Formalizing spatial-causal polysemy of Agent prepositions

Abstract

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 ⟨η,⟨θ,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 s 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.

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