Ellipsis and Multimodal Categorial Type Logic (original) (raw)
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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.
In 7th Amsterdam Colloquium
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. ...
Logic Journal of IGPL, 1995
Recent work within Categorial Grammar has seen the development of a number of multimodal systems, where di erent families of connectives coexist within a single categorial logic. Such systems can be viewed as making available di ering modes of linguistic description within a single grammatical formalism. This paper addresses proposals for constructing multimodal systems due to Hepple 7] and Moortgat & Oehrle 15], which are in many ways similar, but which make apparently contradictory claims concerning the appropriate interrelation of di erent modes of description, which lead in turn to di erences for the kind of linguistic accounts that the two approaches make possible. Although we focus mostly on the view taken in Hepple 7], and its inspiration by earlier work involving structural modalities, the paper proceeds to a discussion of whether the two approaches are genuinely incompatible in the way that they at rst appear.
We present a framework, named the Montagovian generative lexicon, for computing the semantics of natural language sentences, expressed in many sorted higher order logic. Word meaning is depicted by several lambda terms of second order lambda calculus (Girard's system F): the principal lambda term encodes the argument structure, while the other lambda terms implement meaning transfers. The base types include a type for propositions and many types for sorts of a many sorted logic for expressing restriction of selection. This framework is able to integrate a proper treatment of lexical phenomena into a Montagovian compositional semantics, like the (im)possible arguments of a predicate, and the adaptation of a word meaning to some contexts. Among these adaptations of a word's sense to the context, ontological inclusions are handled by coercive subtyping, an extension of system F introduced in the present paper. The benefits of this framework for lexical semantics and pragmatics are illustrated on meaning transfers and coercions, on possible and impossible copredication over different senses, on deverbal ambiguities, and on "fictive motion". Next we show that the compositional treatment of determiners, quantifiers, plurals,... are finer grained in our framework. We then conclude with the linguistic, logical and computational perspectives opened by the Montagovian generative lexicon.
Type-theoretical semantics with coercive subtyping
Semantics and Linguistic Theory, 2010
In the formal semantics based on modern type theories, common nouns are interpreted as types, rather than as functional subsets of entities as in Montague grammar. This brings about important advantages in linguistic interpretations but also leads to a limitation of expressive power because there are fewer operations on types as compared with those on functional subsets. The theory of coercive subtyping adequately extends the modern type theories with a notion of subtyping and, as shown in this paper, plays a very useful role in making type theories more expressive for formal semantics. In particular, it gives a satisfactory treatment of the type-theoretic interpretation of modified common nouns and allows straightforward interpretations of interesting linguistic phenomena such as copredication, whose interpretations have been found difficult in a Montagovian setting. We shall also study some type-theoretic constructs that provide useful representational tools for formal lexical sem...
An Account of Natural Language Coordination in Type Theory with Coercive Subtyping
Lecture Notes in Computer Science, 2013
We discuss the semantics of NL coordination in modern type theories (MTTs) with coercive subtyping. The issue of conjoinable types is handled by means of a type universe of linguistic types. We discuss quantifier coordination, arguing that they should be allowed in principle and that the semantic infelicity of some cases of quantifier coordination is due to the incompatible semantics of the relevant quantifiers. Non-Boolean collective readings of conjunction are also discussed and, in particular, treated as involving the vectors of type V ec(A, n), an inductive family of types in an MTT. Lastly, the interaction between coordination and copredication is briefly discussed, showing that the proposed account of coordination and that of copredication by means of dot-types combine consistently as expected. This work is supported by the research grant F/07-537/AJ of the Leverhulme Trust in the U.K. 3 Examples of modern type theories include Martin-Löf's type theory [21, 26], the Unifying Theory of dependent Types (UTT) [15] and the type theory implemented in the Coq proof assistant (pCIC) [7]. in the examples below, where the same conjoined NP is interpreted distributively in (1) but collectively in (2): (1) John and Mary came to the Party. (2) John and Mary met at the Party. We shall investigate how collective readings can be interpreted by means of the inductive family of types of vectors in an MTT. We further discuss the interaction between dot-types for coordinated NPs. Dot-types have been proposed by Pustejovsky [28, 29] for lexical interpretations of inherently polysemous words in phenomena such as co-predication (see, for example, [2]). 