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Categorial theories of syntax and semantics, both TLG and CCG, show an intuitionistic bias: derivability is modeled asymmetrically as a relation between a tree (with preterminal formulas at the leaves) and a single formula. As a result of this one-sidedness the analysis of deep dependencies (eg in scope construal, displacement, conjoinability) is suboptimal, in that it relies on structural rules and/or special-purpose combinators. In this course, we restore the symmetry by considering a vocabulary with both residuated and dual residuated families of type-forming operations. Symmetry allows us to freely shift between a fusion and a fission perspective on grammatical composition. Interaction principles originally studied by Grishin make it possible to merge these two perspectives in a structure-preserving way. We discuss some basic model-theoretic and proof-theoretic results, accommodating both the TLG and the CCG perspectives. We show how symmetry solves a number of outstanding problems in syntax and semantics.


Theory and practice


Each session will have a theoretical and a practical component. In class, we do some exercises together on the blackboard, so that you get a practical understanding of the material dealt with. In addition, there is a set of homework exercises for each session. You can get feedback on these, if you turn them in before the next sessions. On this page, we will also provide links to some implementations of symmetric categorial grammar that can help you to check some more challenging calculations. Furthermore, a forum for discussing your ideas will be up and running from this wiki.





The course is addressed to any student interested in logic, language and their connections. All the necessary background is covered during the first week of ESSLLI '07 in the course on Type Logical Grammar by Glyn Morrill.


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