SPECIFYING METAPHORS ALGEBRAICALLY WERNER KUH N JEFFREY P . JACKSO N ANDREW U . FRAN K Introductio n A sound engineering approach to user interface desig n requires the formalization of key interaction concepts, on e of them being metaphor . Few formal theories of metaphor exist and most of them have been developed in the contex t of natural language understanding, learning, or reasoning . Work on metaphors in human-computer interaction ha s been largely non-formal so far. We propose to formalize interface metaphors by algebraic specifications. This allows to describe structural mapping s between metaphorical domains by morphisms . It als o provides a formalization of the relation between multipl e metaphors and image schemata . Our background and mai n interest lies in spatial applications and metaphors pertinen t to them . Since image schemata are spatial in nature an d underlie many common metaphors, a wide range of applications is expected to benefit from a formalization o f spatial metaphors . Metaphor and Human-Computer Interactio n Metaphor pervades communication . The use o f metaphorical expressions is not only fundamental to interpersonal communication (Lakoff, & Johnson, 1980) but to human-computer communication as well (Carroll
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