References

Lecture notes

1. V. Grishin On a Generalization of the Ajdukiewicz-Lambek System
2. M. Moortgat Symmetries in NL syntax and semantics: the Lambek-Grishin calculus
3. R. Bernardi and M. Moortgat Continuation semantics for symmetric categorial grammar
4. N. Kurtonina and M. Moortgat Relational semantics for the Lambek-Grishin calculus
5. A. Chernilovskaya, Completeness of the Lambek-Grishin calculus with unary modalities
6. M. Moortgat and M. Pentus Type similarity for the Lambek-Grishin calculus

Lecture notes

A combined version of Ch 2 and 3 in the Lecture notes is in press at Information and Computation.

Here is the final draft (corrected 12 January 2010). For the implementation going with this paper, contact the alphabetically second author.

Further reading

1. R. Goré, Substructural Logics on Display. Logic Journal of the Interest Group in Pure and Applied Logics. 6(3):451-504, 1998.
2. J. Lambek, The mathematics of sentence structure. American Mathematical Monthly, 65:154--169, 1958.
3. M. Moortgat (1997), Categorial type logics. Chapter 2 in J. van Benthem en A. ter Meulen (eds.) Handbook of Logic and Language. Elsevier/MIT Press.
4. M. Moortgat (2002), Categorial grammar and formal semantics. In L. Nagel (ed.) Encyclopedia of Cognitive Science, Vol. 1, pp. 435-447. London, Nature Publishing Group.
5. C. Areces, R. Bernardi and M. Moortgat, Galois Connections in Categorial Type Logic. In Electronic Notes in Theoretical Computer Science 53 (2003).
6. R. Moot (2007) Proof nets for Display Logic. http://arxiv.org/pdf/0711.2444.

Some PhD Theses referred to

1. Herman Hendriks, Studied Flexibility: Categories and Types in Syntax and Semantics. 1993.
2. Natasha Kurtonina, Frames and Labels. A Modal Analysis of Categorial Inference. PhD Thesis, UiL OTS, and ILLC A'dam, 1995.
3. Raffaella Bernardi, Reasoning with Polarity in Categorial Type Logic. PhD Thesis, UiL OTS, 2002.
4. Richard Moot, Proof Nets for Linguistic Analysis. PhD Thesis, UiL OTS, 2002.
5. Willemijn Vermaat The logic of variation. A cross-linguistic account of wh-question formation. PhD Thesis, UiL OTS, Utrecht 2005.
6. Matteo Capelletti, Parsing for structure-preserving categorial grammars. PhD Thesis, UiL OTS, Utrecht 2005.

Background readings for the sessions on continuation semantics

1. P. Curien and H. Herbelin The Duality of Computation, Proceedings of ICFP '00  ©ACM
2. C. Barker and C. Shan (2004) Course on Continuation, ESSLLI 04.
3. C. Barker, Papers on Continuations. See his home page
4. Chung-Chieh Shan, Papers on Continuation. See his home page
5. Ph. de Groote Type raising, continuations, and classical logic, In R. van Rooy and M. Stokhof, editors, Thirteenth Amsterdam Colloquium, pages 97-101, Institute for Logic, Language and Computation, Universiteit van Amsterdam, 2001.

Categorial grammar course page

Michael Moortgat for a number of years has been teaching a course on categorial grammar in the Tarragona International PhD Program on Formal Languages and Applications. You can find lots of additional teaching materials on the course page.