Vagueness, Gradability and Typicality: A Comprehensive Semantic Analysis

The analyses of predicates (and in particular nouns ) in emantics and psychology focus on separated sets of facts. This fact reduces the a dequ cy of the theories in both disciplines. On the one hand, semantic theories usually associat e adjectives, but not nouns, with a gradable structure (mapping of entities to degrees along ordering dimensions). However, the last forty years of research in cognitive psych ology have established beyond doubt that the concepts that nouns denote do possess a gr ad ble structure. The relevance of these facts to semantics is demonstrated by some no v l linguistic data. For example, I show that nouns occur more freely than adjectives in one type of comparison s tatements, whose semantic interpretation is standardly assumed to be mediated by degrees. This fact supports the view that the semantic analysis of nou ns ought to involve mapping to degrees. On the other hand, Kamp and Partee (1995) have anal yzed nouns as gradable, but empirical and theoretical considerations suggest th at their theory is inadequate. Furthermore, psychological theories, which treat no uns as gradable and multidimensional, fail to explain important semantic con trasts: First, gradable adjectives, but not nouns, are compatible with a variety of express ions whose meanings relate to degrees. Second, in multi-dimensional adjectives, b ut not in nouns, the ordering dimensions can be accessed and quantified over. By looking at the entire set of facts, a line of explanation suggests itself, hinging upon d istinctions in the type of graded structure of nominal and adjectival concepts. I def ine the notion of a dimension-set in a precise and formal way, and I provide an improved a ccount for the linguistic contrasts between nouns and adjectives. Finally, cognitive ps ychologists view many of their finding as refuting logical rules which form the ba sis of semantic theories. By showing that these findings are compatible with, and to som e extent motivated by, semantic and pragmatic rules, I pave the way to bridging the gap between semantics and psychology. I propose that mechanisms that are advanced by psycho logical theories can and should be embedded within a semantic model that represents kn owledge and its gradual growth ("a learning model"), to allow for a more adequate repr esentation of psychological and semantic facts. Finally, prominent semantic gradability theories ar e concerned with accounting for polarity effects (differences between positive and negative predicates like tall and short), and with providing a recursive semantic derivation f r comparison statements (like Dan is taller than every boy is). I propose a detailed formal theory concerning th e degree functions that positive and negative predicates den ote and concerning the derivation of semantic interpretation for comparison statements. I show that my theory is superior to previous theories in terms of the set of facts it a dequately predicts. In addition, though this theory enriches the interpretation of predicat es with a new element (a transformation value), it simplifies the interpretation of predica tes by removing from it several other elements (like degree relations, minus operations a nd supremum operations). Thus, my proposal is more economic in these respects.