Lexical relatedness and the lexical entry - a formal unification

Based on the notion of a lexicon with default inheritance, I address the problem of how to provide a template for lexical representations that allows us to capture the relatedness between inflected word forms and canonically derived lexemes within a broadly realizational-inferential model of morphology. To achieve this we need to be able to represent a whole host of intermediate types of lexical relatedness that are much less frequently discussed in the literature. These include transpositions such as deverbal participles, in which a word's morphosyntactic class changes (e.g. verb ⇒ adjective) but no semantic predicate is added to the semantic representation and the derived word remains, in an important sense, a "form" of the base lexeme (e.g. the 'present participle form of the verb'). I propose a model in which morphological properties are inherited by default from syntactic properties and syntactic properties are inherited from semantic properties, such as ontological category (the Default Cascade). Relatedness is defined in terms of a Generalized Paradigm Function (perhaps in reality a relation), a generalization of the Paradigm Function of Paradigm Function Morphology (Stump 2001). The GPF has four components which deliver respectively specifications of a morphological form, syntactic properties, semantic representation and a lexemic index (LI) unique to each individuated lexeme in the lexicon. In principle, therefore, the same function delivers derived lexemes as inflected forms. In order to ensure that a newly derived lexeme of a distinct word class can be inflected I assume two additional principles. First, I assume an Inflectional Specifiability Principle, which states that the form component of the GPF (which defines inflected word forms of a lexeme) is dependent on the specification of the lexeme's morpholexical signature, a declaration of the properties that the lexeme is obliged to inflect for (defined by default on the basis of morpholexical class). I then propose a Category Erasure Principle, which states that 'lower' attributes are erased when the GPF introduces a non-trivial change to a 'higher' attribute (e.g. a change to the semantic representation entails erasure of syntactic and morphological information). The required information is then provided by the Default Cascade, unless overridden by specific declarations in the GPF. I show how this model can account for a variety of intermediate types of relatedness which cannot easily be treated as either inflection or derivation, and conclude with a detailed illustration of how the system applies to a particularly interesting type of transposition in the Samoyedic language Sel'kup, in which a noun is transposed to a similitudinal adjective whose form is in paradigmatic opposition to case-marked noun forms, and which is therefore a kind of inflection

Does Hungarian have a case system?

I argue that case markers in Hungarian are best thought of as ‘fused postpositions’. There is no need to set up a separate syntactic or morphological [Case] attribute as such. Rather, we just need a morphological principle stating that nominals (including pronouns) have a special form, the traditional case form. In this respect Hungarian is crucially different from languages such as Latin (which requires both a morphological and a syntactic [Case] feature) or Finnish (which requires at least a syntactic [Case] feature). I discuss certain typological issues arising from this analysis, arguing that when grammarians refer to Hungarian ‘cases’, they are really referring to a rather more general notion of ‘canonical grammatical function markers on dependents’

Baire measurable paradoxical decompositions via matchings

We show that every locally finite bipartite Borel graph satisfying a strengthening of Hall's condition has a Borel perfect matching on some comeager invariant Borel set. We apply this to show that if a group acting by Borel automorphisms on a Polish space has a paradoxical decomposition, then it admits a paradoxical decomposition using pieces having the Baire property. This strengthens a theorem of Dougherty and Foreman who showed that there is a paradoxical decomposition of the unit ball in $\mathbb{R}^3$ using Baire measurable pieces. We also obtain a Baire category solution to the dynamical von Neumann-Day problem: if $a$ is a nonamenable action of a group on a Polish space $X$ by Borel automorphisms, then there is a free Baire measurable action of $\mathbb{F}_2$ on $X$ which is Lipschitz with respect to $a$.Comment: Minor revision

Borel circle squaring

We give a completely constructive solution to Tarski's circle squaring problem. More generally, we prove a Borel version of an equidecomposition theorem due to Laczkovich. If $k \geq 1$ and $A, B \subseteq \mathbb{R}^k$ are bounded Borel sets with the same positive Lebesgue measure whose boundaries have upper Minkowski dimension less than $k$, then $A$ and $B$ are equidecomposable by translations using Borel pieces. This answers a question of Wagon. Our proof uses ideas from the study of flows in graphs, and a recent result of Gao, Jackson, Krohne, and Seward on special types of witnesses to the hyperfiniteness of free Borel actions of $\mathbb{Z}^d$.Comment: Minor typos correcte

Morphological theory and English

This paper presents a review of a number of recent issues in the field of generative morphology, with their implications for the description of English. After an introduction to the field two types of question are considered. First, 1 examine the nature of word structure and illustrate two competing approaches, one of which assurnes that words have a constituent structure (much like the phrase structure of syntax) and the other of which rejects this assumption. Then we look at the way morphologicai structure interacts with syntax. We examine the extent to which syntactic principles can account for the behaviour of certain types of compounds and aiso the expression of syntactic arguments in nominaiizations