This volume explores the linguistic expression of modality in natural language from a cross-linguistic perspective. Modal expressions provide the basic tools that allow us to dissociate what we say from what is actually going on, allowing us to talk about what might happen or might have happened, as well as what is required, desirable, or permitted. Chapters in the book demonstrate that modality involves many more syntactic categories and levels of syntactic structure than traditionally assumed. The volume (...) distinguishes between three types of modality: 'low modality', which concerns modal interpretations associated with the verbal and nominal cartographies in syntax; 'middle modality', or modal interpretation associated to the syntactic cartography internal to the clause; and 'high modality', relating to the left periphery. It combines cross-linguistic discussions of the more widely-studied sources of modality with analyses of novel or unexpected sources, and shows how the meanings associated with the three types of modality are realized across a wide range of languages. (shrink)

The acquisition of syntactic categories is a crucial step in the process of acquiring syntax. At this stage, before a full grammar is available, only surface cues are available to the learner. Previous computational models have demonstrated that local contexts are informative for syntactic categorization. However, local contexts are affected by sentence-level structure. In this paper, we add sentence type as an observed feature to a model of syntactic category acquisition, based on experimental evidence showing that (...) pre-syntactic children are able to distinguish sentence type using prosody and other cues. The model, a Bayesian Hidden Markov Model, allows for adding sentence type in a few different ways; we find that sentence type can aid syntactic category acquisition if it is used to characterize the differences in word order between sentence types. In these models, knowledge of sentence type permits similar gains to those found by extending the local context. (shrink)

The paper contains an overview of the most important results presented in the monograph of the author "Teorie Językow Syntaktycznie-Kategorialnych" ("Theories of Syntactically-Categorial Languages" (in Polish), PWN, Warszawa-Wrocław 1985. In the monograph four axiomatic systems of syntactically-categorial languages are presented. The first two refer to languages of expression-tokens. The others also takes into consideration languages of expression-types. Generally, syntactically-categorial languages are languages built in accordance with principles of the theory of syntactic categories introduced by S. Leśniewski [1929,1930]; they (...) are connected with- the Ajdukiewicz’s work [1935] which was a continuation of Leśniewski’s idea and further developed and popularized in the research on categorial grammars, by Y. Bar-Hillel [1950,1953,1964]. To assign a suitable syntactic category to each word of the vocabulary is the main idea of syntactically-categorial approach to language. Compound expressions are built from the words of the vocabulary and then a suitable syntactic-category is assigned to each of them. A language built in this way should be decidable, which means that there should exist an algorithm for deciding about each expression of it, whether it is well-formed or is syntactically connected . The traditional, originating from Husserl, understanding of the syntactic category confronts some difficulties. This notion is defined by abstraction using the concept of affiliation of two expressions to the same syntactic category. (shrink)

We give syntactic characterizations of1. the theories whose categories of models are closed under the formation of pullbacks, and of2. the locally ω-polypresentable categories.A somewhat typical example is the category of algebraically closed fields. Case is proved by classical model-theoretic methods; it solves a problem raised by H. Volger . The solution of case is in the spirit of the ones for the locally ω-presentable and ω-multipresentable cases found by M. Coste and P.T. Johnstone respectively. The problem (...) was raised in the context of Domain Theory by F. Lamarche. (shrink)

Two axiomatizations of the nonassociative and commutative Lambek syntactic calculus are given and their equivalence is proved. The first axiomatization employs Permutation as the only structural rule, the second one, with no Permutation rule, employs only unidirectional types. It is also shown that in the case of the Ajdukiewicz calculus an analogous equivalence is valid only in the case of a restricted set of formulas. Unidirectional axiomatizations are employed in order to establish the generative power of categorial grammars based (...) on the nonassociative and commutative Lambek calculus with product. Those grammars produce CF-languages of finite degree generated by CF-grammars closed with respect to permutations. (shrink)

One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is (...) introduced for categorial languages generated by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functorfunction defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

One well known problem regarding quantifiers, in particular the 1st order quantifiers, is connected with their syntactic categories and denotations.The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is (...) introduced for categorial languages generated by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functor-function defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

We characterize Morita equivalence of theories in the sense of Johnstone in terms of a new syntactic notion of a common definitional extension developed by Barrett and Halvorson for cartesian, regular, coherent, geometric and first-order theories. This provides a purely syntactic characterization of the relation between two theories that have equivalent categories of models naturally in any Grothendieck topos.

