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Proceedings of the 15Th Meeting on the Mathematics of Language (MOL 2017), Held at Queen Mary University of London, on July 13–14, 2017

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Proceedings of the 15Th Meeting on the Mathematics of Language (MOL 2017), Held at Queen Mary University of London, on July 13–14, 2017 MOL 2017 The 15th Meeting on the Mathematics of Language Proceedings of the Conference July 13–14, 2017 London, UK Sponsored by c 2017 The Association for Computational Linguistics Association for Computational Linguistics (ACL) 209 N. Eighth Street Stroudsburg, PA 18360 USA Tel: +1-570-476-8006 Fax: +1-570-476-0860 [email protected] ISBN 978-1-945626-72-2 ii Introduction This is the proceedings of the 15th Meeting on the Mathematics of Language (MOL 2017), held at Queen Mary University of London, on July 13–14, 2017. The volume contains eleven regular papers and two invited papers. It also includes an abstract of a third invited talk. The regular papers were selected from a total of 23 submissions, using the EasyChair conference management system. The conference benefited from the financial support of the British Logic Colloquium (http://www. blc-logic.org) and of AYLIEN (http://aylien.com), which we gratefully acknowledge. Last but not least, we would like to express our sincere gratitude to all the reviewers for MOL 2017 and to all the people who helped with the local organization. Makoto Kanazawa, Philippe de Groote, and Mehrnoosh Sadrzadeh (editors) iii Program Chairs: Makoto Kanazawa, National Institute of Informatics (Japan) Philippe de Groote, INRIA Nancy (France) Local Chair: Mehrnoosh Sadrzadeh, Queen Mary University of London (UK) Local Organization: Sophie Chesney, Queen Mary University of London (UK) Maximilian Droog-Hayes, Queen Mary University of London (UK) Dimitri Kartsaklis, University of Cambridge (UK) Shalom Lappin, University of Gothenburg (Sweden) Stephen McGregor, Queen Mary University of London (UK) Graham White, Queen Mary University of London (UK) Sue White, Queen Mary University of London (UK) Gijs Jasper Wijnholds, Queen Mary University of London (UK) Program Committee: Henrik Björklund, Umeå University (Sweden) David Chiang, University of Notre Dame (USA) Alexander Clark, King’s College London (UK) Carlos Gómez-Rodríguez, University of A Coruña (Spain) Jeffrey Heinz, University of Delaware (USA) Gerhard Jäger, University of Tübingen (Germany) Greg Kobele, University of Chicago (USA) Marco Kuhlmann, Linköping University (Sweden) Giorgio Magri, CNRS (France) Andreas Maletti, Universität Leipzig (Germany) Jens Michaelis, Bielefeld University (Germany) Larry Moss, Indiana University, Bloomington (USA) Valeria de Paiva, Nuance Communications (USA) Gerald Penn, University of Toronto (Canada) Carl Pollard, The Ohio State University (USA) Jim Rogers, Earlham College (USA) Ed Stabler, Nuance Communications (USA) Mark Steedman, Edinburgh University (UK) Anssi Yli-Jyrä, University of Helsinki (Finland) Additional Reviewer: Justin Debenedetto, University of Notre Dame (USA) Invited Speakers: Stephen Clark, University of Cambridge (UK) Shay Cohen, University of Edinburgh (UK) Frank Drewes, Umeå University (Sweden) v Table of Contents BE Is Not the Unique Homomorphism That Makes the Partee Triangle Commute Junri Shimada . .1 How Many Stemmata with Root Degree k? Armin Hoenen, Steffen Eger and Ralf Gehrke . 11 On the Logical Complexity of Autosegmental Representations Adam Jardine . 22 Extracting Forbidden Factors from Regular Stringsets James Rogers and Dakotah Lambert . 36 Latent-Variable PCFGs: Background and Applications ShayCohen............................................................................ 47 A Proof-Theoretic Semantics for Transitive Verbs with an Implicit Object Nissim Francez . 59 Why We Speak Rohit Parikh . 68 A Monotonicity Calculus and Its Completeness Thomas Icard, Lawrence Moss and William Tune . 75 DAG Automata for Meaning Representation Frank Drewes . 88 (Re)introducing Regular Graph Languages Sorcha Gilroy, Adam Lopez, Sebastian Maneth and Pijus Simonaitis . 100 Graph Transductions and Typological Gaps in Morphological Paradigms Thomas Graf . 114 Introducing Structure into Neural Network-Based Semantic Models Stephen Clark . 127 Count-Invariance Including Exponentials Stepan Kuznetsov, Glyn Morrill and Oriol Valentín . 128 Conjunctive Categorial Grammars Stepan Kuznetsov and Alexander Okhotin. .140 vii Conference Program Thursday, July 13 09:00-09:30 Registration and Opening Session 1 09:30-10:10 BE Is Not the Unique Homomorphism That Makes the Partee Triangle Commute Junri Shimada 10:10-10:50 How Many Stemmata with Root Degree k? Armin Hoenen, Steffen Eger and Ralf Gehrke 10:50-11:05 Coffee Break Session 2 11:05-11:45 On the Logical Complexity of Autosegmental Representations Adam Jardine 11:45-12:25 Extracting Forbidden Factors from Regular Stringsets James Rogers and Dakotah Lambert 12:25-14:10 Lunch 14:10-14:30 S.