Table Of ContentLecture Notes in Computer Science 7351
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FoLLI Publications on Logic, Language and Information
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Denis Béchet Alexander Dikovsky (Eds.)
Logical Aspects
of Computational
Linguistics
7th International Conference, LACL 2012
Nantes, France, July 2-4, 2012
Proceedings
1 3
VolumeEditors
DenisBéchet
AlexanderDikovsky
UniversitédeNantes,LINAUMR6241
2,ruedelaHoussinière,BP92208,44322NantesCedex3,France
E-mail:{denis.bechet;alexandre.dikovsky}@univ-nantes.fr
ISSN0302-9743 e-ISSN1611-3349
ISBN978-3-642-31261-8 e-ISBN978-3-642-31262-5
DOI10.1007/978-3-642-31262-5
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Preface
Welcome to the proceedings of the 7th International Conference on Logical
AspectsofComputationalLinguistics,whichwasheldJuly2–4,2012,inNantes,
France. The aim of LACL conferences is to bring together active researchers
interested in all aspects concerning the use of logics in computational linguis-
tics to discuss current research,new results, problems, and applications of both
theoretical and practical nature.
LACL 2012 focused on its traditional topics:
– Typelogicalgrammars(LambekGrammars,AbstractCategorialGrammars,
Combinatorial Categorial Grammars, Categorial Dependency Grammars)
and other formal grammars closely related to them (Minimalist Grammars,
extended TAG and other weakly context-sensitive grammars)
– Formalsemanticsofnaturallanguage(type andprooftheoreticalsemantics,
intensionalmodeltheoreticsemantics,dynamicsemantics,lexicalsemantics)
– Logical models of discourse and dialogue (game theoretic models, ludics)
Amongst24thoroughlytriplyrefereedsubmittedpapers,the ProgramCom-
mittee consisting of 33 colleagues listed here selected 15 high-quality contri-
butions by authors from China, France, Germany, Italy, Japan, Poland, Rus-
sia, UK and USA. LACL 2012 included two invited talks: by M. Steedman
(University of Edinburg) and A. Clark (Royal Holloway University of London)
and a tutorial by C. Fouquer´e and M. Quatrini (University Paris 13 and Uni-
versity of Aix Marseille II). Besides this, the technical program also included a
System Demonstration session.
We would like to thank all authors who submitted papers, the four invited
speakers and all conference participants. We are grateful to the members of the
Program Committee and of the Demo Session Committee for their thorough
efforts in reviewing and discussing submitted contributions with expertise and
carefulness. We are also grateful to our institutional sponsors and supporters:
the Association for Logic, Language and Information (FoLLI), CNRS, Ecole
des Mines of Nantes, Laboratory of Informatics of Nantes (LINA), University
of Nantes and its Faculty of Sciences and Technologies. We would also like to
expressourgratitudetotheOrganizingCommitteeandallthepeoplewhomade
this meeting possible.
