Matthew Gotham
Linguistics Research
Here is where you can find a record of my academic research in Linguistics. I’m not sure if or when it will ever be added to, but I’m still interested in many of these issues so do get in touch if you would like to discuss. I wrote my PhD dissertation on copredication* and have also worked on plurals, quantification, dynamic semantics, and the syntax-semantics interface, especially in LFG.
* This is my attempt to describe my PhD topic using only the 1000 most frequently-occurring words in English.
Doctoral dissertation
Copredication, Quantification and Individuation. University College London (2014).
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This thesis addresses the various problems of copredication: the phenomenon whereby two predicates are applied to a single argument, but they appear to require that their argument denote different things. For instance, in the sentence ‘The lunch was delicious but went on for hours’, the predicate ‘delicious’ appears to require that ‘the lunch’ denote food, while ‘went on’ appears to require that it denote an event. Copredication raises philosophical issues regarding the place of a reference relation in semantic theory. It also raises issues concerning the ascription of sortal requirements to predicates in framing a theory of semantic anomaly. Finally, many quantified copredication sentences have truth conditions that cannot be accounted for given standard assumptions, because the predicates used impose distinct criteria of individuation on the objects to which they apply. For instance, the sentence ‘Three books are heavy and informative’ cannot be true in a situation involving only a trilogy (informationally three books, but physically only one), nor in a situation involving only three copies of the same book (physically three books, but informationally only one): the three books involved must be both physically and informationally distinct.
The central claims of this thesis are that nouns supporting copredication denote sets of complex objects, and that lexical entries incorporate information about their criteria of individuation, defined in terms of equivalence relations on subsets of the domain of discourse. Criteria of individuation are combined during semantic composition, then accessed and exploited by quantifiers in order to specify that the objects quantified over are distinct in defined ways. This novel approach is presented formally in Chapters 2 and 3, then compared with others in the literature in Chapter 4. In Chapter 5, the discussion is extended to the question of the implications of this approach for the form that a semantic theory should take. - thesis
Papers
2022
Property Inheritance, Deferred Reference and Copredication. Journal of Semantics 39(1):87–116.
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There are sentences that are coherent and possibly true, but in which there is at the very least the appearance of a conflict between the requirements of two (or more) predicates that are applied to the same argument. This phenomenon, known as copredication, raises various issues for linguistic theory. In this paper I defend and develop an approach to the issues of counting and individuation in copredication put forward in Gotham 2017, in dialogue with criticisms made by Liebesman & Magidor (2019) and their own positive account of copredication (Liebesman & Magidor 2017).
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2021
Approaches to scope islands in LFG+Glue. In Miriam Butt, Jamie Y. Findlay & Ida Toivonen (eds.), Proceedings of the LFG'21 Conference, Online, 146–166.
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In this paper I examine two possible approaches to scope islands in LFG with Glue semantics: one in which constraints on scope level are imposed by means of constraints off the path of an inside-out functional uncertainty, and one in which they are imposed through the structural rules of the fragment of linear logic used for meaning composition, by making the fragment multi-modal. For each approach, I show how it could be made to account for novel empirical arguments made in Barker (2021), and go on to argue in favour of the multi-modal Glue approach.
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Event-related readings and degrees of difference. In Patrick Georg Grosz, Luisa Martí, Hazel Pearson, Yasutada Sudo & Sarah Zobel (eds.), Proceedings of Sinn und Bedeutung 25, 325–339.
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I present an analysis of event-related readings that treats both them and object-related readings as resulting from quantification over temporal stages of individuals, with the distinction between the two arising from a difference in the degree of maximality that quantifiers require those stages to fulfil. The analysis accounts for the compositional-semantic effect of different in these examples, and the possibility of multiple event-related readings. I also examine the connection between this analysis and existing accounts of quantifier domain restriction.
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2019
Constraining scope ambiguity in LFG+Glue. In Miriam Butt, Tracy Holloway King & Ida Toivonen (eds.), Proceedings of the LFG'19 Conference, Australian National University, 111–129. Stanford, CA: CSLI Publications.
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A major strength of the Glue approach to semantic composition for LFG is that it accounts for quantifier scope ambiguity without the need for additional assumptions. However, quantifier scope is more rigid in some languages and constructions than Glue would lead us to expect. I propose a mechanism for constraining scope ambiguity in LFG+Glue, based on ideas taken from Abstract Categorial Grammar. Unlike existing proposals, this account does not depend on representational constraints on linear logic derivations or meaning representations.