During the past several decades, linguists have developed and applied widely techniques which enable them, to a considerable extent, to determine and state the structure of natural languages without semantic reference. It is of interest to inquire seriously into the formality of linguistic method and the adequacy of whatever part of it can be made purely formal, and to examine the possibilities of applying it, as has occasionally been suggested,s to a wider range of problems. In order to pursue these (...) aims it is first necessary to reconstruct carefully the set of procedures by which the linguist derives the statements of a linguistic grammar from the behaviour of language users, distinguishing clearly between formal and experimental in such a way that grammatical notions, appearing as definienda in a constructional system, wM be formally derivable for any language from a fixed sample of linguistic material upon which the primitives of the system are experimentally defined. The present paper will be an attempt to formalize a certain parts of the linguist's generalized syntax language. From another point of view, this paper is an attempt to develop an adequate notion of syntactic category within an inscriptional nominalistic framework. The inscriptional approach seems natural for linguistics, particularly in view of the fact that an adequate extension of the results of this paper will have to deal with the problem of homonymity, i.e., with a statement of the conditions under which tokens of the same type must be assigned to different syntactic classes. It will appear below that the calculus of individuals can often supply quite simple solutions to constructional.. (shrink)

We give a syntactic characterization of (finitary) theories whose categories of models are closed under the formation of connected limits (respectively the formation of pullbacks and substructures) in the category of all structures. They are also those theories whose consistent extensions by new atomic facts admit in each component an initial structure (respectively an initial term structure), and also thoseT for whichM(T) is locally finitely multi-presentable in a canonical way. We also show that these two properties of theories (...) are nonuniform. (shrink)

This book presents a formal and philosophical analysis of language syntax. It refers to some ideas of E.Husserl and G. Frege, to S. Leśniewski's theory of syntactic categories and K. Ajdukiewicz's conception of formal grammar, also to Ch.S. Pierces's distinction between tokens (concrete linguistic entities) and types (ideal linguistic entities) and to A.A. Markov's theory of algorithms. The central aim of the book is - in the spirit of these ideas - to provide both strict yet comprehensive lectures (...) on two axiomatic theories of languages (grammars) irrespective of specific structure of their expression and the notation used in them. The main feature of these theories are that definitions of well-formed expression allow the formulation of algorithms for the examination of syntactic correctness of expressions and that their formalizations are bi-level, in reference to opposite philosophical orientations: nominalistic and idealistic. The theoretical considerations in the book speak in favour of the former. The book contains a translation of the basic contents of the book in Polish "Teorie języków syntaktycznie kategorialnych ("Theories of syntactically categorial languages"), PWN, Warszawa-Wrocław 1985, and extensive Introduction and Final Remarks. In Introduction are discussed the main assumptions, objectives and conditionings of presented theories and intuitive foundations of these theories. Final Remarks are connected with the subject-matter of the book and the ability to build syntax theories in the opposition spirit, because of the Platonic approach to language syntax. -/- . (shrink)

The psycholinguistic literature has identified two syntactic adaptation effects in language production: rapidly decaying short-term priming and long-lasting adaptation. To explain both effects, we present an ACT-R model of syntactic priming based on a wide-coverage, lexicalized syntactic theory that explains priming as facilitation of lexical access. In this model, two well-established ACT-R mechanisms, base-level learning and spreading activation, account for long-term adaptation and short-term priming, respectively. Our model simulates incremental language production and in a series of modeling (...) studies, we show that it accounts for (a) the inverse frequency interaction; (b) the absence of a decay in long-term priming; and (c) the cumulativity of long-term adaptation. The model also explains the lexical boost effect and the fact that it only applies to short-term priming. We also present corpus data that verify a prediction of the model, that is, that the lexical boost affects all lexical material, rather than just heads. (shrink)

The Lambek-Grishin calculus is a symmetric version of categorial grammar obtained by augmenting the standard inventory of type-forming operations (product and residual left and right division) with a dual family: coproduct, left and right difference. Interaction between these two families is provided by distributivity laws. These distributivity laws have pleasant invariance properties: stability of interpretations for the Curry-Howard derivational semantics, and structure-preservation at the syntactic end. The move to symmetry thus offers novel ways of reconciling the demands of natural (...) language form and meaning. (shrink)

