The categorical compositional distributional model of Coecke, Sadrzadeh andClark provides a linguistically motivated procedure for computing the meaningof a sentence as a function of the distributional meaning of the words therein.The theoretical framework allows for reasoning about compositional aspects oflanguage and offers structural ways of studying the underlying relationships.While the model so far has been applied on the level of syntactic structures, asentence can bring extra information conveyed in utterances via intonationalmeans. In the current paper we extend the framework in order to accommodatethis additional information, using Frobenius algebraic structures canonicallyinduced over the basis of finite-dimensional vector spaces. We detail thetheory, provide truth-theoretic and distributional semantics for meanings ofintonationally-marked utterances, and present justifications and extensiveexamples.
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