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Double Negation, Excluded Middle and Accessibility in Dynamic Semantics. In Julian J. Schlöder, Dean McHugh & Floris Roelofsen (eds.), Proceedings of the 22nd Amsterdam Colloquium, 142–151.
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This paper addresses a recalcitrant problem for dynamic semantics: the inaccessibility of discourse referents from under double negation or from a negated left disjunct into a right disjunct. I propose that these discourse referents are made accessible by the discourse being interpreted in the context of designated formulae, which validate double negation elimination in a controlled way.
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Quantificational Subordination as Anaphora to a Function. In Raffaella Bernardi, Greg Kobele & Sylvain Pogodalla (eds.), Formal Grammar: FG 2019, 51–66. Lecture Notes in Computer Science 11668. Berlin, Heidelberg: Springer.
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In [11], a semantics for cross-sentential and donkey anaphora is presented that is inspired by approaches using dependent types but couched in simple type theory with parametric polymorphism. In this paper, the approach is extended to cover quantificational subordination. It is argued that the approach enjoys advantages over existing accounts in type-theoretical semantics.
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2018
Glue semantics for Universal Dependencies. In Miriam Butt & Tracy Holloway King (eds.), Proceedings of the LFG'18 Conference, University of Vienna, 208–226. Stanford, CA: CSLI Publications (with Dag Haug).
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Universal Dependencies (UD) is a very widely-used standard for cross-linguistic annotation of syntactic structure. There is, therefore, interest in deriving semantic representations from UD structures, ideally in a language-independent way. In this paper we report on an approach to deriving semantic representations from UD structures that relies on adapting and exploiting techniques from Glue semantics for LFG.
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Introduction: Approaches to coercion and polysemy. Oslo Studies in Language 10(2):1–7 (with Alexandra Anna Spalek).
Making Logical Form type-logical: Glue semantics for Minimalist syntax. Linguistics and Philosophy 41(5):511–556.
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Glue Semantics is a theory of the syntax-semantics interface according to which the syntactic structure of a sentence produces premises in a fragment of linear logic, and the semantic interpretation(s) of the sentence correspond to the proof(s) derivable from those premises. This paper describes how Glue can be connected to a Minimalist syntactic theory and compares the result with the more mainstream approach to the syntax-semantics interface in Minimalism, according to which the input to semantic interpretation is a syntactic structure (Logical Form) derived by covert movement operations. I argue that the Glue approach has advantages that make it worth exploring.
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A Model-Theoretic Reconstruction of Type-Theoretic Semantics for Anaphora. In Annie Foret, Reinhard Muskens & Sylvain Pogodalla (eds.), Formal Grammar: FG 2017, 37–53. Lecture Notes in Computer Science 10686. Berlin, Heidelberg: Springer.
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I present an analysis of the interpretation of anaphora that takes concepts from type-theoretic semantics, in particular the use of the Σ and Π dependent type constructors, and incorporates them into a model-theoretic framework. The analysis makes use of (parametrically) polymorphic lexical entries. The key ideas are that, in the simplest case, eventualities can play the role that proof objects do in type-theoretic semantics; that more complex, compositionally-defined, structures can play that role in other cases; and that pronouns can be modelled by context-dependent functions from proof objects of the preceding discourse (in this sense) to entities.
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2017
Glue Semantics and Locality. In Miriam Butt & Tracy Holloway King (eds.), Proceedings of the LFG'17 Conference, University of Konstanz, 230–242. Stanford, CA: CSLI Publications.
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In this paper I explore the idea that Glue Semantics enriched with additional unary connectives could provide a natural account of some (positive) locality conditions on binding. I argue that the additional connectives can be independently, semantically motivated.
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Composing Criteria of Individuation in Copredication. Journal of Semantics 34(2):333–371.
Copredication is the phenomenon whereby two or more predicates are applied to a single argument, but those predicates appear to require that their argument denote different things. This article focuses on the problem of individuation and counting in copredication: many quantified copredication sentences have truth conditions that cannot be accounted for given standard assumptions, because the predicates used impose distinct criteria of individuation on the objects to which they apply. I propose a compositional system for criteria of individuation and show that it improves predictions regarding the truth conditions of numerically quantified copredication sentences compared to existing accounts.
Older
Towards Glue Semantics for Minimalist syntax. Cambridge Occasional Papers in Linguistics 8:56–83 (2015).
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Glue Semantics is a theory of the syntax/semantics interface according to which syntax generates premises in a fragment of linear logic, and semantic interpretation proceeds by deduction from those premises. Glue was originally developed within Lexical-Functional Grammar and is now the mainstream view of semantic composition within LFG, but it is in principle compatible with any syntactic framework. In this paper I present an implementation of Glue for Minimalism, and show how it can bring certain advantages in comparison with approaches to the syntax/semantics interface more conventionally adopted.
