Constituentless Compositionality: A Compositional Account of Dependency Grammar MSc Thesis (Afstudeerscriptie) written by Ryan Nefdt Master of Logic University of Amsterdam (born 8th September, 1987 in Cape Town, South Africa) under the supervision of Dr Henk Zeevat, and submitted to the Board of Examiners in partial fulfillment of the requirements for the degree of MSc in Logic at the Universiteit van Amsterdam. Date of the public defense: Members of the Thesis Committee: August 21, 2013 Dr Jakub Szymanik Dr Michael Franke Dr Theo Janssen Dr Henk Zeevat Contents I Compositionality and Natural Language 4 1.1 Introduction....................................5 1.2 Disambiguating Compositionality . .6 1.3 (Bad) Reasons for compositionality . .8 1.3.1 Productivity . .8 1.3.2 Systematicity . 10 1.3.3 Novelty and Learnability . 13 1.3.4 Infinity................................... 14 1.4 Conclusion . 20 II Compositionality and Formal Language 22 2.1 Introduction.................................... 23 2.2 Formal Language Theory . 24 2.2.1 Regular Languages (Type 3) . 25 2.2.2 Context-free Languages (Type 2) . 26 2.2.3 Context-Sensitive Languages (Type 1) and Unrestricted Languages (Type0).................................. 28 2.2.4 Beyond the Chomsky Hierarchy: Mildly context-sensitive Languages . 28 2.2.5 A Computational Caveat . 29 2.3 (Good) Reasons for Compositionality . 30 2.3.1 Computational Complexity . 30 2.3.2 Infinity as a design choice . 31 2.3.3 Subconclusion . 32 2.4 Formal Definition of Compositionality . 33 2.4.1 Formal Preliminaries . 33 2.4.2 Standard Compositionality . 34 2.4.3 Strong Compositionality . 36 2.4.4 Direct Compositionality . 37 2.4.5 A Formal Description of Constituency . 39 2.4.6 The Principle of Syntactic Integrity . 42 2.5 Conclusion . 44 1 III A Compositional Semantics for Dependency Grammar 45 3.1 Dependency Grammar . 46 3.1.1 Elementary Structures and Constituency . 46 3.1.2 Lexicalization and Dependency Grammar . 48 3.1.3 Dependency Structures . 50 3.1.4 Projective and Non-projective structures . 51 3.1.5 Why Dependency Grammar? . 52 3.2 Compositionality applied . 53 3.2.1 Dependency Algebra . 53 3.3 Challenges for a Type Semantics of Dependency Grammar . 56 3.3.1 Extensional Montague Grammar . 56 3.3.2 ScopeAmbiguity ............................. 58 3.3.3 Problems for Type-theoretic Dependency Semantics . 59 3.4 A Resolved Montague Grammar for Dependency Structures . 62 3.4.1 F-Structures in Lexical-Functional Grammar . 62 3.4.2 The Semantics . 63 3.4.3 Montague Semantics for Dependency Grammar . 65 3.4.4 DSs as Semantic Structures . 66 3.4.5 Translation Procedure . 70 3.4.6 Resolving Scope Ambiguity . 74 3.4.7 Compositionality and Underspecification . 83 3.4.8 Advantages of this Framework . 85 3.4.9 OtherFrameworks ............................ 86 3.5 Conclusion . 88 Acknowledgements I would like to thank my parents for their infinite support of my academic career, without them this would not have been possible. I would also like to thank Ms Anastacia Saliukova for her assistance with the verification of the cross-linguistic data used in this thesis. And many thanks to my supervisor Dr. Henk Zeevat who ushered me into the previously unknown territory of formal linguistics from my background in philosophy research. Finally, I would like to thank the Erasmus Mundus to South Africa scholarship scheme for generously funding my research at the ILLC. Preface The problem of compositionality in linguistics and philosophy has become a prominent issue in contemporary scholarship concerning natural language. The debate usually takes two (not unrelated) forms, (1) what are the correct formal descriptions of the principle of compositionality and (2) whether or not such a principle is indeed consonant with linguistic data. In this thesis, I offer no new comment on either of these points. Instead, I plan to argue that notwithstanding the lack of a definitive answer to (2), there is reason to incorporate a compositional semantics for a given syntactic formalism. The first parts of this thesis both offer these reasons and attempt to define more precisely what type of relationship syntax needs to have with semantics to achieve the coveted title of compositional, i.e. an answer to (1). In the second part, I attempt to provide a compositional semantics for dependency grammar, a formalism which has historically been recalcitrant to such description, by means of a modified type-theoretic treatment of its semantics. In part I, I briefly introduce some background and set up the controversy surrounding compositionality. Some of these issues will be relevant for forthcoming sections, others are meant to serve as foregrounding for the debate in general. Part II will focus on formal definitions of compositionality with relation to formal language theory and motivations for the principle in terms of these definitions. I will also discuss the central matter of constituency and its role in the formal definition of the principle of compositionality. Finally, part