A Tradeoff between Compositionality and Complexity in the Semantics of Dimensional Adjectives

A Tradeoff between Compositionality and Complexity in the Semantics of Dimensional Adjectives Geoffrey Simmons Graduiertenkolleg Kognitionswissenschaft Universit£t Hamburg Bodenstedtstr. 16 D-W-2000 Hamburg 50 Germany e-maih simmons@bosun2.informatik.uni-hamburg.de Abstract Linguistic access to uncertain quantita- tive knowledge about physical properties is provided by dimensional adjectives, e.g. long-short in the spatial and tempo- ral senses, near-far, fast-slow, etc. Seman- tic analyses of the dimensional adjectives differ on whether the meaning of the dif- ferential comparative (6 cm shorter than) and the equative with factor term (three times as long as) is a compositional func- tion of the meanings the difference and fac- tor terms (6 cm and three times) and the meanings of the simple comparative and equative, respectively. The compositional treatment comes at the price of a meaning representation that some authors ([Pinkal, 1990], [Klein, 1991]) find objectionally un- parsimonious. In this paper, I compare semantic approaches by investigating the complexity of reasoning that they entail; specifically, I show the complexity of con- straint propagation over real-valued inter- vals using the Waltz algorithm in a system where the meaning representations of sen- tences appear as constraints (cf. [Davis, 1987]). It turns out that the compositional account is more complex on this measure. However, I argue that we face a tradeoff rather than a knock-down argument against compositionality, since the increased com- plexity of the compositional approach may be manageable if certain assumptions about the application domain can be made. TOPIC AREAS: semantics, AI-methods in com- putational linguistics 1 Introduction In the past decade, the field of knowledge represen- tation (KR) has seen impressive growth of sophis- tication in the representation of uncertain quantita- tive knowledge about physical properties in common- sense reasoning and qualitative physics. The input to most of these systems is entered by hand, but some of them, especially those with commonsense domains involving spatial and temporal knowledge, are amenable to interaction by means of a natural language interface. Linguistic access to knowledge about properties such as durations, rates of change, distances, the sizes of the symmetry axes of objects, and so on, is provided by dimensional adjectives (e.g. long-short in the spatial and temporal senses, fast-slow, near-far, tall-short). In this paper, I will investigate two aspects of their semantics that have an impact on the quality of a KR system with an NL interface. One aspect is the complexity of reason- ing entailed by their semantic interpretations. As an example, suppose that we have a text about the in- stallation of new kitchen appliances that contains the following sentences: (1) a. The refridgerator is about 60 cm wide. b. The cupboard is about as deep as the refridgerator is wide. c. The kitchen table is about 5 cm longer than the cupboard is deep. d. The oven is about twice as high as the table is long. We may view the relations expressed by these sen- tences as constraints on the measurements of the ob- ject axes (the width of the fridge, the depth of the cupboard, and so on), …

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