The first part of this article (Sections 1–5) focuses on the classical notions of scope and binding and their formal foundations. It argues that once their semantic core is properly understood, it can be implemented in various different ways: with or without movement, with or without variables. The second part (Sections 6–12) takes up the empirical issues that have redrawn the map in the past two decades. It turns out that scope is not a primitive. Existential scope and distributive scope (...) have to be distinguished, leaving few if any run-of-the-mill quantifiers. Scope behavior is also not uniform. At least three classes of expressions emerge: indefinites, distributive universals, and counters. Likewise, the bound variable interpretation of pronouns is joined by co-variation with situations. As a result, the classical notions of scope and binding are likely to end up as building blocks in the varied mechanisms at work in “scope phenomena” and “binding phenomena”, and not as self-contained analyses of those phenomena. (shrink)

Proof-theoretic models of grammar are based on the view that an explicit characterization of a language comes in the form of the recursive enumeration of strings in that language. That recur-sive enumeration is carried out by a procedure which strongly generates a set of structural de-scriptions Σ and weakly generates a set of strings S; a grammar is thus a function that pairs an element of Σ with elements of S. Structural descriptions are obtained by means of Context-Free phrase structure (...) rules or via recursive combinatorics and structure is assumed to be uniform: binary branching trees all the way down. In this work we will analyse natural language constructions for which such a rigid conception of phrase structure is descriptively inadequate, and pro-pose a solution for the problem of phrase structure grammars assigning too much or too little structure to natural language strings: we propose that the grammar can oscillate between levels of computational complexity in local domains, which correspond to elementary trees in a lexicalised Tree Adjoining Grammar. (shrink)

This paper attempts to describe and address a specific puzzle related to compositionality in artificial networks such as Deep Neural Networks and machine learning in general. The puzzle identified here touches on a larger debate in Artificial Intelligence related to epistemic opacity but specifically focuses on computational applications of human level linguistic abilities or properties and a special difficulty with relation to these. Thus, the resulting issue is both general and unique. A partial solution is suggested.

I argue that alternative-denoting expressions interact with their semantic context by taking scope. With an empirical focus on indefinites in English, I show how this approach improves on standard alternative-semantic architectures that use point-wise composition to subvert islands, as well as on in situ approaches to indefinites more generally. Unlike grammars based on point-wise composition, scope-based alternative management is thoroughly categorematic, doesn’t under-generate readings when multiple sources of alternatives occur on an island, and is compatible with standard treatments of binding. (...) Unlike all in situ treatments of indefinites, relying on a true scope mechanism prevents over-generation when an operator binds into an indefinite. My account relies only on function application, some mechanism for scope-taking, and two freely-applying type-shifters: the first is Karttunen’s :3–44, 1977. https://doi.org/10.1007/BF00351935) proto-question operator, aka Partee’s Studies in discourse representation theory and the theory of generalized quantifiers, Foris, Dordrecht, 1986) IDENT, and the second can be factored out of extant approaches to the semantics of questions in the tradition of Karttunen. These type-shifters form a decomposition of LIFT, the familiar function mapping values into scope-takers. Exceptional scope of alternative-generating expressions arises via scopal pied-piping: indefinites take scope over their island, which then itself takes scope. (shrink)

One of the main motivations for having a compositional semantics is the account of the productivity of natural languages. Formal languages are often part of the account of productivity, i.e., of how beings with finite capaci- ties are able to produce and understand a potentially infinite number of sen- tences, by offering a model of this process. This account of productivity con- sists in the generation of proofs in a formal system, that is taken to represent the way speakers grasp (...) the meaning of an indefinite number of sentences. The informational basis is restricted to what is represented in the lexicon. This constraint is considered as a requirement for the account of productivity, or at least of an important feature of productivity, namely, that we can grasp auto- matically the meaning of a huge number of complex expressions, far beyond what can be memorized. However, empirical results in psycholinguistics, and especially particular patterns of ERP, show that the brain integrates informa- tion of different sources very fast, without any felt effort on the part of the speaker. This shows that formal procedures do not explain productivity. How- ever, formal models are still useful in the account of how we get at the seman- tic value of a complex expression, once we have the meanings of its parts, even if there is no formal explanation of how we get at those meanings. A practice-oriented view of modeling gives an adequate interpretation of this re- sult: formal compositional semantics may be a useful model for some ex- planatory purposes concerning natural languages, without being a good model for dealing with other explananda. (shrink)

The standard approach to model how human beings understand natural languages is the symbolic, compositional approach according to which the meaning of a complex expression is a function of the meanings of its constituents. In other words, meaning plays a fundamental role in the model. In this work, because of the polysemous, flexible, dynamic, and contextual structure of natural languages, this approach is rejected. Instead, a connectionist model which eliminates the concept of meaning is proposed.