4 For example, book according to [28] can be represented with the dot-type Phy • Info, a type whose objects have both a physical and an informational aspect. Dot-types have been formally introduced into MTTs with coercive subtyping [17, 18] and a computational implementation of this account in Plastic 5 has also been done [35]. What we want to look at in this paper is the interaction between these types and coordination, i.e. examples of the following sort: (3) The book and my lunch were sent by mistake to someone else. (4) John picked up the newspaper and the book from the floor. Given that the dot-types of the coordinated phrases are different and assuming that the NL coordination operate on the same types, we will have to explain how coordination is possible in these cases. The problem that arises in examples like (3) and (4) is that the individual NPs of the conjunction (e.g. the book and my lunch in (3) have different types (Phy • Info for book and Event • Phy for lunch). The challenge is to account for the possibility of coordination in these cases by, at the same time, retaining the assumption that coordination operates on elements of the same type. As we shall see, the coercive subtyping mechanism actually allows us to combine the proposed typing for NL coordinations and the account with dot-types in a rather straightforward way.
Heads and Phrases. Type Calculus for Dependency and Constituent Structure
From a logical perspective, categorial type systems can be situated within a landscape of substructural logics --- logics with a structure-sensitive consequence relation. Research on these logics has shown that the inhabitants of the substructural hierarchy can be systematically related by embedding translations on the basis of structural modalities. The modal operators offer controlled access to stronger logics from within weaker ones by licensing of structural operations. Linguistic material exhibits structure in dimensions not covered by the standard structural rules. The purpose of this paper is to generalize the modalisation and licensing strategy to two such dimensions: phrasal structure and headedness. Phrasal domain-sensitive type systems capture the notion of constituent structure; constituency relaxation can be licensed via an associativity modality. The opposition between heads and non-heads introduces dependency structure, an autonomous dimension of linguistic structure ...
Modern Type Theories for Natural Language Semantics ( Introductory Course in Language and Logic )
2016
Modern Type Theories (MTTs) provide us with a new framework for formal semantics with attractive advantages as compared to Montague Grammar. First, MTTs have rich type structures that can be employed effectively to capture various linguistic features that have proved difficult in the Montagovian setting. Second, MTTs are prooftheoretically specified and can hence be usefully implemented in proof assistants such as Coq, where the MTT-semantics has been implemented for computer-assisted reasoning. These two respects may be characterised as saying that the MTT-semantics is both modeltheoretic and proof-theoretic. They offer unique features unavailable in traditional logical systems that have proved very useful in formal semantics. We shall introduce MTTs and how they can be used for formal semantics. The lectures will be informal and explanatory. They will be rigorous but contain a lot of examples, to illustrate the use of MTTs, on the one hand, and to compare the MTT-semantics with Mo...
Underspecification and interpretive parallelism in Dependent Type Semantics
Proceedings of the IWCS 2019 Workshop on Computing Semantics with Types, Frames and Related Structures
The scope parallelism in the Geach sentence (Every boy loves, and every girl detests, some saxophonist) and the related parallel interpretation requirement in pronominal binding is a pervasive phenomenon found across different types of coordination and ellipsis phenomena. Previous accounts all resort to additional constraints of some sort that restrict the otherwise flexible syntax-semantics interface to avoid overgeneration. In this paper, we propose a novel approach to this long-standing problem. We show that, by taking a proof-theoretic perspective on natural language semantics and by viewing the ambiguity resolution for pronouns and indefinites as underspecification resolution that invokes extra proof search, a conceptually natural solution emerges for the problem of interpretive parallelism. The analysis is cast in Dependent Type Semantics, with Hybrid Type-Logical Categorial Grammar as the syntax-semantics interface backbone. For empirical illustration, we show how the proposed approach correctly accounts for the classical Geach paradigm and its pronominal variant.