April 2012 Denis B´echet
Alexander Dikovsky
Organization
Program Committee
Michele Abrusci Universit`a di Roma Tre, Italy
Nicholas Asher IRIT/CNRS, France
Raffaella Bernardi University of Trento, Italy
Philippe Blache LPL/CNRS, Aix-en-Provence,France
Wojciech Buszkowski Poznan University, Poland
Denis B´echet LINA - University of Nantes, France
Phillipe De Groote LORIA/INRIA, Nancy Grand Est, France
Michael Dekhtyar University of Tver, Russia
Alexander Dikovsky LINA CNRS UMR 6241,Universit´ede Nantes,
France
Markus Egg Humboldt Universita¨t Berlin, Germany
Annie Foret University of Rennes 1, France
Nissim Francez Technion, Haifa, Israel
Makoto Kanazawa NII, Japan
Gregory M. Kobele University of Chicago, USA
Marcus Kracht University of Bielefeld, Germany
Alain Lecomte Universit´e Paris 8, France
Hans Leiss Universit¨at Mu¨nchen, Germany
Michael Moortgat Universiteit Utrecht, UiL OTS,
The Netherlands
Richard Moot LaBRI/CNRS, France
Glyn Morrill Universitat Polit`ecnica de Catalunya,
Barcelona, Spain
Reinhard Muskens Tilburg University, The Netherlands
Uwe M¨onnich Universita¨t Tu¨bingen, Germany
Gerald Penn University of Toronto, Canada
Mati Pentus Moscow State University, Russia
Sylvain Pogodalla LORIA/INRIA, Nancy Grand Est, France
Carl Pollard The Ohio State University, USA
Anne Preller LIRMM/CNRS, France
Christian Retor´e LaBRI/CNRS, France
Sylvain Salvati INRIA, Bordeaux Sud-Ouest, France
Chung-Chieh Shan Rutgers, The State University of New Jersey,
USA
Edward Stabler University of California, Los Angeles, USA
Mark Steedman University of Edinburgh, UK
Isabelle Tellier Universit´e Paris 3, France
VIII Organization
Demo Session Committee
Denis B´echet LINA - University of Nantes
Florian Boudin LINA - University of Nantes
Alexander Dikovsky LINA - University of Nantes
Nicolas Hernandez LINA - University of Nantes
Organizing Committee
Ramadan Alfared LINA - University of Nantes
Denis B´echet LINA - University of Nantes
Florian Boudin LINA - University of Nantes
Alexander Dikovsky LINA - University of Nantes
Anna Even LINA - University of Nantes
Nicolas Hernandez LINA - University of Nantes
Oph´elie Lacroix LINA - University of Nantes
Annie Lardenois LINA
Anne-Franc¸oise Quin LINA - CNRS
Table of Contents
Logical Grammars, Logical Theories................................ 1
Alexander Clark
Ludics and Natural Language: First Approaches ..................... 21
Christophe Fouquer´e and Myriam Quatrini
The Non Cooperative Basis of Implicatures.......................... 45
Nicholas Asher
Movement-GeneralizedMinimalist Grammars........................ 58
Thomas Graf
Toward the Formulation of Presupposition by Illative Combinatory
Logic........................................................... 74
Yuri Ishishita and Daisuke Bekki
Abstract Automata and a Normal Form for Categorial Dependency
Grammars ...................................................... 86
Boris Karlov
Importing MontagovianDynamics into Minimalism .................. 103
Gregory M. Kobele
CoTAGs and ACGs .............................................. 119
Gregory M. Kobele and Jens Michaelis
Gapping as Like-Category Coordination ............................ 135
Yusuke Kubota and Robert Levine
L-Completeness of the Lambek Calculus with the Reversal Operation... 151
Stepan Kuznetsov
Distributive Full Nonassociative Lambek Calculus with S4-Modalities
Is Context-Free .................................................. 161
Zhe Lin
Common Nouns as Types ......................................... 173
Zhaohui Luo
Extractability as the Deduction Theorem in Subdirectional
Combinatory Logic............................................... 186
Hiroko Ozaki and Daisuke Bekki
X Table of Contents
Agnostic Possible Worlds Semantics ................................ 201
Andrew Plummer and Carl Pollard
Abstract Machines for Argumentation .............................. 213
Kurt Ranalter
On the Completeness of Lambek Calculus with Respect to Cofinite
Language Models ................................................ 229
Alexey Sorokin
Dot-Types and Their Implementation .............................. 234
Tao Xue and Zhaohui Luo
Author Index.................................................. 251
Logical Grammars, Logical Theories
Alexander Clark
Department of Computer Science
RoyalHolloway, University of London
Egham, TW20 0EX
United Kingdom
[email protected]
Abstract. Residuatedlattices form oneofthetheoretical backbonesof
the Lambek Calculus as the standard free models. They also appear in
grammaticalinferenceasthesyntacticconceptlattice,analgebraicstruc-
ture canonically defined for every language L based on the lattice of all
distributionallydefinablesubsetsofstrings.Recentresultsshowthatitis
possible to build representations, such as context-free grammars, based
ontheselattices, andthattheserepresentationswill beefficientlylearn-
able using distributional learning. In this paper we discuss the use of
thesesyntacticconceptlatticesasmodelsofLambekgrammars,anduse
thetools of algebraic logic totry tolink theproof theoretic ideas of the
Lambekcalculuswiththemorealgebraicapproachtakeningrammatical
inference. We can then reconceive grammars of various types as equa-
tional theories of the syntacticconcept lattice of thelanguage. Wethen
extend this naturally from models based on concatenation of strings,
to ones based on concatenations of discontinuous strings, which takes
us from context-free formalisms to mildly context sensitive formalisms
(multiple context-freegrammars) and Morrill’s displacement calculus.