-Y. Kuroda Prize Ceremony 14:30-14:35 Break ix Thursday, July 13 (continued) Session 3: Invited Talk 14:35-15:35 Latent-Variable PCFGs: Background and Applications Shay Cohen 15:35-15:50 Coffee Break Session 4 15:50-16:30 A Proof-Theoretic Semantics for Transitive Verbs with an Implicit Object Nissim Francez 16:30-17:10 Why We Speak Rohit Parikh 17:10-17:50 A Monotonicity Calculus and Its Completeness Thomas Icard, Lawrence Moss and William Tune 19:00- Conference Dinner at QMUL Octagon Friday, July 14 x Friday, July 14 (continued) Session 5: Invited Talk 09:30-10:30 DAG Automata for Meaning Representation Frank Drewes 10:30-10:45 Coffee Break Session 6 10:45-11:25 (Re)introducing Regular Graph Languages Sorcha Gilroy, Adam Lopez, Sebastian Maneth and Pijus Simonaitis 11:25-12:05 Graph Transductions and Typological Gaps in Morphological Paradigms Thomas Graf 12:05-13:50 Lunch 13:50-14:30 Business Meeting 14:30-14:35 Break xi Friday, July 14 (continued) Session 7: Invited Talk 14:35-15:35 Introducing Structure into Neural Network-Based Semantic Models Stephen Clark 15:35-15:50 Coffee Break Session 8 15:50-16:30 Count-Invariance Including Exponentials Stepan Kuznetsov, Glyn Morrill and Oriol Valentín 16:30-17:10 Conjunctive Categorial Grammars Stepan Kuznetsov and Alexander Okhotin 17:10 Closing xii BE Is Not the Unique Homomorphism That Makes the Partee Triangle Commute Junri Shimada Tokyo Keizai Univeristy, Tokyo, Japan Meiji Gakuin University, Tokyo, Japan Keio University, Tokyo, Japan [email protected] Abstract Fact 2. BE is the unique homomorphism that makes the diagram commute. Partee (1986) claimed without proof that the function BE is the only homomor- While Fact1 is immediate, Fact2 is not ob- phism that makes the Partee triangle com- vious. Partee (1986) nevertheless did not give a mute. This paper shows that this claim is proof of Fact2, but only a note saying, “Thanks to incorrect unless “homomorphism” is un- Johan van Benthem for the fact, which he knows derstood as “complete homomorphism.” It how to prove but I don’t.” Meanwhile, van Ben- also shows that BE and A are the inverses them (1986) referred to Partee’s work and stated of each other on certain natural assump- Fact2 on p. 68, but gave no proof either. Despite tions. this quite obscure exposition, because of the clas- sic status of Partee’s and van Benthem’s work, I 1 Introduction suspect that many linguists take Fact2 for granted In a famous and influential paper, Partee (1986) while unable to explain it. Not only is this unfortu- discussed type-shifting operators for NP interpre- nate, but it is actually as expected, because Fact2 tations, including lift, ident and BE: turns out to be not quite correct unless “homomor- phism” is read as “complete homomorphism.” The lift = λxλP. P (x), main purpose of this paper is to rectify this detri- ident = λxλy. [y = x], mental situation. BE = λPλx. P(λy. [y = x]). Van Benthem (1986) took the domain of entities to be finite, writing, “Our general feeling is that She pointed out that these operators satisfy the natural language requires the use of finite models equality BE lift = ident, so the following dia- ◦ only” (p. 7). Fact2 is indeed correct on this as- gram, now often referred to as the Partee triangle, sumption. However, natural language has pred- commutes. icates like natural number whose extensions are lift De D e,t ,t obviously infinite. Also, if we take the domain of hh i i portions of matter in the sense of Link (1983) to be ident a nonatomic join-semilattice, then the domain of BE entities will surely be infinite, whether countable or uncountable. It is a fact that a single sentence D e,t h i of natural language, albeit only finitely long, can Diagram 1: The Partee triangle talk about an infinite number of entities, as exem- Partee declared that BE is “natural” because of the plified in (1). following two “facts.” (1) a. Every natural number is odd or even. Fact 1. BE is a homomorphism from e, t , t to hh i i b. All water is wet. (Link, 1983) e, t viewed as Boolean structures, i.e., h i Given this, it is linguistically unjustified to assume BE(P P ) = BE(P ) BE(P ), 1 u 2 1 u 2 the domain of entities to be finite. Since Partee BE(P P ) = BE(P ) BE(P ), 1 t 2 1 t 2 (1986) herself discussed Link (1983), she was cer- BE( P ) = BE(P ). tainly aware that the domain of entities might very ¬ 1 ¬ 1 1 Proceedings of the 15th Meeting on the Mathematics of Language, pages 1–10, London, UK, July 13–14, 2017. c 2017 Association for Computational Linguistics well be infinite, so it is unlikely that Partee fol- D lift ℘(℘(D)) lowed van Benthem about the size of the domain of entities. ident BE What difference does it make if the domain De of entities is infinite, then? Fact2 would be cor- ℘(D) rect if “homomorphism” were read as “complete Diagram 2: The Partee triangle homomorphism.” A complete Boolean homomor- (set talk rendition) phism is a Boolean homomorphism that in addi- tion preserves infinite joins and meets. It is clear Theorem 1. BE is a complete homomorphism from the equalities given in Partee’s Fact1 that from ℘(℘(D)) to ℘(D). she did not mean complete homomorphism by the Proof.
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