Semantically Inactive Multiplicatives and Words as Types (original) (raw)
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We take the opportunity of the publication of some of the papers of the ESSLLI workshop TYTLES (TYpe Theory and LExical Semantics, ESSLLI 2015, Barcelona) to provide an overview of the possibilities that type theory offers to model lexical semantics, especially the type-theoretical frameworks that properly model compositional semantics. origins of this issue: esslli workshop on type theory and lexical semantics 2015 The program of the ESSLLI 2015 workshop held in Barcelona 1 consisted of twelve selected talks. The corresponding extended abstracts, together with an introduction and a conclusion by the workshop organisers, are available on the web as Cooper and Retoré (2015); it includes: A. Introduction (slides), by Robin Cooper and Christian Retoré.
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This paper represents categorial grammar as an implicational type theory in the spirit of Girard's linear logic, and illustrates linguistic applications of a range of type- constructors over and above implication. ...
Adjectival and Adverbial Modification: The View from Modern Type Theories
Journal of Logic, Language and Information, 2017
In this paper we present a study of adjectival/adverbial modification using modern type theories (MTTs), i.e. type theories within the tradition of Martin-Löf. We present an account of various issues concerning adjectival/adverbial modification and argue that MTTs can be used as an adequate language for interpreting NL semantics. MTTs are not only expressive enough to deal with a range of modification phenomena, but are furthermore well-suited to perform reasoning tasks that can be easily implemented (e.g. in proof-assistants) given their proof-theoretic nature. In MTT-semantics, common nouns are interpreted as types rather than predicates. Therefore, in order to capture the semantics of adjectives adequately, one needs to meet the challenge of modeling CNs modified by adjectives as types. To explicate that this can be done successfully, we first look at the mainstream classification of adjectives, i.e. intersective, subsective and non-subsective adjectives. There, we show that the rich type structure available in MTTs, along with a suitable subtyping framework, offers an adequate
Natural Language & Linguistic Theory, 2015
This paper proposes a unified analysis of the 'respective' readings of plural and conjoined expressions, the internal readings of symmetrical predicates such as same and different, and the summative readings of expressions such as a total of $10,000. These expressions pose significant challenges to compositional semantics, and have been studied extensively in the literature. However, almost all previous studies focus exclusively on one of these phenomena, and the close parallels and interactions that they exhibit have been mostly overlooked to date. We point out two key properties common to these phenomena: (i) they target all types of coordination, including nonconstituent coordination such as Right-Node Raising and Dependent Cluster Coordination; (ii) the three phenomena all exhibit multiple dependency, both by themselves and with respect to each other. These two parallels suggest that one and the same mechanism is at the core of their semantics. Building on this intuition, we propose a unified analysis of these phenomena, in which the meanings of expressions involving coordination are formally modelled as multisets, that is, sets that allow for duplicate occurrences of identical elements. The analysis is couched in Hybrid Type-Logical Categorial Grammar. The flexible syntax-semantics interface of this framework enables an analysis of 'respective' readings and related phenomena which, for the first time in the literature, yields a simple and principled solution for both the interactions with nonconstituent coordination and the multiple dependency noted above.
Type Theory and Natural Language: Do We Need Two Basic Types? 1
2012
0. A universal, or almost universal distinction, in syntax: Sentence and NP.........................................................1 1. A possibly universal foundation for natural language semantics: types e and t..................................................1 2. Thought experiments: “Monocategoric”? and just one basic semantic type?....................................................3 3. Ingredients for a possible one-basic-type semantics..........................................................................................3 3.1. Neo-Davidsonian semantics of event sentences..........................................................................................3 3.2. Kamp-Heim semantics for indefinite NPs..................................................................................................3 3.3. Open formulas are “almost ” type-neutral....................................................................................................4 3.4. Exploit the similarit...
Towards a More Lexical and Functional Type-Logical Theory of Grammar
Type-Logical Lexical Functional Grammar is a new, radically lexicalist, and formally parsimonious theory, in essence a re-incarnation of Lexical Func- tional Grammar (Kaplan and Bresnan, 1982) in a type-logical formal frame- work very similar in formal nature to that of Type-Logical Categorial Gram- mar (Morrill, 1994; Moortgat, 1997). It puts emphasis on having a simple logical foundation as its formal basis and no empirically unmotivated primi- tives, representations, and mappings between them. It differs from TLCG in basing syntactic analyses on functional rather than constituent structure, to both LFG and TLCG in that it rejects syntactic categories as primitives, and to LFG in that it rejects c-structure as a linguistically significant representa- tion and in being radically lexicalist. The present paper presents TL-LFG, the sequence of developments that lead to it, and its key differences from LFG.
Tuples, Discontinuity, and Gapping in Categorial Grammar
Proceedings of the Sixth Conference on European Chapter of the Association For Computational Linguistics, 1993
This paper solves some puzzles in the formalisation of logic for discontinuity in categorial grammar. A 'tuple' operation introduced in [Solias, 1992] is defined as a mode of prosodic combination which has associated projection functions, and consequently can support a property of unique prosodic decomposability. Discontinuity operators are defined model-theoretically by a residuation scheme which is particularly arnmenable proof-theoretically. This enables a formulation which both improves on the logic for wrapping and infixing of [Moortgat, 1988] which is only partial, and resolves some problems of determinacy of insertion point in the application of these proposals to in-sits binding phenomena. A discontinuons product is also defined by the residuation scheme, enabling formulation of rules of both use and proof for a 'substring' product that would have been similarly doomed to partial logic. We show how the apparatus enables characterisation of discontinous functors such as particle verbs and phrasal idioms, and binding phenomena such as quantifier raising and pied piping. We conclude by showing how the apparatus enables a simple categorial analysis of (SVO) gapping using the discontinuity product and the wrapping operator.
Type Logical Grammar: Categorial Logic of Signs
2002
Look under the hood of most theories of grammar or computational linguistic formalisms and you will find a "machine," often fueled by "rules," that grinds together (descriptions of) linguistic objects to produce other (descriptions of) linguistic objects. Such machines are justified by their descriptive success, or by claims that they explain (aspects of) linguistic ability. However, the puzzle of the origins of the machine remains. In our present state of knowledge about language, proposed machines can be only indirectly justified. And even if our knowledge were sufficient for more direct justifications, the broader question still remains of what are the necessary properties of any sign system that associates an open-ended set of meanings with elements of a
Introduction: Modern Perspectives in Type Theoretical Semantics
2017
Type theories, from the early days of Montague Semantics (Montague 1974) to the recent work of using rich or modern type theories, have a long history of being employed as foundational languages of natural language semantics. In this introductory chapter, we will describe and discuss the development of type theories as foundational languages of mathematics, as well as their applications as foundational languages for formal semantics. In the end, a brief description of each chapter in the volume will follow.