Prepositional Aspect and the Algebra of Paths

The semantics of directional prepositions is investigated from the perspective of aspect. What distinguishes telic PPs (like to the house) from atelic PPs (like towards the house), taken as denoting sets of paths, is their algebraic structure: atelic PPs are cumulative, closed under the operation of concatenation, telic PPs are not. Not only does this allow for a natural and compositional account of how PPs contribute to the aspect of a sentence, but it also guides our understanding of the lexical semantics of prepositions in important ways. Semantically, prepositions turn out to be quite similar to nouns and verbs. Nominal distinctions (like singular and plural, mass and count) and verbal classes (like semelfactives and degree achievements) have their prepositional counterparts.

[1]  Nicholas Asher,et al.  A Typology and Discourse Semantics for Motion Verbs and Spatial PPs in French , 1995, J. Semant..

[2]  Susan Rothstein.  Structuring Events: A Study in the Semantics of Lexical Aspect , 2004 .

[3]  Max J. Cresswell.  Prepositions and points of view , 1978 .

[4]  Joost Zwarts,et al.  Vectors as Relative Positions: A Compositional Semantics of Modified PPs1 , 1997, J. Semant..

[5]  Seungho Nam.  A Typology of Locatives and Event Composition in English , 2000 .

[6]  Godehard Link.  Algebraic semantics in language and philosophy , 1997 .

[7]  H. Verkuyl.  A Theory of Aspectuality: The Interaction between Temporal and Atemporal Structure , 1996 .

[8]  Marcus Kracht,et al.  On the Semantics of Locatives , 2002 .

[9]  L. M. Faltz,et al.  Boolean semantics for natural language , 1984 .

[10]  Hana Filip,et al.  Prefixes and the Delimitation of Events , 2003 .

[11]  R. Jackendoff.  The proper treatment of measuring out, telicity, and perhaps even quantification in english , 1996 .

[12]  B. Landau,et al.  “What” and “where” in spatial language and spatial cognition , 1993 .

[13]  Carol Lee Tenny,et al.  Aspectual roles and the syntax-semantics interface , 1994 .

[14]  Vivienne Fong,et al.  The order of things : what directional locatives denote , 1998 .

[15]  M. Krifka.  The Origins of Telicity , 1998 .

[16]  H. Verkuyl,et al.  Time and space in conceptual and logical semantics: the notion of Path , 1992 .

[17]  Lars Kulik,et al.  Lexical Specifications of Paths , 2000, Spatial Cognition.

[18]  Emmon Bach,et al.  The algebra of events , 1986, The Language of Time - A Reader.

[19]  Seungho Nam,et al.  The semantics of locative prepositional phrases in English , 1995 .

[20]  Adele E. Goldberg,et al.  It Can't Go Down the Chimney Up: Paths and the English Resultative , 1991 .

[21]  R. Jackendoff.  Parts and boundaries , 1991, Cognition.

[22]  Joost Zwarts.  Vectors across Spatial Domains: From Place to Size, Orientation, Shape, and Parts , 2003 .

[23]  George Lakoff,et al.  Women, Fire, and Dangerous Things , 1987 .

[24]  Jürgen Bohnemeyer,et al.  The unique vector constraint: The impact of direction changes on the linguistic segmentation of motion events. , 2003 .

[25]  Manfred Krifka,et al.  Nominal Reference, Temporal Constitution and Quantification in Event Semantics , 1989 .

[26]  Leonard Talmy,et al.  How Language Structures Space , 1983 .

[27]  Yoad Winter,et al.  Vector Space Semantics: A Model-Theoretic Analysis of Locative Prepositions , 2000, J. Log. Lang. Inf..

[28]  Pascal Denis,et al.  V-PP goal motion complexes in English: an HPSG account , 2003, ACL 2003.

[29]  Gennaro Chierchia,et al.  Plurality of Mass Nouns and the Notion of “Semantic Parameter” , 1998 .

[30]  Ray Jackendoff.  Semantics and Cognition , 1983 .