By creating certain marks on paper, or by making certain sounds-breathing past a moving tongue-or by articulation of hands and bodies, language users can give expression to their mental lives. With language we command, assert, query, emote, insult, and inspire. Language has meaning. This fact can be quite mystifying, yet a science of linguistic meaning-semantics-has emerged at the intersection of a variety of disciplines: philosophy, linguistics, computer science, and psychology. Semantics is the study of meaning. But what exactly is "meaning"? (...) What is the exact target of semantic theory? Much of the early work in natural language semantics was accompanied by extensive reflection on the aims of semantic theory, and the form a theory must take to meet those aims. But this meta-theoretical reflection has not kept pace with recent theoretical innovations. This volume re-addresses these questions concerning the foundations of natural language semantics in light of the current state-of-the-art in semantic theorising. (shrink)

The goal of this paper is to revisit the phenomenon of bridging anaphora Thinking: readings in cognitive science, Cambridge University Press, Cambridge, pp 411–420, 1977) from the perspective of the German demonstrative plural pronoun die ‘they’. I argue that antecedentless die ‘they’ can be analyzed as a novel definite that is licensed by a suitable, contextually given situation and denotes the salient person who stand in a contextually given relation to that situation. Subsequently, I propose a formal semantic implementation of (...) my analysis in terms of Elbourne, analyzing the antecedentless demonstrative pronoun die ‘they’ as a definite description in disguise. (shrink)

Categorial grammar is well-known for its elegant analysis of coordination enabled by the flexible notion of constituency it entertains. However, to date, no systematic study exists that examines whether this analysis has any obvious empirical advantage over alternative analyses of nonconstituent coordination available in phrase structure-based theories of syntax. This paper attempts precisely such a comparison. We compare the direct constituent coordination analysis of non-canonical coordinations in categorial grammar with an ellipsis-based analysis of the same phenomena in the recent HPSG (...) literature. We provide a set of empirical evidence, consisting of cases in which non-canonical coordinations interact with scopal operators of various sorts, which systematically falsifies the predictions of the latter, ‘linearization-based’ ellipsis approach to coordination. We propose an alternative analysis in a variant of categorial grammar called Hybrid Type-Logical Categorial Grammar. The proposed framework builds on both the Lambek-inspired variants of categorial grammar and a more recent line of work modelling word order via a lambda calculus for the prosodic component. The flexible syntax–semantics interface of this framework straightforwardly captures the interactions between non-canonical coordinations and scopal expressions, demonstrating the broader empirical payoff of the direct constituent coordination analysis of non-canonical coordinations pioneered by Steedman :523–568, 1985; Linguist Philos 13:207–263, 1990) and Dowty hitherto not explicitly recognized in the literature. (shrink)

‘Fred must open the door’ concerns Fred’s obligations. This obligative meaning is turned off by adding aspect: ‘Fred must have opened/be opening/have been opening the door’ are one and all epistemic. Why? In a nutshell: obligative ’must’ operates on procedural contents of imperative sentences, epistemic ‘must’ on propositional contents of declarative sentences; and adding aspect converts procedural into propositional content.

Starting from the familiar observation that no straightforward treatment of pure quotation can be compositional in the standard (homomorphism) sense, we introduce general compositionality, which can be described as compositionality that takes linguistic context into account. A formal notion of linguistic context type is developed, allowing the context type of a complex expression to be distinct from those of its constituents. We formulate natural conditions under which an ordinary meaning assignment can be non-trivially extended to one that is sensitive to (...) context types and satisfies general compositionality. As our main example we work out a Fregean treatment of pure quotation, but we also indicate that the method applies to other kinds of context, e.g. intensional contexts. (shrink)

This article is concerned with the principle of compositionality, i.e. the principle that the meaning of a complex expression is a function of the meanings of its parts and its mode of composition. After a brief historical background, a formal algebraic framework for syntax and semantics is presented. In this framework, both syntactic operations and semantic functions are partial. Using 20 the framework, the basic idea of compositionality is given a precise statement, and several variants, both weaker and stronger, as (...) well as related properties, are distinguished. Several arguments for compositionality are discussed, and the standard arguments are found inconclusive. Also, several arguments against compositionality, and for the claim that it is a trivial property, are discussed, 25 and are found to be flawed. Finally, a number of real or apparent problems for compositionality are considered, and some solutions are proposed. (shrink)