1 Introduction
Logicis concernedwith proof;in the logicalgrammartraditionthe roleofproof
is central and well understood [1]. But logic is also concerned with truth – and
whatdoesitmeanforagrammar,suchasaLambekgrammar,tobetrue?What
canitbetrueof?Thisisaproblemnotofprooftheorybutofmodeltheory,and
whiletherehasbeenagreatdealofworkonmodelsforthe Lambekcalculus[2],
thesearemodelsforthe calculus,notforthe grammars.Thesemodels arefree–
the only statements that are true in these models are things that are true of all
languages – but this seems to be inappropriate – there are things that are true
of some languages and not of others; true about English but not about French
or Dyirbal.
A Lambek grammar consists only of a finite set of type assignments: (w,T)
wherewisanonemptysequence,typicallyoflength1,andT isatype.Therefore
the questionofthe truth of the grammarreduces to the question ofthe truth of
the type assignments. The metatheory of Lambek grammar is explained in [3]
and [4]. Several things are clear: first the types in the grammar are intended to
D.B´echetandA.Dikovsky(Eds.):LACL2012,LNCS7351,pp.1–20,2012.
(cid:2)c Springer-VerlagBerlinHeidelberg2012
2 A. Clark
refertosetsofstringsinagivenlanguage,andthe compositetypesA•B, C/B,
A\C and the associated calculus are motivated and justified by the algebraic
properties of the associated operations on these sets. The following quotes from
[4] lay out the metatheoretical assumptions. First
Sets of strings of English words will be called (syntactic) types.
Secondly, that the operations are ‘free’:
Whenapplyingthisnotationtoanaturallanguage...wearethinking
ofthe ...system...freely generatedbythe wordsofthe languageunder
concatenation.
Finally, thatthe startingpointforconstructingagrammaristo model anexist-
ing language. Lambek does not conceive of this as a learning problem, but as a
modelingprobleminthestructuralisttradition.Ratherthandefiningagrammar
G in vacuo and then showing how that grammar defines a language L — the
generative stance — he starts with a language L∗, and constructs a grammar
G(L∗), — the descriptive approach— using a non-algorithmic method:
One can continue playing this game until every English word has
been assigned a finite number of types.
One hopes that the grammardefined in this way will define a languagewhich is
equal to the original language L∗, a condition Lambek states as follows:
Onemayconsiderthecategorialgrammartobeadequate providedit
assigns type S to w if and only if the latter is a well-formed declarative
sentence according to some other standard.
Lambek’s specific proposals within this metatheoretical program include what
are now called Lambek grammars, and later, pregroup grammars. Others have
studiedtherelationshipbetweentypesandsetsofstrings;specificallyBuszkowski
in [5], and the possibilities of developing the informal process of construction of
a grammar into an algorithmically well-defined learning procedure [6,7].
In this paper we will take a different tack, motivated again by a focus on
learnability. We are interested in identifying formalisms that are not only de-
scriptively adequate but that also can be learned from the data in a principled
way – in Chomskyan terms, in achieving explanatory adequacy. Defining the
types as sets of strings seems a reasonable first step. We can in a similar vein
consider nonterminal symbols in a context-free grammar to be sets of strings:
namely the set of strings that can be derived from that nonterminal. For a cfg
G, with a nonterminal N we define as usual L(G,N)={w|N ⇒∗ w}. A sym-
G
bol NP which represents noun phrases can be considered as the set of strings
that can be noun phrases; the start symbol S corresponds to the language L
itself.
In Lambek grammars and other categorial grammars, we have the same cor-
respondence,butitismorecomplex.We canassociatewitheachtype,primitive
