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\title{Workshop: Proof nets and their linguistic applications}


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{\LARGE\bf Workshop: Proof nets and their linguistic
applications} \\
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Eric Auer, Feb. 12, 2002
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{\small
This is a short report on the UiL OTS Workshop on Computational
Linguistics and Logic on January 31st 2002 in Utrecht, titled
\B{Proof nets and their linguistic applications}. The task was
to write a short summary/newsitem for an imaginary scientific
newspaper. As a result, this will be both short and superficial.
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\section*{Introduction} % section* is a section without number


In the course of our lecture on proof nets, we were invited
to join this workshop and follow the four talks about using
proof nets, in particular their linguistic applications.
Each of the talks had a time slot of 45 minutes, and most of
the speakers were visitors from other universities. We were
bound for an afternoon packed with information about ongoing
research in this field. To begin with, a list of the
presentations:


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\item \B{Aravind Joshi (University of Pennsylvania): }
  Some new directions for applications of NLP techniques for
  modeling biological sequences
\item \B{Quintijn Puite (Rome University): }
  A bilateral-free notion of modules for non-commutative logic
\item \B{Francois Lamarche (Calligrame Nancy): }
  A generic cut-elimination theorem
\item \B{Willemijn Vermaat (UiL OTS Utrecht): }
  Inflection: Minimalist Grammar versus Type Logical Grammar
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\section*{Joshi: trees and structures}


In contrast to the other talks, Joshi presented some application
outside of the realm of linguistics: His research involves the
use of TAG (tree adjoining grammar) to predict
\B{folding structures}
of biological sequences such as proteines and DNA
sequences. Such sequences show far more complex structure than
simple chains of molecules: Driven by attraction of matching
subsequences, the molecules fold. The folding works on several
layers: the simplest structure is linear, next are alpha helices
and beta sheets, further folding leads to complex three
dimensional structures.
% Other approaches to predict the
% resulting structures are using e.g. HMMs (hidden Markov
% models) or probabilistic CFGs (context free grammars).
Joshi uses the \B{topology of TAG trees} as predictor for the
molecular proximity structure, which he demonstrated in several
examples. As for the relation of this research to linguistics,
Joshi reminded of the analogy between certain folding patterns
and linguistic dependency structures.


\section*{Puite: modules as building blocks}


Puite reported about research towards a notion of orthogonality
of modules (parts of proof nets) which he is doing together with
a colleague: A module and an \B{orthogonal} module can be
combined to a proof net. The representation of modules is done
in a graphical way, for which Puite showed some abbreviated
notation. He also presented some especially suited graph notation
for proof nets. Given that notation, modules can be seen as
\B{building blocks} which clip together in an intuitive way iff
they are orthogonal to each other.


\section*{Lamarche: Generic cut-elimination}


Lamarche introduced his presentation as one starting with the
conclusion, so even people with very limited attention span
would be satisfied with it\ldots His philosophy says that any
logic consists of a theory of structural context augmented by
connectives: For the sequent calculus, \B{cut elimination}
is an important connective. Adding input/output polarity,
algebra becomes logic (reasoning). Lamarche showed two graphical
approaches on the example of Lambek calculus: Have polarity
built into a (bigger) set of connectives, or pair the polarity
with the formula using explicit rules. Finally, an elegant
implementation of cut and cut-elimination in this framework was
presented.


\section*{Vermaat: Comparing grammars}


In the final talk, Vermaat presented a fast paced comparison
of the treatment of several linguistic effects by two different
grammar frameworks: Minimalist Grammar (Chomsky, making heavy
use of Move and Merge operations) and TLG. Vermaat showed
intermediate results of work in progress, so her data was
sometimes sketchy. As an example, word/inflection order
effects in French and English sentences are compared:
In \B{Guillaume n'aime pas (n'a jamais aimé) du Maxima} and
\B{William does not love (has never loved) Maxima}, movement
constraints on verbs, auxiliaries and negation particles vary
across languages. Comparing handling of those and other effects
by the two mentioned grammar frameworks is the main topic of the
presented research.

For the fulltime participants, the workshop was later continued
in a more relaxed meeting including some calories to be worked
on\ldots

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