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Although direction plays an important role in the semantics of prepositions and verbs, there are not many precise and systematic treatments of this notion. This article offers a characterization and typology of directionality, based on two algebraic properties of spatial paths: cumulativity and reversability. This typology makes clear how directionality relates to the aspectual property of telicity, it generates implicational predictions about directional marking in systems of cases and adpositions around the world, and it suggests broad parallels between the realizations of directionality in prepositions and verbs. Like all parts of speech, prepositions can be classified in different ways. When we focus on the semantic side of spatial prepositions, we find a major division between locative prepositions (like in and under) and directional prepositions (like into and through): (1) a. Alex is in/under the car. (locative) b. Alex went into/through the forest. (directional) Locative prepositions correspond to places (where something is), directional prepositions to paths (where something is going) (see Jackendoff 1983 and many others). Further classifications can be made within both locative and directional expressions, like the
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