Formalizing spatial-causal polysemy of Agent prepositions*

Current formal approaches to by -phrases in passives analyze the Agent preposition by as semantically vacuous: the denotation of by is merely such that its argument fulfills the same function as the external argument in the corresponding active sentence. This leads to a view of agentive by as essentially homonymous with spatial and temporal by. We argue, on the basis of work in the cognitive linguistic tradition and a new analysis of the French Agent prepositions par and de, that Agent markers do have non -trivial semantic content, and are polysemous rather than homonymous with their spatial counterparts. To formalize this we propose to model these prepositions with general schematic denotations of a polymorphic type (eta, (theta ,t)), which can be instantiated with a concrete type in a specific syntactic and semantic context, such as (e, (e,t)) for the spatial meaning of by. The use as an Agent preposition is simply one of these instantiations, with type (e, (s,t)) (where stands for events). The concrete meaning in context depends on both the general, polymorphically typed denotation and the specific type in the given context. In this way our proposal integrates a useful insight from cognitive linguistics in a semantic formalization of the passive, and opens up possibilities for similar accounts of other highly grammaticalized prepositions.