Publications
The Generative Capacity of the Lambek–Grishin Calculus: A New Lower Bound.
Proceedings of the 14th Formal Grammar conference, Bordeaux, July 2009 (in print).
The Lambek–Grishin calculus LG is a categorial grammar obtained by turning the one-sided sequents of the non-associative Lambek calculus NL into two-sided sequents, and adding interaction postulates between the two families of connectives thus obtained. In this paper, we prove a new lower bound on the generative capacity of LG,
namely the class of languages that are the intersection of a context-free language and the permutation closure of a context-free language. This implies that LG recognizes languages like {a^n b^n c^n d^n e^n | n ∈ N} and the
permutation closure of {a^n b^n c^n | n ∈ N}.
Lambek–Grishin Calculus Extended to Connectives of Arbitrary Arity.
Master's thesis, Cognitive Artificial Intelligence, Universiteit Utrecht.
In my thesis, I introduce the generalized Lambek–Grishin calculus and study its properties. The second part of this thesis studies the Lambek calculus and the Lambek–Grishin calculus from the perspective of formal language theory. The main result of this thesis is a new lower-bound on the generative complexity of the Lambek–Grishin calculus.
Lambek–Grishin Calculus Extended to Connectives of Arbitrary Arity.
Proceedings of the 20th Belgian-Netherlands Conference on Artificial Intelligence, Enschede, October 2008, pp 161-168.
This paper introduces Lambek–Grishin calculus for n-ary connectives, which can be seen as a generalization of binary and unary Lambek–Grishin calculus. A cut-free presentation of the calculus is showed, proving the decidability of the calculus. Finally we investigate the symmetries of the calculus by making use of group theory.
A solution to the emptiness problem for Lambek calculus and some of its extensions.
Proceedings of the 2nd NSVKI Student Conference, Utrecht, June 2008, pp. 19-24.
This paper presents a way of solving the emptiness problem, that is the problem of telling whether a given
language contains no strings at all, for associative and nonassociative Lambek calculus, and the logic of pure residuation in general. The corectness of this method is proved by first converting the Lambek grammar to context-free grammar, and then solving the emptiness problem for context-free grammar.
See also the other articles I wrote for my BSc and MSc courses in Cognitive Artificial Intelligence.