Formal Semantic Studies of "Degrees" and "Differences"

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This research project investigated the semantics of degree expressions such as comparative constructions and the out-prefix sentence in English, and (tentatively) concluded the following. (1) Positive extents and differences are both regarded as sets of points on a scale, so that they are in the same semantic type, but they are different in sorts, and therefore cannot co-occur. Negative extents can be regarded as the same sort of differences in that they are defined as a difference between the whole scale and a positive extent. If so, negative extents are not independent sorts in the ontology of degrees. (2) It is widely assumed that truth conditions of comparative sentences like A is taller than B are represented as tall(A)>tall(B), but as far as the Japanese comparative construction is concerned, they should be represented as $d[d=tall(A)-tall(B)], in which the existential quantifier binds the degree variable. Given that Japanese yori/izyooni 'than'-clauses have anaphoric degree variables, the compositional relation between the matrix and the subordinate 'than'-clauses can be captured by dynamic binding.