \langle \boxed{e} \oplus \boxed{f} \rangle}
\end{array} \right \rbrack
\end{array}\right  \rbrack
\end{displaymath}
\end{tiny}

\end{slide}
%------------------------------------


\begin{slide}
\begin{center}
\textcolor{red}{\textbf{One last Well-Formedness condition}}\\
\end{center}


\textbf{Initial Symbol Definition}\\
\begin{tiny}\\
A CFG must include a statement of which category (or categories) can start a tree derivation. The analogue of this `initial symbol' definition in this grammar is a constraint guaranteening that for a phrase to stand alone, its synsem-struct must satisfy the following description:

\begin{center}
\begin{displaymath}
\left \lbrack \begin{array}{ll}
phrase & \\
SYN & \left \lbrack \begin{array}{ll}
HEAD & \left \lbrack \begin{array}{ll}
verb &\\
FORM & fin
\end{array} \right \rbrack \\
SPR & \langle \rangle \\   
COMPS & \langle \rangle \\
\end{array}\right  \rbrack
\end{array} \right \rbrack
\end{displaymath}

\end{center}
\end{tiny}

\end{slide}
%------------------------------------


\begin{slide}
\begin{center}
\textcolor{red}{\textbf{Applying the Head-PreModifier Rule\\ to \textit{`tall' and `boy'}}}\\
\end{center}

\begin{tiny}
\begin{displaymath}
\lbrack phrase \rbrack 
\rightarrow
\left \lbrack \begin{array}{ll}
phrase & \\
MOD & \langle \boxed{1}\rangle
\end{array} \right \rbrack 
H \boxed{1} \lbrack phrase \rbrack\ \ \  
\end{displaymath}

%----NP-------------------------------------
\begin{displaymath}
NP\left \lbrack \begin{array}{ll}
\textcolor{red}{phrase} & \\
SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\boxed{0}} \\
\textcolor{blue}{SPR} &  \textcolor{blue}{ \langle \boxed{2} \rangle} \\
\textcolor{blue}{COMPS} & \textcolor{blue}{\langle \rangle} \\
\end{array} \right \rbrack \\

SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{MODE} & \textcolor{blue}{ref} \\
\textcolor{blue}{INDEX} & \textcolor{blue}{i} \\
\textcolor{blue}{RESTR} & \textcolor{blue}{\langle \boxed{a} \oplus \boxed{b}}
\end{array} \right \rbrack 
\end{array} \right \rbrack
\rightarrow
%----ADJP-------------------------------------
AdjP\left \lbrack \begin{array}{ll}
\textcolor{red}{phrase} & \\
\textcolor{red}{MOD} & \textcolor{red}{\boxed{1}} \\
SYN & \left \lbrack \begin{array}{ll}
HEAD & \left \lbrack \begin{array}{ll}
adj & 
\end{array} \right \rbrack \\
SPR & \langle (\lbrack \rbrack) \rangle \\
\end{array} \right \rbrack \\

SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{RESTR} & \textcolor{blue}{\langle \boxed{a} \left \lbrack \begin{array}{ll}
RELN & tall \\
SIT & r \\
INSTANCE & i
\end{array} \right \rbrack \rangle}
\end{array} \right \rbrack \\
\end{array} \right \rbrack 
\end{displaymath}


%----NOM-------------------------------------
\begin{displaymath}
 NOM \textcolor{red}{\boxed{1}} \left \lbrack \begin{array}{ll}
\textcolor{red}{phrase} & \\

SYN & \left \lbrack \begin{array}{ll}
\textcolor{blue}{HEAD} & \textcolor{blue}{\boxed{0} \left \lbrack \begin{array}{ll}
noun &\\
AGR & \boxed{3} \left \lbrack \begin{array}{ll}
PERS & 3rd \\
NUM & sg\\
\end{array} \right \rbrack \\
\end{array} \right \rbrack} \\
\textcolor{blue}{SPR} & \textcolor{blue}{ \left \langle \boxed{2} \lbrack \begin{array}{ll}
DetP & \\
COUNT  & + \\
\lbrack AGR & \boxed{3} \rbrack 
\end{array} \right \rbrack \rangle} \\
\textcolor{blue}{COMPS} & \textcolor{blue}{\langle \rangle} \\
\end{array} \right \rbrack \\

SEM & \left \lbrack \begin{array}{ll}
\textcolor{blue}{MODE} & \textcolor{blue}{ref} \\
\textcolor{blue}{INDEX} & \textcolor{blue}{i} \\
\textcolor{blue}{RESTR} & \textcolor{blue}{\langle \boxed{b} \left \lbrack \begin{array}{ll}
RELN & boy \\
SIT & s \\
INSTANCE & i \\
\end{array}  \right \rbrack \rangle}
\end{array} \right 
\rbrack 
\end{array} \right
\rbrack
\end{displaymath}

\end{tiny}

\end{slide}

%------------------------------------

\begin{slide}
\begin{center}
\textcolor{red}{\textbf{Final Summary\/}}
\end{center}
\begin{small}
\begin{itemize}
\item Lexical entries:
\begin{itemize}
\item Lexical items are of different types.
\item They encode the syntactic and semantic template of the word's usage.
\item The lexicon is organized in a type hierarchy with default inheritance.
\end{itemize}
\item Lexical rules:
\begin{itemize}
\item Lexical rules turns lexemes (dictionary entries) into words (as observed in the sentence).
\item Lexical rules derive word forms, e.g. plural nouns, past tense verbs.
\end{itemize}
\item Grammar rules:
\begin{itemize}
\item Lexical SDs can be combined into larger SDs in the ways permitted by the grammar rules, filtering in features as required by 4 principles: the Semantic Compositionality Principle, the Head Feature Principle, the Valence Principle and the Semantic Inheritance Principle. 
\item Grammar rules are generally phrase-independent, but they have linear ordering of the constraints.
\end{itemize}
\item Principles:
\begin{itemize}
\item The principles ensure that the parse tree is constructed correctly and that all the well-formedness conditions are satisfied.
\item E.g. the Head-Feature Principle enforces that, in any headed phrase, the HEAD value of the head daughter must be unified with the HEAD value of the mother.
\end{itemize}
\end{itemize}
\end{small}
\end{slide}
%------------------------------------

\begin{slide}
\begin{center}
\textcolor{red}{\textbf{Psycholinguistic Plausibility\/}}
\end{center}
\begin{small}
\begin{itemize}
\item Available psycholinguistic evidence fits rather well with the HPSG conception of the grammar (more in [Pollard and Sag] than in [Sag and Wasow]).

\item Constraint-Based Lexicalism
\begin{itemize}
\item incremental
\item process-neutral, i.e. order independent [Pollard and Sag]. The grammar is a declarative system of constraints.
\item strong lexicalization
\item learnability

\end{itemize}
\end{itemize}
\end{small}
\end{slide}


\end{document}