III offers a novel compositional account of dependency grammar in terms of Montague Grammar. Importantly, this analysis aims to respect the structures generated by the dependency syntax. The final part also tests this account on recalcitrant natural language phenomena. The main contribution of the current work is to provide a compositional treatment of a traditionally constituentless syntactic formalism thereby reconceiving and expanding upon the definition of compositionality as it is interpreted in the literature. Part I Compositionality and Natural Language 5 1.1 Introduction The genesis of the principle of compositionality has most often been linked to the writings of Gottleb Frege, hence the term \Frege's principle" (sometimes used synonymously). In 'Sinn und Bedeutung', Frege challenges a simple notion of compositional meaning in terms of co-reference due to Mill by testing the substitution thesis (which has been shown to be equivalent to a version of compositionality which we will be using, Hodges (1998)). Yet his distinction between sense (Sinn) and reference (Bedeutung) aims to rescue a compositional account of meaning in some form. The modern idea of the principle can be found in Partee (2004) and Montague (1974) among others and it is can be summed up as: The meaning of a complex expression is determined by the meaning of its component parts and the way in which they are combined. Janssen (2012) argues that Frege was not the source (nor an adherent) of the concept of compositionality. In fact, he prescribed to a quite different principle for natural language semantics. He argues that its true origins can actually be traced further back than Frege to Lotze, Wundt and Trendelenburg. Furthermore, he claims that there is no evidence to suggest that Frege ever truly abandoned the context principle (given below) which is also referred to as Frege's principle: Never ask for the meaning of a word in isolation, but only in the context of a sentence (1884, xe). In Pagin and Westerstahl (2010a) these two principles are reconciled. The context principle is interpreted as a constraint on compositional meaning.1 In addition, they trace the principle of compositionality back to 4th century indian thought, others to Aristotle. The exact beginnings of the principle and Frege's exact position on it are somewhat irrelevant for the present discussion. It is important, however, to note that it has held sway with formal logicians and philosophers such as Montague where it derived one of its most influential incarnations. Clearly, the principle has been assumed to be susceptible to formal description and we will follow that assumption in this paper. In the methodology of logic and computer science, it has been considered the standard way of interpreting formal or programming languages (although alternatives do exist). Tarski's (1933) definition of truth for formal languages has a natural compositional interpretation (Janssen 2012). Davidson (1967) used what he called Tarski's T-theorem as a basis for a compositional semantics for natural language. In the 20th century the principle was widely adopted in the philosophy of language and logic, through Carnap, Quine, Davidson and various others. Now, it has become an essential part of most linguistic theories including generative theories. The connectionist debate has brought this issue to the fore in the cognitive scientific arena and in the philosophy of mind. There are many issues which connect the compositionality debate in language and mind, in fact Fodor (2001) argues that only one of these can be compositional and since language seems not to be in certain cases, concepts 1Dummett (1973) attempts to do something similar from a more philosophical perspective. 6 must be. For the most part, neither the compositionality of mind nor natural language will directly concern us here. In this part, however, we investigate the debate surrounding the principle as it is applied to natural language. 1.2 Disambiguating Compositionality Unfortunately, there is no consensus on the correct definition of compositionality (see section 2.4 for details). Furthermore, it is not clear if it is exclusively a methodological principle or can be empirically tested (Dowty 2007). For the purposes of this thesis, we will assume some preliminaries. For one, compositionality will not be thought of as a property of a given semantics or syntax for that matter. We will follow Montague in defining it as a relationship between a certain syntax and a certain semantics. Consider the expression above again: The meaning of a complex expression is determined by the meaning of its component parts and the way in which they are combined. This statement is vague and in need of clarification. The problem is that there doesn't seem to be a neutral way of going about this clarification. In this section, I attempt to stay as neutral as possible. Starting with the term \complex expression" which will be characterised as a syntactic object, as will its components.