This paper uses the distribution and interpretation of antonymous adjectives in comparative constructions as an empirical basis to argue that abstract representations of measurement, or ‘degrees’, must be modeled as intervals on a scale, rather than as points, as commonly assumed. I begin by demonstrating that the facts in this domain must be accounted for in terms of the interaction of the semantics of adjectival polarity and the semantics of the comparative, rather than principles governing the (overt) expression of particular (...) types of adjectives in comparatives. I then show that a principled account of the full range of data under consideration can be constructed within a model in which degrees are formalized as intervals on a scale and adjectival polarity is characterized in terms of two structurally distinct and complementary sorts of `positive' and `negative' degrees. (shrink)

This work adopts the perspective of plural logic and measurement theory in order first to focus on the microstructure of comparative determiners; and second, to derive the properties of comparative determiners as these are studied in Generalized Quantifier Theory, locus of the most sophisticated semantic analysis of natural language determiners. The work here appears to be the first to examine comparatives within plural logic, a step which appears necessary, but which also harbors specific analytical problems examined here.Since nominal comparatives involve (...) plural and mass reference, we begin with a domain of discourse upon which a lattice structure (Link's) is imposed, and which maps (via abstract dimensions such asweight in kilograms) to concrete measures (in N,R+). The mapping must be homomorphic and Archimedean. Comparisons begin as simple predicates on dimensions or measures; from these we derive classes of predicates on the domain, i.e., generalized determiners (quantifiers), and show, e.g., how monotonicity properties follow in the derivation. This results in a proposal for a logical language which includes derived determiners, and which is an attractive target for semantics interpretation; it also turns out that some interesting comparative determiners are first order, at least when restricted to nonparametric and noncollective predications. (shrink)

The proponents of strong lexicalism hold the view that “words” are formed in the lexicon and are opaque for the syntax ((Dowty 1979), (DiSciullo and Williams 1987), (Jackendoff 1990) and many others). Modular morphology, on the other hand, offers the possibility that at least some words are partially formed in the syntax ((Baker 1988), (Borer 1988), (Hale and Keyser 1994), (Chomsky 1995) and many others). In (Stechow 1995) and (Stechow 1996) it has been argued that facts observed with German wieder (...) “again” cannot be accounted for within the framework of strong lexicalism and therefore favour the second position. The authors of this paper want to check these claims by investigating the behaviour of the German adverb fast “ almost”, the other classical adverb to which the method of decomposition has been applied in the linguistic literature (cf. (McCawley 1971)). Most adverbs cannot look into lexical decomposition structures, but some can. In order to have a suitable name, let us call these D-adverbs. Again and almost are the prototypical representatives of this class. The method adopted is to investigate whether fast has access to different aspects of verbal meaning depending on its position. Following (Dowty 1979), resultative verbs and prepositions are decomposed into BECOME + XP, where XP is the result state. Agentive verbs contain an additional AGENT part. Other thematic relations connecting the subject and the event are HOLDER and cause. If the syntax tells us that an adverb like wieder or fast must have wide scope with respect to BECOME, then we expect other readings than in a configuration where fast can have narrow scope with respect to BECOME. In other words, the motivation for decomposition is syntactic and semantic. The idea is that certain function projections in the classical VP have a meaning and hence scopally interact with adverbs. (shrink)

This paper focuses on the semantic and pragmatic properties of certain aspectual predicates (e.g. start) and degree modifiers (e.g. half). As is wellknown, such terms typically give rise to SCALAR IMPLICATURES (SIs). For instance, an utterance such as (1a) or (2a) is often taken to carry the implicature in (1b) and (2b) respectively.