Given appropriate representations of the semantic relations between carpenter and wood and between mason and stone (for example, vectors in a vector space model), a suitable algorithm should be able to recognize that these relations are highly similar (carpenter is to wood as mason is to stone; the relations are analogous). Likewise, with representations of dog, house, and kennel, an algorithm should be able to recognize that the semantic composition of dog and house, dog house, is highly similar to kennel (dog house and kennel are synonymous). It seems that these two tasks, recognizing relations and compositions, are closely connected. However, up to now, the best models for relations are significantly different from the best models for compositions. In this paper, we introduce a dual-space model that unifies these two tasks. This model matches the performance of the best previous models for relations and compositions. The dual-space model consists of a space for measuring domain similarity and a space for measuring function similarity. Carpenter and wood share the same domain, the domain of carpentry. Mason and stone share the same domain, the domain of masonry. Carpenter and mason share the same function, the function of artisans. Wood and stone share the same function, the function of materials. In the composition dog house, kennel has some domain overlap with both dog and house (the domains of pets and buildings). The function of kennel is similar to the function of house (the function of shelters). By combining domain and function similarities in various ways, we can model relations, compositions, and other aspects of semantics.
Modern approaches to semantic analysis if reformulated as Hilbert-space problems reveal formal structures known from quantum mechanics. A similar situation is found in distributed representations of cognitive structures developed for the purpose of neural networks. We take a closer look at similarities and differences between the above two fields and quantum information theory.  The are two main approaches to the representation of meaning in Computational Linguistics: a symbolic approach and a distributional approach. This paper considers the fundamental question of how these approaches might be combined. The proposal is to adapt a method from the Cognitive Science literature, in which symbolic and connectionist representations are combined using tensor products. Possible applications of this method for language processing are described. Finally, a potentially fruitful link between Quantum Mechanics, Computational Linguistics, and other related areas such as Information Retrieval and Machine Learning, is proposed. Abstract A general method, the tensor product representation, is defined for the connectionist representation of value variable bindings. The technique is a formalization of the idea that a set of value variable pairs can be represented by accumulating activity in a collection of units each of which computes the product of a feature of a variable and a feature of its value. The method allows the fully distributed representation of bindings and symbolic structures. Fully and partially localized special cases of the tensor product representation reduce to existing cases of connectionist representations of structured data. The representation rests on a principled analysis of structure; it saturates gracefully as larger structures are represented; it permits recursive construction of complex representations from simpler ones; it respects the independence of the capacities to generate and maintain multiple bindings in parallel; it extends naturally to continuous structures and continuous representational patterns; it permits values to also serve as variables; and it enables analysis of the interference of symbolic structures stored in associative memories. It has also served as the basis for working connectionist models of high-level cognitive tasks.  Formal and distributional semantic models offer complementary benefits in modeling meaning. The categorical compositional distributional model of meaning of (2010) (abbreviated to DisCoCat in the title) combines aspects of both to provide a general framework in which meanings of words, obtained distributionally, are composed using methods from the logical setting to form sentence meaning. Concrete consequences of this general abstract setting and applications to empirical data are under active study (, 2011; Grefenstette and Sadrzadeh, 2011). In this paper, we extend this study by examining transitive verbs, represented as matrices in a DisCoCat. We discuss three ways of constructing such matrices, and evaluate each method in a disambiguation task developed by Grefenstette and Sadrzadeh (2011).