Quantum logic unites compositional functional semantics and distributional semantic models Anne Preller, Violaine Prince * † Informatique LIRMM/CNRS Montpellier, France 1 Introduction When we retrieve information from text by statistical methods, we apply these methods not to random strings of words but to sentences, paragraphs etc. They are ruled by laws of logic inherent to language. Natural language conveys in- formation about individuals (extension) using concepts (intension). The exten- sional aspect is captured by the familiar logical models, the intensional aspect by distributional semantic models, DSM’s. We propose a unique frame for both DSM’s and functional logical models and show how compositionality of the latter transfers to compositionality of the former. The frame is the theory of compact closed monoidal categories, materialised by the category of finite-dimensional vector spaces for semantics and the category of proofs of compact bilinear logic for syntax, [Lambek 1993]. An essential difference with previous approaches is that we consider a DSM as a finite-dimensional space over the lattice of real numbers and not over the field of real numbers as do for example [Clark, Coecke, Sadrzadeh]. In this way, we capture both the logical and the numerical content of a DSM. Indeed, the lattice structure of subspaces, with logical operators defined by quantum logic, [van Rijsbergen], on one hand and the partial order of vectors on the other hand are isomorphic. Moreover, the lattice structure is distributive, unlike in Hilbert spaces. Negation, however, remains orthogonality. Next, we study compositionality in the particular case where the basis vec- tors of the DSM correspond to strings of key words, the so-called concept space. The logic of a concept spaces corresponds to a classification of words by a the- saurus. A particular meaning of a word is given by a set of (present or absent) features. This meaning is represented by the vector standing for the conjunc- tion of the features. In the case where the features are the same as the key words, the conjunction coincides with a tensor product. An ambiguous word * Support by TALN/LIRMM is gratefully acknowledged † preller, prince@lirmm.fr 1