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Numeric quantification in copredication. UCL Working Papers in Linguistics 24:1–20 (2012).
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Copredication is the apparent attribution of incompatible properties to a single object, in a sentence that is nevertheless acceptable and can readily be interpreted. Various attempts have been made to devise theories that predict truth conditions for copredication sentences that avoid this attribution of incompatible properties. In this paper I examine three kinds of such theories: those based on merological accounts of what nouns supporting copredication denote, accounts based on type manipulation and the operation of repair rules in the process of semantic composition, and ambiguity accounts supplemented by pragmatically-driven predicate meaning transfer. I concentrate on the nature of the problems that these attempts face in correctly predicting the truth conditions of copredication sentences involving numeric quantifiers, and evaluate some possible ways of overcoming those problems. I conclude that native speaker judgements about copredication sentences involving numeric quantification do not perfectly reflect the counting and individuation criteria that the existing accounts predict, because copredication presents us with divergent criteria for identifying objects falling under the denotation of the noun, and hence potentially divergent criteria for individuating and counting those objects.
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Edited volumes
Approaches to Coercion and Polysemy. Oslo Studies in Language 10(2), 2018 (with Alexandra Anna Spalek).
Presentations
2021
Approaches to scope islands in LFG+Glue. 26th International Lexical-Functional Grammar Conference, Online.
2020
Event-related readings and degrees of difference. Sinn und Bedeutung 25, Online.
- project page
- (includes talk, slides and handout)
- proceedings paper
Intensional independence without world variables in LFG+Glue. 25th International Lexical-Functional Grammar Conference, Online.
2019
Double negation, excluded middle and accessibility in dynamic semantics. Amsterdam Colloquium, University of Amsterdam.
Double negation, excluded middle and accessibility in dynamic semantics. Semantics Research Seminar, University College London.
A response to Liebesman and Magidor on copredication. 11th Semantics and Philosophy in Europe colloquium, University of Warsaw.
Quantificational Subordination as Anaphora to a Function. 24th Conference on Formal Grammar, University of Latvia.
Constraining scope ambiguity in LFG+Glue. 24th International Lexical-Functional Grammar Conference, Australian National University.
Double negation, excluded middle and accessibility in dynamic semantics. London Semantics Symposium, Queen Mary University of London.
2018
Glue semantics for Universal Dependencies. 23rd International Lexical-Functional Grammar Conference, University of Vienna (with Dag Haug).
Glue semantics for Universal Dependencies. Workshop on meaning construction, Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo (with Dag Haug).
2017
Closing comments and discussion. Workshop on Approaches to Coercion and Polysemy (CoPo 2017), University of Oslo (with Alexandra Anna Spalek).
Comments on Jakub Dotlačil's presentation. 11th Paris-Amsterdam-London Logic Meeting for Young Researchers (PALLMYR-XI), University College London.
Glue Semantics and Locality. 22nd International Lexical-Functional Grammar Conference, University of Konstanz.
A Model-Theoretic Reconstruction of Type-Theoretic Semantics for Anaphora. 22nd Conference on Formal Grammar, University of Toulouse.
Comments on Uli Sauerland's presentation. Non-At-Issue Meaning and Information Structure, XPRAG workshop at the University of Oslo.
2016
Individuation and quantification in semantic theory. Expressing sameness seminar, University of Cologne.
Making Logical Form type-logical. University of Oslo Forum for Theoretical Linguistics.
Conceptualization, individuation and quantification. Referential Semantics One Step Further: Incorporating Insights from Conceptual and Distributional Approaches to Meaning, workshop at the 28th European Summer School in Logic, Language and Information, Free University of Bozen-Bolzano.
Copredication: quantificational issues and methodological implications. Invited seminar at the University of Gothenburg.
2015
Criteria of individuation determined compositionally. 8th Semantics and Philosophy in Europe colloquium, University of Cambridge.
Glue Semantics for Minimalist Syntax. Annual meeting of the Linguistics Association of Great Britain, University College London.
Towards Glue Semantics for Minimalist Syntax. Interactions between syntax and semantics across frameworks, workshop at the Department for Theoretical and Applied Linguistics, University of Cambridge.
2014
Composing criteria of individuation. 1st London Semantics Day, Queen Mary University of London.
A compositional theory of criteria of individuation for copredication, Newcastle upon Tyne Postgraduate Conference in Linguistics.