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A count invariant for Lambek calculus with additives and bracket modalities

Author
Valentin Fernandez, J.; Serret, D.; Morrill, G.
Type of activity
Presentation of work at congresses
Name of edition
18th International Conference on Formal Grammar
Date of publication
2013
Presentation's date
2013-08
Book of congress proceedings
Proceedings of the 18th International Conference on Formal Grammar
First page
263
Last page
276
Publisher
Springer-Verlag Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-39998-5_17 Open in new window
Repository
http://hdl.handle.net/2117/20347 Open in new window
URL
http://link.springer.com/chapter/10.1007%2F978-3-642-39998-5_17 Open in new window
Abstract
The count invariance of van Benthem (1991) is that for a sequent to be a theorem of the Lambek calculus, for each atom, the number of positive occurrences equals the number of negative occurrences. (The same is true for multiplicative linear logic.) The count invariance provides for extensive pruning of the sequent proof search space. In this paper we generalize count invariance to categorial grammar (or linear logic) with additives and bracket modalities. We define by mutual recursion two count...
Citation
Valentin Fernandez, J.; Serret, D.; Morrill, G. A count invariant for Lambek calculus with additives and bracket modalities. A: Formal Grammar. "Proceedings of the 18th International Conference on Formal Grammar". Dusseldorf: Springer-Verlag Berlin Heidelberg, 2013, p. 263-276.
Keywords
Categorial grammar, Lambek calculus, Linear logic, Multiplicative linear logic, Mutual recursion, Proof search
Group of research
LARCA - Laboratory of Relational Algorithmics, Complexity and Learnability

Participants

  • Valentin Fernandez Gallart, Jose Oriol  (author and speaker )
  • Serret, Daniel  (author and speaker )
  • Morrill, Glyn Verden  (author and speaker )