One of the many roles of linguistics is to address the semantics of natural languages, that is, the meaning of sentences in natural languages. An important part of the meaning of sentences can be characterized by stating the conditions that need to hold fo

[10]G.V.Morrill.Type Logical Grammar:Categorial Logic of Signs.Kluwer Academic Publishers,1994.

[11]A.Ranta.Type-Theoretical Grammar.Oxford University Press,1994.

[12]J.van Benthem.The semantics of variety in categorial grammar.In W.Buszkowski,J.van Benthem,and W.Mar-

ciszewski,editors,Categorial Grammar,number25in Linguistics and Literary Studies in Eastern Europe,pages 37–55.John Benjamins,1986.Previously appeared as Report83-29,Department of Mathematics,Simon Fraser University(1983).

[13]M.M.Wood.Categorial Grammars.Routledge,1993.

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