  The ability to compose parts to form a more complex whole, and to analyze a
whole as a combination of elements, is desirable across disciplines. This
workshop bring together researchers applying compositional approaches to
physics, NLP, cognitive science, and game theory. Within NLP, a long-standing
aim is to represent how words can combine to form phrases and sentences. Within
the framework of distributional semantics, words are represented as vectors in
vector spaces. The categorical model of Coecke et al. [2010], inspired by
quantum protocols, has provided a convincing account of compositionality in
vector space models of NLP. There is furthermore a history of vector space
models in cognitive science. Theories of categorization such as those developed
by Nosofsky [1986] and Smith et al. [1988] utilise notions of distance between
feature vectors. More recently G\"ardenfors [2004, 2014] has developed a model
of concepts in which conceptual spaces provide geometric structures, and
information is represented by points, vectors and regions in vector spaces. The
same compositional approach has been applied to this formalism, giving
conceptual spaces theory a richer model of compositionality than previously
[Bolt et al., 2018]. Compositional approaches have also been applied in the
study of strategic games and Nash equilibria. In contrast to classical game
theory, where games are studied monolithically as one global object,
compositional game theory works bottom-up by building large and complex games
from smaller components. Such an approach is inherently difficult since the
interaction between games has to be considered. Research into categorical
compositional methods for this field have recently begun [Ghani et al., 2018].
Moreover, the interaction between the three disciplines of cognitive science,
linguistics and game theory is a fertile ground for research. Game theory in
cognitive science is a well-established area [Camerer, 2011]. Similarly game
theoretic approaches have been applied in linguistics [J\"ager, 2008]. Lastly,
the study of linguistics and cognitive science is intimately intertwined
[Smolensky and Legendre, 2006, Jackendoff, 2007]. Physics supplies
compositional approaches via vector spaces and categorical quantum theory,
allowing the interplay between the three disciplines to be examined.