We should not admit categorial restrictions on the significance of syntactically well formed strings. Syntactically well formed but semantically absurd strings, such as ‘Life’s but a walking shadow’ and ‘Caesar is a prime number’, can express thoughts; and competent thinkers both are able to grasp these and ought to be able to. Gareth Evans’ generality constraint, though Evans himself restricted it, should be viewed as a fully general constraint on concept possession and propositional thought. For (a) even well formed but (...) semantically cross-categorial strings often do possess substantive inferential roles; (b) hearers exploit these inferential roles in interpreting such strings metaphorically; (c) there is no good reason to deny truth-conditions to strings with inferential roles. (shrink)

Language acquisition may be one of the most difficult tasks that children face during development. They have to segment words from fluent speech, figure out the meanings of these words, and discover the syntactic constraints for joining them together into meaningful sentences. Over the past couple of decades, computational modeling has emerged as a new paradigm for gaining insights into the mechanisms by which children may accomplish these feats. Unfortunately, many of these models assume a computational complexity and linguistic (...) knowledge likely to be beyond the abilities of developing young children. This article shows that, using simple statistical procedures, significant correlations exist between the beginnings and endings of a word and its lexical category in English, Dutch, French, and Japanese. Therefore, phonetic information can contribute to individuating higher level structural properties of these languages. This article also presents a simple 2‐layer connectionist model that, once trained with an initial small sample of words labeled for lexical category, can infer the lexical category of a large proportion of novel words using only word‐edge phonological information, namely the first and last phoneme of a word. The results suggest that simple procedures combined with phonetic information perceptually available to children provide solid scaffolding for emerging lexical categories in language development. (shrink)

This book takes apart and problematises the whole process of identifying and explaining the patterning of words in sentences. It brings together two concepts - syntax and text - that are normally treated separately, and shows how they can best be understood in relation to each other. Part 1, Processing the text, concentrates on getting texts ready for syntactic analysis. Since the data needs to be mediated through the processing of the text, the nature of that processing and its (...) effects on subsequent analysis need to be made explicit. Part 2, Analysing the clause, introduces the relevant syntactic phenomena and the sorts of concepts normally used to explain them. It shows how many of the assumptions of traditional syntactic analysis derive from the languages which form the basis of the European tradition, and that different languages require the so-called basic categories of syntactic analysis to be rethought. Part 3, Theorising syntax, sketches the range of syntactic theories available for the consumer. It gives a sense of developments in the field over the last 50 years not just in terms of the usual schools, but by picking up on concepts such as the key complementarity between syntagmatic and paradigmatic to characterise the emphases and biases of different theories. (shrink)

The overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved syntactic language to tackle these problems from the set-theoretic to the category-theoretic mode, together with a study of the consequent semantic transition in the logical interpretation of quantum event structures. In the present work, this is realized by representing categorically the global structure of a (...) quantum algebra of events (or propositions) in terms of sheaves of local Boolean frames forming Boolean localization functors. The category of sheaves is a topos providing the possibility of applying the powerful logical classification methodology of topos theory with reference to the quantum world. In particular, we show that the topos-theoretic representation scheme of quantum event algebras by means of Boolean localization functors incorporates an object of truth values, which constitutes the appropriate tool for the definition of quantum truth-value assignments to propositions describing the behavior of quantum systems. Effectively, this scheme induces a revised realist account of truth in the quantum domain of discourse. We also include an Appendix, where we compare our topos-theoretic representation scheme of quantum event algebras with other categorial and topos-theoretic approaches. (shrink)

Names are referring expressions and interact with the determiner system only exceptionally, in stark contrast with count nouns. The-predicativists like Sloat, Matushansky, and Fara claim otherwise, maintaining that syntactic data offers indicates that names belong to a special syntactic category which differs from common count nouns only in how they interact with ‘the’. I argue that the-predicativists have incorrectly discerned the syntactic facts. They have bypassed a large range of important syntactic data and misconstrued a critical (...) data point on which they ground the-predicativism. The right data offers new compelling syntactic grounds for referentialism. (shrink)

The standard versions of predicativism are committed to the following two theses: proper names are count nouns in all their occurrences, and names do not refer to objects but express name-bearing properties. The main motivation for predicativism is to provide a uniform explanation of referential names and predicative names. According to predicativism, predicative names are fundamental and referential names are explained by appealing to a null determiner functioning like “the” or “that.” This paper has two goals. The first is to (...) reject the predicativists’ explanation of the two types of names. I present three syntactic counterexamples to the predicativists’ account of referential names: incorporation, modification, and measure phrase uses. The second goal is to present a novel strategy to explain the two types of names. I propose that referential names are fundamental but that there are null morphemes available for transforming a name into a count noun (and possibly into other syntactic categories). (shrink)