Comparison of Complex Predicates: and, or and more

Are complex predicates—in particular, negated (e.g., not expensive), conjunctive (e.g., expensive and time consuming) and disjunctive predicates (e.g., tall or bald)—associated with a graded structure, namely a mapping of entities to degrees? On the one hand, most up to date semantic theories of gradability and comparison in natural language disregard this question. On the other hand, contemporary fuzzy logical theories provide compositional rules to construct a degree function for a complex expression based on the degree functions of its constituents. These composition rules have been found useful for a variety of practical applications. The question is then whether these rules can correctly represent the interpretation of complex natural language expressions and its relation to the interpretation of their constituents. The relevance of this question is enhanced by recent findings from a variety of studies (Ripley 2011; Serchuk et al., 2010; Alxatib and Pelletier 2011), according to which high percentages of subjects count contradictory predicates such as tall and not tall as true of borderline cases (neither short nor tall entities). While these findings stand in sharp contrast to predictions of vaguenessbased theories of adjectives, they are in accord with the predictions of a fuzzy analysis, as extensively argued by Kamp and Partee (1995). Given these new findings, then, the fact that fuzzy analyses allow for non-zero truth values to contradictions can no longer count against them (for a more detailed discussion see Sauerland, this volume). It is therefore increasingly important to test other predictions of applications of fuzzy analyses to natural language conjunctions and disjunctions. To this end, this paper discusses preliminary results based on a questionnaire eliciting judgments from 35 Hebrew speakers. The results suggest that, counter the predictions of fuzzy analyses, comparative and equative morphemes cannot apply to conjunctions and disjunctions of gradable adjectives.