Summary: The categorical compositional distributional model of B. Coecke, M. Sadrzadeh and S. Clark [“Mathematical foundations for a compositional distributional model of meaning. Lambek Festschrift”, Linguistic Analysis 36, 345–384 (2010)] provides a linguistically motivated procedure for computing the meaning of a sentence as a function of the distributional meaning of the words therein. The theoretical framework allows for reasoning about compositional aspects of language and offers structural ways of studying the underlying relationships. While the model so far has been applied on the level of syntactic structures, a sentence can bring extra information conveyed in utterances via intonational means. In the current paper we extend the framework in order to accommodate this additional information, using Frobenius algebraic structures canonically induced over the basis of finite-dimensional vector spaces. We detail the theory, provide truth-theoretic and distributional semantics for meanings of intonationally-marked utterances, and present justifications and extensive examples.
For the entire collection see [Zbl 1376.68010].